Marco Polini

Two rich and vibrant fields of investigation—graphene physics and plasmonics—strongly overlap. Not only does graphene possess intrinsic plasmons that are tunable and adjustable, but a combination of graphene with noble-metal nanostructures promises a variety of exciting applications for conventional plasmonics. The versatility of graphene means that graphene-based plasmonics may enable the manufacture of novel optical devices working in different frequency ranges—from terahertz to the visible—with extremely high speed, low driving voltage, low power consumption and compact sizes. Here we review the field emerging at the intersection of graphene physics and plasmonics. Many researchers hope to merge plasmonics and graphene photonics to combine their useful features. The properties and characteristics of plasmons on graphene are reviewed. Prospects for possible future applications are discussed.

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

The unique optoelectronic properties of graphene [1] make it an ideal platform for a variety of photonic applications [2], including fast photodetectors [3], transparent electrodes [4], optical modulators [5], and ultra-fast lasers [6]. Owing to its high carrier mobility, gapless spectrum, and frequency-independent absorption coefficient, it has been recognized as a very promising element for the development of detectors and modulators operating in the Terahertz (THz) region of the electromagnetic spectrum (wavelengths in the hundreds of micrometers range), which is still severely lacking in terms of solid-state devices. Here we demonstrate efficient THz detectors based on antenna-coupled graphene field-effect transistors (FETs). These exploit the non-linear FET response to the oscillating radiation field at the gate electrode, with contributions of thermoelectric and photoconductive origin. We demonstrate room temperature (RT) operation at 0.3 THz, with noise equivalent power (NEP) levels < 30 nW/Hz^(1/2), showing that our devices are well beyond a proof-of-concept phase and can already be used in a realistic setting, enabling large area, fast imaging of macroscopic samples.

Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this letter we exploit near-field microscopy to image propagating plasmons in high quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine dispersion and particularly plasmon damping in real space. We find unprecedented low plasmon damping combined with strong field confinement, and identify the main damping channels as intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key for the development of graphene nano-photonic and nano-optoelectronic devices.

Graphene hosts a unique electron system in which electron-phonon scattering is extremely weak but electron-electron collisions are sufficiently frequent to provide local equilibrium above liquid nitrogen temperature. Under these conditions, electrons can behave as a viscous liquid and exhibit hydrodynamic phenomena similar to classical liquids. Here we report strong evidence for this transport regime. We find that doped graphene exhibits an anomalous (negative) voltage drop near current injection contacts, which is attributed to the formation of submicrometer-size whirlpools in the electron flow. The viscosity of graphene's electron liquid is found to be ~0.1 m$^2$ /s, an order of magnitude larger than that of honey, in agreement with many-body theory. Our work shows a possibility to study electron hydrodynamics using high quality graphene.

Graphene is emerging as a viable alternative to conventional optoelectronic, plasmonic, and nanophotonic materials. The interaction of light with carriers creates an out-of-equilibrium distribution, which relaxes on an ultrafast timescale to a hot Fermi-Dirac distribution, that subsequently cools via phonon emission. Here we combine pump-probe spectroscopy, featuring extreme temporal resolution and broad spectral coverage, with a microscopic theory based on the quantum Boltzmann equation, to investigate electron-electron collisions in graphene during the very early stages of relaxation. We identify the fundamental physical mechanisms controlling the ultrafast dynamics in graphene, in particular the significant role of ultrafast collinear scattering, enabling Auger processes, including charge multiplication, key to improving photovoltage generation and photodetectors.

We report on a comprehensive combined experimental and theoretical study of Curie temperature trends in (Ga,Mn)As ferromagnetic semiconductors. Broad agreement between theoretical expectations and measured data allows us to conclude that ${T}_{c}$ in high-quality metallic samples increases linearly with the number of uncompensated local moments on ${\mathrm{Mn}}_{\mathrm{Ga}}$ acceptors, with no sign of saturation. Room temperature ferromagnetism is expected for a 10% concentration of these local moments. Our magnetotransport and magnetization data are consistent with the picture in which Mn impurities incorporated during growth at interstitial ${\mathrm{Mn}}_{\mathrm{I}}$ positions act as double-donors and compensate neighboring ${\mathrm{Mn}}_{\mathrm{Ga}}$ local moments because of strong near-neighbor ${\mathrm{Mn}}_{\mathrm{Ga}}{\mathrm{Mn}}_{\mathrm{I}}$ antiferromagnetic coupling. These defects can be efficiently removed by post-growth annealing. Our analysis suggests that there is no fundamental obstacle to substitutional ${\mathrm{Mn}}_{\mathrm{Ga}}$ doping in high-quality materials beyond our current maximum level of 6.8%, although this achievement will require further advances in growth condition control. Modest charge compensation does not limit the maximum Curie temperature possible in ferromagnetic semiconductors based on (Ga,Mn)As.

A hallmark of graphene is its unusual conical band structure that leads to a zero-energy band gap at a single Dirac crossing point. By measuring the spectral function of charge carriers in quasi-freestanding graphene with angle-resolved photoemission spectroscopy, we showed that at finite doping, this well-known linear Dirac spectrum does not provide a full description of the charge-carrying excitations. We observed composite "plasmaron" particles, which are bound states of charge carriers with plasmons, the density oscillations of the graphene electron gas. The Dirac crossing point is resolved into three crossings: the first between pure charge bands, the second between pure plasmaron bands, and the third a ring-shaped crossing between charge and plasmaron bands.

Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e-e scattering. Only recently, sufficiently clean electron systems with transport dominated by e-e collisions have become available, showing behavior characteristic of highly viscous fluids. Here we study electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature, in stark contrast to the metallic character of doped graphene. Notably, the measured conductance exceeds the maximum conductance possible for free electrons. This anomalous behavior is attributed to collective movement of interacting electrons, which 'shields' individual carriers from momentum loss at sample boundaries. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, our work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behavior for designing graphene-based devices.

Terahertz (THz) fields are widely applied for sensing, communication and quality control. In future applications, they could be efficiently confined, enhanced and manipulated - well below the classical diffraction limit - through the excitation of graphene plasmons (GPs). These possibilities emerge from the strongly reduced GP wavelength, lp, compared to the photon wavelength, l0, which can be controlled by modulating the carrier density of graphene via electrical gating. Recently, GPs in a graphene-insulator-metal configuration have been predicted to exhibit a linear dispersion (thus called acoustic plasmons) and a further reduced wavelength, implying an improved field confinement, analogous to plasmons in two-dimensional electron gases (2DEGs) near conductive substrates. While infrared GPs have been visualised by scattering-type scanning near-field optical microscopy (s-SNOM), the real-space imaging of strongly confined THz plasmons in graphene and 2DEGs has been elusive so far - only GPs with nearly free-space wavelength have been observed. Here we demonstrate real-space imaging of acoustic THz plasmons in a graphene photodetector with split-gate architecture. To that end, we introduce nanoscale-resolved THz photocurrent near-field microscopy, where near-field excited GPs are detected thermoelectrically rather than optically. The on-chip GP detection simplifies GP imaging, as sophisticated s-SNOM detection schemes can be avoided. The photocurrent images reveal strongly reduced GP wavelengths (lp = l0/66), a linear dispersion resulting from the coupling of GPs with the metal gate below the graphene, and that plasmon damping at positive carrier densities is dominated by Coulomb impurity scattering. Acoustic GPs could thus strongly benefit the development of deep subwavelength-scale THz devices.

Plasmons probe the quantum response Electronic systems are typically considered as classical Fermi liquids, and the quantum mechanical interactions and processes are usually only accessed at very low temperatures and high magnetic fields. Lundeberg et al. used tunable plasmons to probe the quantum response of the electron gas of graphene (see the Perspective by Basov and Fogler). They studied shape deformations of the Fermi surface during a plasmon oscillation, as well as many-body electronic effects. Science , this issue p. 187 ; see also p. 132

We report a theoretical study of the influence of electron-electron interactions on the one-particle Green's function of a doped graphene sheet based on the random-phase approximation and on graphene's massless Dirac equation continuum model. We find that states near the Dirac point interact strongly with plasmons with a characteristic frequency ${\ensuremath{\omega}}_{\mathrm{pl}}^{\ensuremath{\star}}$ that scales with the sheet's Fermi energy and depends on its interaction coupling constant ${\ensuremath{\alpha}}_{\mathrm{gr}}$, partially explaining prominent features of recent angle-resolved photoemission spectroscopy data.

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of $N$ two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like $\sqrt{N}$ for $N\gg 1$.

Due to the absence of a strong electron-acoustic phonon interaction, a system made up of graphene sheets encapsulated between thin hexagonal boron nitride slabs is ideal for investigating the hydrodynamic behavior of an electron liquid. Using a fully analytical theoretical approach, the authors demonstrate that nonlocal dc transport measurements can be used to extract the hydrodynamic shear viscosity of 2D electrons in graphene far from the neutrality point. They also suggest that the currently available scanning probe techniques should be able to spatially resolve viscosity-dominated electron flow regions.

Electron hydrodynamics in graphene Electrons can move through graphene in a manner reminiscent of fluids, if the conditions are right. Two groups studied the nature of this hydrodynamic flow in different regimes (see the Perspective by Lucas). Gallagher et al. measured optical conductivity using a waveguide-based setup, revealing signatures of quantum criticality near the charge neutrality point. Berdyugin et al. focused on electron transport in the presence of a magnetic field and measured a counterintuitive contribution to the Hall response that stems from hydrodynamic flow. Science , this issue p. 158 , p. 162 ; see also p. 125

Optical harmonic generation occurs when high intensity light ($>10^{10}$W/m$^{2}$) interacts with a nonlinear material. Electrical control of the nonlinear optical response enables applications such as gate-tunable switches and frequency converters. Graphene displays exceptionally strong-light matter interaction and electrically and broadband tunable third order nonlinear susceptibility. Here we show that the third harmonic generation efficiency in graphene can be tuned by over two orders of magnitude by controlling the Fermi energy and the incident photon energy. This is due to logarithmic resonances in the imaginary part of the nonlinear conductivity arising from multi-photon transitions. Thanks to the linear dispersion of the massless Dirac fermions, ultrabroadband electrical tunability can be achieved, paving the way to electrically-tuneable broadband frequency converters for applications in optical communications and signal processing.

Plasmons, collective oscillations of electron systems, can efficiently couple light and electric current, and thus can be used to create sub-wavelength photodetectors, radiation mixers, and on-chip spectrometers. Despite considerable effort, it has proven challenging to implement plasmonic devices operating at terahertz frequencies. The material capable to meet this challenge is graphene as it supports long-lived electrically tunable plasmons. Here we demonstrate plasmon-assisted resonant detection of terahertz radiation by antenna-coupled graphene transistors that act as both plasmonic Fabry-Perot cavities and rectifying elements. By varying the plasmon velocity using gate voltage, we tune our detectors between multiple resonant modes and exploit this functionality to measure plasmon wavelength and lifetime in bilayer graphene as well as to probe collective modes in its moiré minibands. Our devices offer a convenient tool for further plasmonic research that is often exceedingly difficult under non-ambient conditions (e.g. cryogenic temperatures) and promise a viable route for various photonic applications.

Abstract Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS 2 (1L-MoS 2 ): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS 2 is approximately three times higher than that for graphene, which was reported to have a large χ (3) . We explain this by calculating the nonlinear response functions of 1L-MoS 2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging.

We investigate a quantum battery made of N two-level systems, which is charged by an optical mode via an energy-conserving interaction. We quantify the fraction of energy stored in the battery that can be extracted in order to perform thermodynamic work. We first demonstrate that this quantity is highly reduced by the presence of correlations between the charger and the battery or between the subsystems composing the battery. We then show that the correlation-induced suppression of extractable energy, however, can be mitigated by preparing the charger in a coherent optical state. We conclude by proving that the charger-battery system is asymptotically free of such locking correlations in the N→∞ limit.

A novel liquid-phase exfoliation of layered crystals enables the production of defect-free and high quality 2D-crystal dispersions on a large scale.

The energy charging of a quantum battery is analyzed in an open quantum setting, where the interaction between the battery element and the external power source is mediated by an ancilla system (the quantum charger) that acts as a controllable switch. Different implementations are analyzed putting emphasis on the interplay between coherent energy pumping mechanisms and thermalization.

The exactly-solvable Sachdev-Ye-Kitaev (SYK) model has recently received considerable attention in both condensed matter and high energy physics because it describes quantum matter without quasiparticles, while being at the same time the holographic dual of a quantum black hole. In this Letter, we examine SYK-based charging protocols of quantum batteries with N quantum cells. Extensive numerical calculations based on exact diagonalization for N up to 16 strongly suggest that the optimal charging power of our SYK quantum batteries displays a super-extensive scaling with N that stems from genuine quantum mechanical effects. While the complexity of the nonequilibrium SYK problem involved in the charging dynamics prevents us from an analytical proof, we believe that this Letter offers the first (to the best of our knowledge) strong numerical evidence of a quantum advantage occurring due to the maximally-entangling underlying quantum dynamics.

The field of 2D materials-based nanophotonics has been growing at a rapid pace, triggered by the ability to design nanophotonic systems with in situ control, unprecedented degrees of freedom, and to build material heterostructures from bottom up with atomic precision. A wide palette of polaritonic classes have been identified, comprising ultra confined optical fields, even approaching characteristic length scales of a single atom. These advances have been a real boost for the emerging field of quantum nanophotonics, where the quantum mechanical nature of the electrons and-or polaritons and their interactions become relevant. Examples include, quantum nonlocal effects, ultrastrong light matter interactions, Cherenkov radiation, access to forbidden transitions, hydrodynamic effects, single plasmon nonlinearities, polaritonic quantization, topological effects etc. In addition to these intrinsic quantum nanophotonic phenomena, the 2D material system can also be used as a sensitive probe for the quantum properties of the material that carries the nanophotonics modes, or quantum materials in its vicinity. Here, polaritons act as a probe for otherwise invisible excitations, e.g. in superconductors, or as a new tool to monitor the existence of Berry curvature in topological materials and superlattice effects in twisted 2D materials.

We predict that neutral graphene bilayers are pseudospin magnets in which the charge density contribution from each valley and spin spontaneously shifts to one of the two layers. The band structure of this system is characterized by a momentum-space vortex, which is responsible for unusual competition between band and kinetic energies, leading to symmetry breaking in the vortex core. We discuss the possibility of realizing a pseudospin version of ferromagnetic metal spintronics in graphene bilayers based on hysteresis associated with this broken symmetry.

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.

Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice with honeycomb geometry. We probe the excitation spectrum in a magnetic field identifying novel collective modes that emerge from the Coulomb interaction in the artificial lattice as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a novel Coulomb-driven ground state. This approach offers new venues for the study of quantum phenomena in a controllable solid-state system.

At low energy, electrons in doped graphene sheets behave like massless Dirac fermions with a Fermi velocity, which does not depend on carrier density. Here we show that modulating a two-dimensional electron gas with a long-wavelength periodic potential with honeycomb symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphenelike system and discuss an experimental realization in a modulation-doped GaAs quantum well. Ultrahigh-mobility electrons with linearly dispersing bands might open new venues for the studies of Dirac-fermion physics in semiconductors.

Electrons most often organize into Fermi-liquid states in which electron-electron interactions play an inessential role. A well known exception is the case of one-dimensional (1D) electron systems (1DES). In 1D the electron Fermi-surface consists of points, and divergences associated with low-energy particle-hole excitations abound when electron-electron interactions are described perturbatively. In higher space dimensions, the corresponding divergences occur only when Fermi lines or surfaces satisfy idealized nesting conditions. In this article we discuss electron-electron interactions in 2D graphene bilayer systems which behave in many ways as if they were one-dimensional, because they have Fermi points instead of Fermi lines and because their particle-hole energies have a quadratic dispersion which compensates for the difference between 1D and 2D phase space. We conclude, on the basis of a perturbative RG calculation similar to that commonly employed in 1D systems, that interactions in neutral graphene bilayers can drive the system into a strong-coupling broken symmetry state with layer-pseudospin ferromagnetism and an energy gap.

We present a combined analytical and numerical study of the early stages (sub-100fs) of the non-equilibrium dynamics of photo-excited electrons in graphene. We employ the semiclassical Boltzmann equation with a collision integral that includes contributions from electron-electron (e-e) and electron-optical phonon interactions. Taking advantage of circular symmetry and employing the massless Dirac Fermion (MDF) Hamiltonian, we are able to perform an essentially analytical study of the e-e contribution to the collision integral. This allows us to take particular care of subtle collinear scattering processes - processes in which incoming and outgoing momenta of the scattering particles lie on the same line - including carrier multiplication (CM) and Auger recombination (AR). These processes have a vanishing phase space for two dimensional MDF bare bands. However, we argue that electron-lifetime effects, seen in experiments based on angle-resolved photoemission spectroscopy, provide a natural pathway to regularize this pathology, yielding a finite contribution due to CM and AR to the Coulomb collision integral. Finally, we discuss in detail the role of physics beyond the Fermi golden rule by including screening in the matrix element of the Coulomb interaction at the level of the Random Phase Approximation (RPA), focusing in particular on the consequences of various approximations including static RPA screening, which maximizes the impact of CM and AR processes, and dynamical RPA screening, which completely suppresses them.

We demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet are strongly renormalized by electron-electron interactions even in the long-wavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids and is due to coupling between the center of mass motion and the pseudospin degree of freedom of the graphene's massless Dirac fermions. Making use of diagrammatic perturbation theory to first order in the electron-electron interaction, we show that this coupling enhances both the plasmon frequency and the Drude weight relative to the RPA value. We also show that interactions are responsible for a significant enhancement of the optical conductivity at frequencies just above the absorption threshold. Our predictions can be checked by far-infrared spectroscopy or inelastic light scattering.

Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior electrical and optoelectronic properties 1–7 . Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting 8–16 require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons 17–19 in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier density and lattice temperature, and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures. Observation of an efficient out-of-plane energy transfer channel in van der Waals heterostructures, where charge carriers in graphene couple to hyperbolic phonon–polaritons on a picosecond timescale.

Hydrodynamic flow occurs in an electron liquid when the mean free path for electron-electron collisions is the shortest length scale in the problem. In this regime, transport is described by the Navier-Stokes equation, which contains two fundamental parameters, the bulk and shear viscosities. In this paper, we present extensive results for these transport coefficients in the case of the two-dimensional massless Dirac fermion liquid in a doped graphene sheet. Our approach relies on microscopic calculations of the viscosities up to second order in the strength of electron-electron interactions and in the high-frequency limit, where perturbation theory is applicable. We then use simple interpolation formulas that allow to reach the low-frequency hydrodynamic regime where perturbation theory is no longer directly applicable. The key ingredient for the interpolation formulas is the ``viscosity transport time'' ${\ensuremath{\tau}}_{\mathrm{v}}$, which we calculate in this paper. The transverse nature of the excitations contributing to ${\ensuremath{\tau}}_{\mathrm{v}}$ leads to the suppression of scattering events with small momentum transfer, which are inherently longitudinal. Therefore, contrary to the quasiparticle lifetime, which goes as $\ensuremath{-}1/[{T}^{2}ln(T/{T}_{\mathrm{F}})]$, in the low-temperature limit we find ${\ensuremath{\tau}}_{\mathrm{v}}\ensuremath{\sim}1/{T}^{2}$.

In a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We here propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a given quantum system, termed charger, to another one, i.e. the proper battery. In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting them in the global energy balance of the model.

Wave propagation control by spatial modulation of velocity has a long history in optics and acoustics. We address velocity-modulation control of electron wave propagation in graphene and other two-dimensional Dirac-electron systems, pointing out a key distinction of the Dirac-wave case. We also propose a strategy for pattern transfer from a remote metallic layer that is based on many-body velocity renormalization.

It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy.

We present numerical and analytical results for the optical and acoustic plasmon collective modes of coupled massless-Dirac two-dimensional electron systems. Our results apply to topological insulator (TI) thin films and to two graphene sheets separated by a thin dielectric barrier layer. We find that because of strong bulk dielectric screening TI acoustic modes are locked to the top of the particle-hole continuum and therefore probably unobservable.

For many of the envisioned optoelectronic applications of graphene it is crucial to understand the sub-picosecond carrier dynamics immediately following photoexcitation, as well as the effect on the electrical conductivity - the photoconductivity. Whereas these topics have been studied using various ultrafast experiments and theoretical approaches, controversial and incomplete explanations have been put forward concerning the sign of the photoconductivity, the occurrence and significance of the creation of additional electron-hole pairs, and, in particular, how the relevant processes depend on Fermi energy. Here, we present a unified and intuitive physical picture of the ultrafast carrier dynamics and the photoconductivity, combining optical pump - terahertz probe measurements on a gate-tunable graphene device, with numerical calculations using the Boltzmann equation. We distinguish two types of ultrafast photo-induced carrier heating processes: At low (equilibrium) Fermi energy ($E_{\rm F} \lesssim$ 0.1 eV for our experiments) broadening of the carrier distribution involves interband transitions - interband heating. At higher Fermi energy ($E_{\rm F} \gtrsim$ 0.15 eV) broadening of the carrier distribution involves intraband transitions - intraband heating. Under certain conditions, additional electron-hole pairs can be created (carrier multiplication) for low $E_{\rm F}$, and hot carriers (hot-carrier multiplication) for higher $E_{\rm F}$. The resultant photoconductivity is positive (negative) for low (high) $E_{\rm F}$, which originates from the effect of the heated carrier distributions on the screening of impurities, consistent with the DC conductivity being mostly due to impurity scattering. The importance of these insights is highlighted by a discussion of the implications for graphene photodetector applications.

Quantum batteries are quantum-mechanical systems with many degrees of freedom which can be used to store energy and that display fast charging. The physics behind fast charging is still unclear. Is it just due to the collective behavior of the underlying interacting many-body system, or does it have its roots in the quantum-mechanical nature of the system itself? In this work we address these questions by studying three examples of quantum-mechanical many-body batteries with rigorous classical analogs. We find that the answer is model dependent and, even within the same model, depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.

In highly viscous electron systems such as high-quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge.

In spite of decades of work it has remained unclear whether or not superradiant quantum phases, referred to here as photon condensates, can occur in equilibrium. In this Rapid Communication, we first show that when a nonrelativistic quantum many-body system is coupled to a cavity field, gauge invariance forbids photon condensation. We then present a microscopic theory of the cavity quantum electrodynamics of an extended Falicov-Kimball model, showing that, in agreement with the general theorem, its insulating ferroelectric and exciton condensate phases are not altered by the cavity and do not support photon condensation.

Vertical heterostructures combining different layered materials offer novel opportunities for applications and fundamental studies. Here we report a new class of heterostructures comprising a single-layer (or bilayer) graphene in close proximity to a quantum well created in GaAs and supporting a high-mobility two-dimensional electron gas. In our devices, graphene is naturally hole-doped, thereby allowing for the investigation of electron-hole interactions. We focus on the Coulomb drag transport measurements, which are sensitive to many-body effects, and find that the Coulomb drag resistivity significantly increases for temperatures <5-10 K. The low-temperature data follow a logarithmic law, therefore displaying a notable departure from the ordinary quadratic temperature dependence expected in a weakly correlated Fermi-liquid. This anomalous behaviour is consistent with the onset of strong interlayer correlations. Our heterostructures represent a new platform for the creation of coherent circuits and topologically protected quantum bits.

The shear viscosity of a variety of strongly interacting quantum fluids, ranging from ultracold atomic Fermi gases to quark-gluon plasmas, can be accurately measured. On the contrary, no experimental data exist, to the best of our knowledge, on the shear viscosity of two-dimensional quantum electron liquids hosted in a solid-state matrix. In this Letter we propose a Corbino disk device, which allows a determination of the viscosity of a quantum electron liquid from the dc potential difference that arises between the inner and the outer edge of the disk in response to an oscillating magnetic flux.

The photoresponse of graphene has recently received considerable attention. The main mechanisms yielding a finite dc response to an oscillating radiation field which have been investigated include responses of photovoltaic, photothermoelectric, and bolometric origin. In this article, we present a fully analytical theory of a photoresponse mechanism which is based on the excitation of plasma waves in a gated graphene sheet. By employing the theory of relativistic hydrodynamics, we demonstrate that plasma-wave photodetection is substantially influenced by the massless Dirac fermion character of carriers in graphene, and that the efficiency of photodetection can be improved with respect to that of ordinary parabolic-band electron fluids in semiconductor heterostructures.

Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs display superb electronic properties due to very limited scattering from extrinsic disorder sources such as Coulomb impurities and corrugations. Such samples are therefore expected to be ideal platforms for highly-tunable low-loss plasmonics in a wide spectral range. In this Article we present a theory of collective electron density oscillations in a graphene sheet encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes. We focus on scattering of these modes against graphene's acoustic phonons and hBN optical phonons, two sources of scattering that are expected to play a key role in hBN/G/hBN stacks. We find that at room temperature the scattering against graphene's acoustic phonons is the dominant limiting factor for hBN/G/hBN stacks, yielding theoretical inverse damping ratios of hybrid plasmon-phonon modes of the order of $50$-$60$, with a weak dependence on carrier density and a strong dependence on illumination frequency. We confirm that the plasmon lifetime is not directly correlated with the mobility: in fact, it can be anti-correlated.

We measure transport through a Ga[Al]As heterostructure at temperatures between $32\phantom{\rule{3.33333pt}{0ex}}\mathrm{mK}$ and $30\phantom{\rule{3.33333pt}{0ex}}\mathrm{K}$. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To probe this regime we measure so-called vicinity voltages and use a voltage-biased scanning tip to induce a movable local perturbation. We find that the scanning gate images differentiate reliably between the different regimes of electron transport. Our data are in good agreement with recent theories for interacting electron liquids in the ballistic and viscous regimes stimulated by measurements in graphene. However, the range of temperatures and densities where viscous effects are observable in Ga[Al]As are very distinct from the graphene material system.

An energy gap can be opened in the electronic spectrum of graphene by lifting its sublattice symmetry. In bilayers, it is possible to open gaps as large as 0.2 eV. However, these gaps rarely lead to a highly insulating state expected for such semiconductors at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity. Here we investigate spatial distributions of proximity-induced superconducting currents in gapped graphene and, also, compare measurements in the Hall bar and Corbino geometries in the normal state. By gradually opening the gap in bilayer graphene, we find that the supercurrent at the charge neutrality point changes from uniform to such that it propagates along narrow stripes near graphene edges. Similar stripes are found in gapped monolayers. These observations are corroborated by using the "edgeless" Corbino geometry in which case resistivity at the neutrality point increases exponentially with increasing the gap, as expected for an ordinary semiconductor. This is in contrast to the Hall bar geometry where resistivity measured under similar conditions saturates to values of only about a few resistance quanta. We attribute the metallic-like edge conductance to a nontrivial topology of gapped Dirac spectra.

The collective and quantum behavior of many-body systems may be harnessed to achieve fast charging of energy storage devices, which have been recently dubbed quantum batteries. In this paper, we present an extensive numerical analysis of energy flow in a quantum battery described by a disordered quantum Ising chain Hamiltonian, whose equilibrium phase diagram presents many-body localized (MBL), Anderson localized (AL), and ergodic phases. We demonstrate that (i) the low amount of entanglement of the MBL phase guarantees much better work extraction capabilities, measured by the ergotropy, than the ergodic phase and (ii) interactions suppress temporal energy fluctuations in comparison with those of the noninteracting AL phase. Finally, we show that the statistical distribution of values of the optimal charging time is a clear-cut diagnostic tool of the MBL phase.

The realization of equilibrium superradiant quantum phases (photon condensates) in a spatially-uniform quantum cavity field is forbidden by a "no-go" theorem stemming from gauge invariance. We here show that the no-go theorem does not apply to spatially-varying quantum cavity fields. We find a criterion for its occurrence that depends solely on the static, non-local orbital magnetic susceptibility $\chi_{\rm orb}(q)$, of the electronic system (ES) evaluated at a cavity photon momentum $\hbar q$. Only 3DESs satisfying the Condon inequality $\chi_{\rm orb}(q)>1/(4\pi)$ can harbor photon condensation. For the experimentally relevant case of two-dimensional (2D) ESs embedded in quasi-2D cavities the criterion again involves $\chi_{\rm orb}(q)$ but also the vertical size of the cavity. We use these considerations to identify electronic properties that are ideal for photon condensation. Our theory is non-perturbative in the strength of electron-electron interaction and therefore applicable to strongly correlated ESs.

Recent advances in materials science have made it possible to achieve conditions under which electrons in metals start behaving as highly viscous fluids, "thicker than honey", and exhibit fascinating hydrodynamic effects. In this short review we provide a popular introduction to the emerging field of electron hydrodynamics.

Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron interactions. Our theory provides a straightforward conceptual framework to explain experimental results, especially those in atomically thin crystals, plagued with short-range edge disorder.

The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great deal of interest, sparked by the discovery of correlated insulating and superconducting states, for twist angle $\theta$ close to a so-called 'magic angle' $\approx 1.1{\deg}$. In this work, we unveil, via near-field optical microscopy, a collective plasmon mode in charge-neutral TBG near the magic angle, which is dramatically different from the ordinary single-layer graphene intraband plasmon. In selected regions of our samples, we find a gapped collective mode with linear dispersion, akin to the bulk magnetoplasmons of a two-dimensional (2D) electron gas. We interpret these as interband plasmons and associate those with the optical transitions between quasi-localized states originating from the moir\'e superlattice. Surprisingly, we find a higher plasmon group velocity than expected, which implies an enhanced strength of the corresponding optical transition. This points to a weaker interlayer coupling in the AA regions. These intriguing optical properties offer new insights, complementary to other techniques, on the carrier dynamics in this novel quantum electron system.

We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatially varying cavity electromagnetic vector potential $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{A}}(\mathbit{r})$. Specifically, we choose a temporally chiral cavity hosting a uniform magnetic field $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{B}}$, as this is the simplest instance in which a transverse spatially varying $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{A}}(\mathbit{r})$ is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs.

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices.

A two-dimensional gas of massless Dirac fermions (MDFs) is a very useful model to describe low-energy electrons in monolayer graphene. Because the MDF current operator is directly proportional to the (sublattice) pseudospin operator, the MDF current-current response function, which describes the response to a vector potential, happens to coincide with the pseudospin-pseudospin response function. In this work, we present analytical results for the wave vector- and frequency-dependent longitudinal and transverse pseudospin-pseudospin response functions of noninteracting MDFs. The transverse response in the static limit is then used to calculate the noninteracting orbital magnetic susceptibility. These results are a starting point for the construction of approximate pseudospin-pseudospin response functions that would take into account electron-electron interactions (for example at the random-phase-approximation level). They also constitute a very useful input for future applications of current-density-functional theory to graphene sheets subjected to time and spatially varying vector potentials.

We outline a Kohn-Sham-Dirac density functional theory (DFT) scheme for graphene sheets that treats slowly varying inhomogeneous external potentials and electron-electron interactions on equal footing. The theory is able to account for the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene. The consequences of this property and advantages and disadvantages of using the DFT approach to describe it are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged pointlike impurities located close to the graphene plane. The influence of electron-electron interactions on these nonlinear screening calculations is discussed at length in light of recent experiments reporting evidence for the presence of electron-hole puddles in nearly neutral graphene sheets.

Doped graphene sheets are pseudochiral two-dimensional Fermi liquids with abnormal electron–electron interaction physics. We address graphene’s Fermi liquid properties quantitatively using a microscopic random-phase-approximation theory and comment on the importance of using exchange-correlation potentials based on the properties of a chiral two-dimensional electron gas in density-functional-theory applications to graphene nanostructures.

Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.

Electron-plasmon coupling in graphene has recently been shown to give rise to a "plasmaron" quasiparticle excitation. The strength of this coupling has been predicted to depend on the effective screening, which in turn is expected to depend on the dielectric environment of the graphene sheet. Here we compare the strength of enviromental screening for graphene on four different substrates by evaluating the separation of the plasmaron bands from the hole bands using Angle Resolved PhotoEmission Spectroscopy. Comparison with G0W-RPA predictions are used to determine the effective dielectric constant of the underlying substrate layer. We also show that plasmaron and electronic properties of graphene can be independently manipulated, an important aspect of a possible use in "plasmaronic" devices.

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting massless Dirac fermions (the so-called "Lindhard" function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the Random Phase Approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.

We calculate the intrinsic lifetime of a Dirac plasmon in a doped graphene sheet by analyzing the role of electron-electron interactions beyond the random phase approximation. The damping mechanism at work is intrinsic since it operates also in disorder-free samples and in the absence of lattice vibrations. We demonstrate that graphene's sublattice-pseudospin degree of freedom suppresses intrinsic plasmon losses with respect to those that occur in ordinary two-dimensional electron liquids. As a byproduct, we are able to present a microscopic calculation of the homogeneous dynamical conductivity at energies below the single-particle absorption threshold.

In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric field dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this work, we present angle resolved photoemission spectroscopy (ARPES) data which show with high resolution the electronic band structure of trilayer graphene obtained on {\alpha}-SiC(0001) and {\beta}-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic hopping parameters for Bernal and rhombohedral stacked trilayers. Low energy electron microscopy (LEEM) measurements demonstrate that the trilayer domains extend over areas of tens of square micrometers, suggesting the feasibility of exploiting this material in electronic and photonic devices. Furthermore, our results suggest that on SiC substrates the occurrence of rhombohedral stacked trilayer is significantly higher than in natural bulk graphite.

Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the experimental realization of electron systems moving on plane fractals. In this work, we present the results of computer simulations for the conductance and optical absorption spectrum of a 2D electron gas roaming on a Sierpinski carpet, i.e. a plane fractal with Hausdorff dimension intermediate between one and two. We find that the conductance is sensitive to the spatial location of the leads and that it displays fractal fluctuations whose dimension is compatible with the Hausdorff dimension of the sample. Very interestingly, electrons in this fractal display a broadband optical absorption spectrum, which possesses sharp "molecular" peaks at low photon energies.

Phase velocity of graphene plasmons is electrically controlled in a set-up enabling tuning of the phase between 0 and 2π. Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping1, transformation optics2,3, phased arrays4, modulators5 and sensors6. Performing this task with high efficiency and small footprint is a formidable challenge7,8. Metasurfaces5,9 and plasmonics10 are promising, but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages11,12. Here, we show a graphene plasmonic phase modulator that is capable of tuning the phase between 0 and 2π in situ. The device length of 350 nm is more than 30 times shorter than the 10.6 μm free-space wavelength. The modulation is achieved by spatially controlling the plasmon phase velocity in a device where the spatial carrier density profile is tunable. We provide a scattering theory for plasmons propagating through spatial density profiles. This work constitutes a first step towards two-dimensional transformation optics3 for ultracompact modulators7 and biosensing13.

We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e. a three-dimensional metal with linear band touchings acting as point-like sources of Berry curvature in momentum space, termed "Weyl-Berry monopoles". We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a universal dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.

Helicons are transverse electromagnetic waves propagating in three-dimensional (3D) electron systems subject to a static magnetic field. We present a theory of helicons propagating through a 3D Weyl semimetal. Our approach relies on the evaluation of the optical conductivity tensor from semiclassical Boltzmann transport theory, with the inclusion of certain Berry curvature corrections that have been neglected in the earlier literature (such as the one due to the orbital magnetic moment). We demonstrate that the axion term characterizing the electromagnetic response of Weyl semimetals dramatically alters the helicon dispersion with respect to that in nontopological metals. We also discuss axion-related anomalies that appear in the plasmon dispersion relation.

Abstract Conversion of mechanical forces to electric signal is possible in non-centrosymmetric materials due to linear piezoelectricity. The extraordinary mechanical properties of two-dimensional materials and their high crystallinity make them exceptional platforms to study and exploit the piezoelectric effect. Here, the piezoelectric response of non-centrosymmetric hexagonal two-dimensional crystals is studied using the modern theory of polarization and k · p model Hamiltonians. An analytical expression for the piezoelectric constant is obtained in terms of topological quantities, such as the valley Chern number . The theory is applied to semiconducting transition metal dichalcogenides and hexagonal Boron Nitride. We find good agreement with available experimental measurements for MoS 2 . We further generalize the theory to study the polarization of samples subjected to inhomogeneous strain (e.g., nanobubbles). We obtain a simple expression in terms of the strain tensor, and show that charge densities ≳10 11 cm −2 can be induced by realistic inhomogeneous strains, ϵ ≈ 0.01–0.03.

Abstract Electron-electron interactions play a critical role in many condensed matter phenomena, and it is tempting to find a way to control them by changing the interactions’ strength. One possible approach is to place a studied system in proximity of a metal, which induces additional screening and hence suppresses electron interactions. Here, using devices with atomically-thin gate dielectrics and atomically-flat metallic gates, we measure the electron-electron scattering length in graphene and report qualitative deviations from the standard behavior. The changes induced by screening become important only at gate dielectric thicknesses of a few nm, much smaller than a typical separation between electrons. Our theoretical analysis agrees well with the scattering rates extracted from measurements of electron viscosity in monolayer graphene and of umklapp electron-electron scattering in graphene superlattices. The results provide a guidance for future attempts to achieve proximity screening of many-body phenomena in two-dimensional systems.

Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of $N$ QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy stored, we show that temporal fluctuations are strongly suppressed by the presence of nonlocal correlations at all time scales. A comparison with other paradigmatic examples of many-body QBs shows that this is linked to the collective dynamics of the SYK model and its high level of entanglement. We argue that such feature relies on the fast scrambling property of the SYK Hamiltonian, and on its fast thermalization properties, promoting this as an ideal model for the ultimate temporal stability of a generic QB. Finally, we show that the temporal evolution of the ergotropy, a quantity that characterizes the amount of extractable work from a QB, can be a useful probe to infer the thermalization properties of a many-body quantum system.

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $\beta$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised in [Cheipesh et al., Phys. Rev. D 104, 116004 (2021)], and discuss the relevant time scales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.

We study Andreev reflection in graphene nanoribbon/superconductor hybrid junctions. By using a tight-binding approach and the scattering formalism we show that finite-size effects lead to notable differences with respect to the bulk-graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflection induces an insulating behavior even when the junction is biased; electron conduction can however be restored by applying a gate voltage. Finally, we check that these findings remain valid also in the case of nonideal nanoribbons in which the number of transverse sites varies along the transport direction.

In single-layer graphene sheets non-local interband exchange leads to a renormalized Fermi-surface effective mass which vanishes in the low carrier-density limit. We report on a comparative study of Fermi surface effective mass renormalization in single-layer and AB-stacked bilayer graphene. We explain why the mass does not approach zero in the bilayer case, although its value is still strongly suppressed.

Folded graphene flakes are a natural byproduct of the micromechanical exfoliation process. In this article we show by a combination of analytical and numerical methods that such systems behave as intriguing interferometers due to the interplay between an externally applied magnetic field and the gauge field induced by the deformations in the region of the fold.

We demonstrate that single-layer graphene in the presence of a metal gate displays a gapless collective (plasmon) mode that has a linear dispersion at long wavelengths. We calculate exactly the acoustic-plasmon group velocity at the level of the random phase approximation and carry out microscopic calculations of the one-body spectral function of such system. Despite screening exerted by the metal, we find that graphene's quasiparticle spectrum displays a very rich structure characterized by composite hole-acoustic plasmon satellite bands (that we term for brevity "soundarons"), which can be observed by e.g. angle-resolved photoemission spectroscopy.

Bilayer graphene (BLG) has recently attracted a great deal of attention because of its electrically tunable energy gaps and its unusual electronic structure. In this Rapid Communication we present analytical and semianalytical expressions, based on the four-band continuum model, for the layer-sum and layer-difference density-response functions of neutral and doped BLG. These results demonstrate that BLG density fluctuations can exhibit either single-component massive-chiral character or standard two-layer character, depending on energy and doping.

We show that the plasmon spectrum of an ordinary two-dimensional electron gas (2DEG) hosted in a GaAs heterostructure is significantly modified when a graphene sheet is placed on the surface of the semiconductor in close proximity to the 2DEG. Long-range Coulomb interactions between massive electrons and massless Dirac fermions lead to a new set of optical and acoustic intra-subband plasmons. Here we compute the dispersion of these coupled modes within the Random Phase Approximation, providing analytical expressions in the long-wavelength limit that shed light on their dependence on the Dirac velocity and Dirac-fermion density. We also evaluate the resistivity in a Coulomb-drag transport setup. These Dirac/Schroedinger hybrid electron systems are experimentally feasible and open new research opportunities for fundamental studies of electron-electron interaction effects in two spatial dimensions.

The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode. We point out that in the strong coupling limit the Dicke model of cavity cyclotron resonance must be supplemented by a term that is quadratic in the cavity photon field and suppresses the model's transition to a super-radiant state. We develop the theory of graphene cavity cyclotron resonance and show that the quadratic term, which is absent in graphene's low-energy Dirac model Hamiltonian, is in this case dynamically generated by virtual inter-band transitions.

Recent scattering-type scanning near-field optical spectroscopy (s-SNOM) experiments on single-layer graphene have reported Dirac plasmon lifetimes that are substantially shorter than the dc transport scattering time ${\ensuremath{\tau}}_{\mathrm{tr}}$. We argue that this discrepancy arises from the fact that the plasmon lifetime is fundamentally different from ${\ensuremath{\tau}}_{\mathrm{tr}}$ since it is controlled by the imaginary part of the current-current linear response function at finite momentum and frequency. Taking this into account, we show that a minimal theory of the extrinsic lifetime of Dirac plasmons due to scattering against charged impurities yields a plasmon damping rate which is in good agreement with s-SNOM experimental results.

By means of the time-dependent density-matrix renormalization-group (TDMRG) method we are able to follow the real-time dynamics of a single impurity embedded in a one-dimensional bath of interacting bosons. We focus on the impurity breathing mode, which is found to be well described by a single oscillation frequency and a damping rate. If the impurity is very weakly coupled to the bath, a Luttinger-liquid description is valid and the impurity suffers an Abraham-Lorentz radiation-reaction friction. For a large portion of the explored parameter space, the TDMRG results fall well beyond the Luttinger-liquid paradigm.

We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random phase approximation in the linear-response limit, is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional (2D) gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved by virtue of the finiteness of the quasi-homogeneous second-order nonlinear response of this inversion-symmetric 2D material.

We present a finite-temperature diagrammatic perturbation theory of third-harmonic generation in doped graphene. We carry out calculations of the third-order conductivity in the scalar potential gauge, highlighting a subtle cancellation between a Fermi surface contribution, which contains only power laws, and power-law contributions of interband nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the upconversion efficiency at zero and finite temperature. Our approach can be easily generalized to other materials and to include many-body effects.

Graphene plasmons have recently attracted a great deal of attention because of their tunability, long lifetime, and high degree of field confinement in the vertical direction. Nearby metal gates have been shown to modify the graphene plasmon dispersion and further confine their electric field. We study the plasmons of a graphene sheet deposited on a metal, in the regime in which metal bands do not hybridize with massless Dirac fermion bands. We derive exact results for the dispersion and lifetime of the plasmons of such a hybrid system, taking into account metal nonlocalities. The graphene plasmon dispersion is found to be acoustic and pushed down in energy toward the upper boundary of the intraband graphene particle-hole continuum, thereby strongly enhancing the vertical confinement of these excitations. Landau damping of such acoustic plasmons due to particle-hole excitations in the metal gate is found to be surprisingly weak, with quality factors exceeding $Q={10}^{2}$.

We present extensive calculations of the optical and plasmonic properties of a graphene sheet carrying a dc current. By calculating analytically the density-density response function of current-carrying states at finite temperature, we demonstrate that an applied dc current modifies the Pauli blocking mechanism and that absorption acquires a birefringent character with respect to the angle between the in-plane light polarization and current flow. Employing the random phase approximation at finite temperature, we show that graphene plasmons display a degree of non-reciprocity and collimation that can be tuned with the applied current. We discuss the possibility to measure these effects.

Collective charge-density modes (plasmons) of the clean two-dimensional unpolarized electron gas are stable, for momentum conservation prevents them from decaying into single-particle excitations. Collective spin-density modes (spin plasmons) possess no similar protection and rapidly decay by production of electron-hole pairs. Nevertheless, if the electron gas has a sufficiently high degree of spin polarization ($P>1/7$, where $P$ is the ratio of the equilibrium spin density and the total electron density, for a parabolic single-particle spectrum) we find that a long-lived spin plasmon---a collective mode in which the densities of up and down spins oscillate with opposite phases---can exist within a ``pseudogap'' of the single-particle excitation spectrum. The ensuing collectivization of the spin excitation spectrum is quite remarkable and should be directly visible in Raman-scattering experiments. The predicted mode could dramatically improve the efficiency of coupling between spin-wave-generating devices, such as spin-torque oscillators.

Atomically-thin magnetic crystals have been recently isolated experimentally, greatly expanding the family of two-dimensional materials. In this Article we present an extensive comparative analysis of the electronic and magnetic properties of , based on density functional theory (DFT). We first show that the often-used approaches fail in predicting the ground-state properties of this material in both its monolayer and bilayer forms, and even more spectacularly in its bulk form. In the latter case, the fundamental gap decreases by increasing the Hubbard-U parameter, eventually leading to a metallic ground state for physically relevant values of U, in stark contrast with experimental data. On the contrary, the use of hybrid functionals, which naturally take into account nonlocal exchange interactions between all orbitals, yields good account of the electronic gap as measured by ARPES. We then calculate all the relevant exchange couplings (and the magneto-crystalline anisotropy energy) for monolayer, bilayer, and bulk with a hybrid functional, with super-cells containing up to 270 atoms, commenting on existing calculations with much smaller super-cell sizes. In the case of bilayer , we show that two distinct intra-layer second-neighbor exchange couplings emerge, a result which, to the best of our knowledge, has not been noticed in the literature.

The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e. disjoint segments of a two-dimensional Fermi contour. We present a quantum-mechanical non-local theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry. These are collective excitations constructed from topological Fermi arc and bulk electron states and arising from electron-electron interactions, which are treated in the realm of the random phase approximation. Our theory includes quantum effects associated with the penetration of the Fermi arc surface states into the bulk and dissipation, which is intrinsically non-local in nature and arises from decay processes mainly involving bulk electron-hole pair excitations.

We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of twisted bilayer graphene (TBG) at different filling factors and twist angles $\theta$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters, $u_0$ and $u_1$, which parametrize the intra-sublattice inter-layer and inter-sublattice inter-layer tunneling rate, respectively. In this Article we focus on two key aspects: i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\leq u_0\leq u_1$; ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e. at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intra-band contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects i) and ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5~{\rm K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.

Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes, however, can decay due to several possible mechanisms. In this Letter we expose a new facet of spin-charge separation: not only the speeds but also the damping rates of spin and charge excitations are different. While the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive. We suggest that cold Fermi gases trapped inside a tight atomic waveguide offer the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet.

Motivated by a number of recent experimental studies we have revisited the problem of the microscopic calculation of the quasiparticle self-energy and many-body effective mass enhancement in a two-dimensional electron liquid. Our systematic study is based on the many-body local fields theory and takes advantage of the results of the most recent Diffusion Monte Carlo calculations of the static charge and spin response of the electron liquid. We report extensive calculations of both the real and imaginary parts of the quasiparticle self-energy. We also present results for the many-body effective mass enhancement and the renormalization constant over an extensive range of electron density. In this respect we critically examine the relative merits of the on-shell approximation versus the self-consistent solution of the Dyson equation. We show that in the strongly-correlated regime a solution of the Dyson equation proves necessary in order to obtain a well behaved effective mass. The inclusion of both charge- and spin-density fluctuations beyond the Random Phase Approximation is indeed crucial to get reasonable agreement with recent measurements.

The orbital magnetic susceptibility (OMS) of a gas of noninteracting massless Dirac fermions is zero when the Fermi energy is away from the Dirac point. Making use of diagrammatic perturbation theory, we calculate exactly the OMS of massless Dirac fermions to first order in the Coulomb interaction demonstrating that it is finite and positive. Doped graphene sheets are thus unique systems in which the OMS is completely controlled by many-body effects.

Multilayer graphene on the carbon face of silicon carbide is an intriguing electronic system which typically consists of a stack of ten or more layers. Rotational stacking faults in this system dramatically reduce interlayer coherence. In this paper we report on the influence of interlayer interactions, which remain strong even when coherence is negligible, on the Fermi-liquid properties of charged graphene layers. We find that interlayer interactions increase the magnitudes of correlation energies and decrease quasiparticle velocities, even when remote-layer carrier densities are small, and that they lessen the influence of exchange and correlation on the distribution of carriers across layers.

Coulomb drag between two unhybridized graphene sheets separated by a dielectric spacer has recently attracted considerable theoretical interest. We first review, for the sake of completeness, the main analytical results which have been obtained by other authors. We then illustrate pedagogically the minimal theory of Coulomb drag between two spatially separated two-dimensional systems of massless Dirac fermions which are both away from the charge-neutrality point. This relies on second-order perturbation theory in the screened interlayer interaction and on Boltzmann-transport theory. In this theoretical framework and in the low-temperature limit, we demonstrate that, to leading (i.e. quadratic) order in temperature, the drag transresistivity is completely insensitive to the precise intralayer momentum-relaxation mechanism (i.e. to the functional dependence of the transport scattering time on energy). We also provide analytical results for the low-temperature drag transresistivity for both cases of 'thick' and 'thin' spacers and for arbitrary values of the dielectric constants of the media surrounding the two Dirac-fermion layers. Finally, we present numerical results for the low-temperature drag transresistivity for the case when one of the media surrounding the Dirac-fermion layers has a frequency-dependent dielectric constant. We conclude by suggesting an experiment that can potentially allow for the observation of departures from the canonical quadratic-in-temperature behavior of the transresistivity.

We study by means of the recursive Green's function technique the local density of states of (finite and semi-infinite) multiband spin-orbit-coupled semiconducting nanowires in proximity to an $s$-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreev-bound-state spectrum in superconductor-normal metal-superconductor junctions and find that in multiband nanowires the distinction between topologically trivial and nontrivial systems based on the number of zero-energy crossings is preserved.

Radiative heat transfer (RHT) between macroscopic bodies at separations that are much smaller than the thermal wavelength is ruled by evanescent electromagnetic modes and can be orders of magnitude more efficient than its far-field counterpart, which is described by the Stefan-Boltzmann law. In this Letter we present a microscopic theory of RHT in van der Waals stacks comprising graphene and a natural hyperbolic material, i.e. hexagonal boron nitride (hBN). We demonstrate that RHT between hot carriers in graphene and hyperbolic phonon-polaritons in hBN is extremely efficient at room temperature, leading to picosecond time scales for the carrier cooling dynamics.

Deterministic fractal antennas are employed to realize multimodal plasmonic devices. Such structures show strongly enhanced localized electromagnetic fields typically in the infrared range with a hierarchical spatial distribution. Realization of engineered fractal antennas operating in the optical regime would enable nanoplasmonic platforms for applications, such as energy harvesting, light sensing, and bio-/chemical detection. Here, we introduce a novel plasmonic multiband metamaterial based on the Sierpinski carpet (SC) space-filling fractal, having a tunable and polarization-independent optical response, which exhibits multiple resonances from the visible to mid-infrared range. We investigate gold SCs fabricated by electron-beam lithography on CaF2 and Si/SiO2 substrates. Furthermore, we demonstrate that such resonances originate from diffraction-mediated localized surface plasmons, which can be tailored in deterministic fashion by tuning the shape, size, and position of the fractal elements. Moreover, our findings illustrate that SCs with high order of complexity present a strong and hierarchically distributed electromagnetic near-field of the plasmonic modes. Therefore, engineered plasmonic SCs provide an efficient strategy for the realization of compact active devices with a strong and broadband spectral response in the visible/mid-infrared range. We take advantage of such a technology by carrying out surface enhanced Raman spectroscopy (SERS) on Brilliant Cresyl Blue molecules deposited onto plasmonic SCs. We achieve a broadband SERS enhancement factor up to 104, thereby providing a proof-of-concept application for chemical diagnostics.

Graphene is known to possess strong optical nonlinearity.Its nonlinear response can be further enhanced by graphene plasmons.Here, we report a novel nonlinear electroabsorption effect observed in nanostructured graphene due to excitation of graphene plasmons.We experimentally detect and theoretically explain enhanced nonlinear mixing of near-infrared and mid-infrared light in arrays of graphene nanoribbons.Strong compression of light by graphene plasmons implies that the effect is non-local in nature and orders of magnitude larger than the conventional local graphene nonlinearity.The effect can be used in variety of applications including nonlinear light modulators, light multiplexors, light logic, and sensing devices.

Hot electrons dominate the ultrafast (∼fs–ps) optical and electronic properties of metals and semiconductors, and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third-harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power law expected for a third-harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency converters, can be affected by changes in the electronic temperature, which might occur due to an increase in absorbed optical power or Joule heating.