H. L. Störmer

When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction--a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.

We have achieved mobilities in excess of 200,000 cm2 V −1 s−1 at electron densities of ∼2 ×1011 cm−2 by suspending single layer graphene. Suspension ∼150 nm above a Si/SiO2 gate electrode and electrical contacts to the graphene was achieved by a combination of electron beam lithography and etching. The specimens were cleaned in situ by employing current-induced heating, directly resulting in a significant improvement of electrical transport. Concomitant with large mobility enhancement, the widths of the characteristic Dirac peaks are reduced by a factor of 10 compared to traditional, nonsuspended devices. This advance should allow for accessing the intrinsic transport properties of graphene.

A quantized Hall plateau of ${\ensuremath{\rho}}_{\mathrm{xy}}=\frac{3h}{{e}^{2}}$, accompanied by a minimum in ${\ensuremath{\rho}}_{\mathrm{xx}}$, was observed at $T<5$ K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is $\frac{1}{3}$ filled. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation.

The quantum Hall effect (QHE), one example of a quantum phenomenon that occurs on a truly macroscopic scale, has attracted intense interest since its discovery in 1980 and has helped elucidate many important aspects of quantum physics. It has also led to the establishment of a new metrological standard, the resistance quantum. Disappointingly, however, the QHE has been observed only at liquid-helium temperatures. We show that in graphene, in a single atomic layer of carbon, the QHE can be measured reliably even at room temperature, which makes possible QHE resistance standards becoming available to a broader community, outside a few national institutions.

GaAs-AlxGa1−xAs superlattice structures in which electron mobilities exceed those of otherwise equivalent epitaxial GaAs as well as the Brooks-Herring predictions near room temperature and at very low temperatures are reported. This new behavior is achieved via a modulation-doping technique that spatially separates conduction electrons and their parent donor impurity atoms, thereby reducing the influence of ionized and neutral impurity scattering on the electron motion.

Infrared spectra of graphene deposited on a silicon oxide substrate suggest that many-body effects have a more significant role in determining its electronic behaviour than in free-standing graphene A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian1. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy–momentum dispersion, have been confirmed by recent observations2,3,4,5. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene.

The resistivity of ultraclean suspended graphene is strongly temperature (T) dependent for 5<T<240 K. At T-5 K transport is near-ballistic in a device of approximately 2 microm dimension and a mobility approximately 170,000 cm2/V s. At large carrier density, n>0.5 x 10(11) cm(-2), the resistivity increases with increasing T and is linear above 50 K, suggesting carrier scattering from acoustic phonons. At T=240 K the mobility is approximately 120,000 cm2/V s, higher than in any known semiconductor. At the charge neutral point we observe a nonuniversal conductivity that decreases with decreasing T, consistent with a density inhomogeneity <10(8) cm(-2).

An even-denominator rational quantum number has been observed in the Hall resistance of a two-dimensional electron system. At partial filling of the second Landau level \ensuremath{\nu}=2+(1/2= 5) / 2 and at temperatures below 100 mK, a fractional Hall plateau develops at ${\mathrm{\ensuremath{\rho}}}_{\mathrm{xy}}$=(h/${\mathrm{e}}^{2}$)/(5/2 defined to better than 0.5%. Equivalent even-denominator quantization is absent in the lowest Landau level under comparable conditions.

The conductivity of graphene samples with various levels of disorder is investigated for a set of specimens with mobility in the range of 1-20x10(3) cm2/V sec. Comparing the experimental data with the theoretical transport calculations based on charged impurity scattering, we estimate that the impurity concentration in the samples varies from 2-15x10(11) cm(-2). In the low carrier density limit, the conductivity exhibits values in the range of 2-12e2/h, which can be related to the residual density induced by the inhomogeneous charge distribution in the samples. The shape of the conductivity curves indicates that high mobility samples contain some short-range disorder whereas low mobility samples are dominated by long-range scatterers.

The fractional quantum Hall effect is a quintessential manifestation of the collective behaviour associated with strongly interacting charge carriers confined to two dimensions and subject to a strong magnetic field. It is predicted that the charge carriers present in graphene — an atomic layer of carbon that can be seen as the 'perfect' two-dimensional system — are subject to strong interactions. Nevertheless, the phenomenon had eluded experimental observation until now: in this issue two groups report fractional quantum Hall effect in suspended sheets of graphene, probed in a two-terminal measurement setup. The researchers also observe a magnetic-field-induced insulating state at low carrier density, which competes with the quantum Hall effect and limits its observation to the highest-quality samples only. These results pave the way for the study of the rich collective behaviour of Dirac fermions in graphene. The fractional quantum Hall effect (FQHE) is the quintessential collective quantum behaviour of charge carriers confined to two dimensions but it has not yet been observed in graphene, a material distinguished by the charge carriers' two-dimensional and relativistic character. Here, and in an accompanying paper, the FQHE is observed in graphene through the use of devices containing suspended graphene sheets; the results of these two papers open a door to the further elucidation of the complex physical properties of graphene. When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid1,2. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. The experimental discovery of an anomalous integer quantum Hall effect in graphene has enabled the study of a correlated two-dimensional electronic system, in which the interacting electrons behave like massless chiral fermions3,4. However, owing to the prevailing disorder, graphene has so far exhibited only weak signatures of correlated electron phenomena5,6, despite intense experimental and theoretical efforts7,8,9,10,11,12,13,14. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields.

The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical applications. Here, we demonstrate the fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the megahertz range, and the strong dependence of resonant frequency on applied gate voltage can be fitted to a membrane model to yield the mass density and built-in strain of the graphene. Following the removal and addition of mass, changes in both density and strain are observed, indicating that adsorbates impart tension to the graphene. On cooling, the frequency increases, and the shift rate can be used to measure the unusual negative thermal expansion coefficient of graphene. The quality factor increases with decreasing temperature, reaching ∼1 × 104 at 5 K. By establishing many of the basic attributes of monolayer graphene resonators, the groundwork for applications of these devices, including high-sensitivity mass detectors, is put in place. A detailed understanding of the response of graphene resonators to changes in mass and temperature could lead to the development of ultrasensitive mass detectors and other nanoelectromechanical systems.

The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $\nu=0,\pm 1,\pm 4$ are discovered at magnetic fields $B>$20 T, indicating the lifting of the four-fold degeneracy of the previously observed QH states at $\nu=\pm(|n|+1/2)$, where $n$ is the Landau level index. In particular, the presence of the $\nu=0, \pm 1$ QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at $\nu=\pm 4$ is investigated in tilted magnetic field and can be attributed to lifting of the spin-degeneracy of the $n=1$ Landau level.

Using single-electron capacitance spectroscopy, we map the magnetic field dependence of the ground state energies of a single quantum dot containing from 0 to 50 electrons. The experimental spectra reproduce many features of a noninteracting electron model with an added fixed charging energy. However, in detailed observations deviations are apparent: Exchange induces a two-electron singlet-triplet transition, self-consistency of the confinement potential causes the dot to assume a quasi-two-dimensional character, and features develop which are suggestive of the fractional quantum Hall effect.

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to $B=18\text{ }\text{ }\mathrm{T}$ at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to $\sqrt{B}$, and the deduced band velocity is $\stackrel{\texttildelow{}}{c}\ensuremath{\approx}1.1\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\mathrm{m}/\mathrm{s}$. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.

We observe the capacitance signal resulting from single electrons tunneling into discrete quantum levels. The electrons tunnel between a metallic layer and confined states of a single disk in a microscopic capacitor fabricated in GaAs. Charge transfer occurs only for bias voltages at which a quantum level resonates with the Fermi energy of the metallic layer. This creates a sequence of distinct capacitance peaks whose bias positions directly reflect the electronic spectrum of the confined structure. From the magnetic field evolution of the spectrum, we deduce the nature of the bound states.

We report the first observation of a two-dimensional electron gas at a semiconductor-semiconductor (GaAs-AℓGaAs) interface. A novel, high-mobility, persistent-photoconductive effect allows one to vary the two-dimensional carrier concentration continuously from 1.1 × 1012 cm−2 to 1.6 × 1012 cm−2, as obtained by Shubnikov-deHaas measurements. Cyclotron resonance data establish an effective mass of 1.11 m☆b, where m☆b is the mass at the conduction-band edge of GaAs. Hall data and cyclotron resonance yield a mobility of μ ≈ 5000 cm2/Vsec.

We have measured the transport properties of high-quality quantum wires fabricated in GaAs-AlGaAs by using cleaved edge overgrowth. The low temperature conductance is quantized as the electron density in the wire is varied. While the values of the conductance plateaus are reproducible, they deviate from multiples of the universal value of ${2e}^{2}/h$ by as much as 25%. As the temperature or dc bias increases the conductance steps approach the universal value. Several aspects of the data can be explained qualitatively using Luttinger liquid theory although there remain major inconsistencies with such an interpretation.

A modulation-doped Al0.35Ga0.65As/GaAs single interface structure with a 700 Å undoped setback grown by solid-source molecular beam epitaxy (MBE) shows a Hall mobility of 11.7×106 cm2/V s at a carrier density of 2.4×1011 electrons/cm2 measured in van der Pauw geometry after exposure to light at 0.35 K. This is the highest carrier mobility ever measured in a semiconductor. Similar Al0.32Ga0.68As/GaAs structures with 1000–2000 Å setbacks show Hall mobilities in the dark at 0.35 K as high as 4.9×106 cm2 /V s for carrier densities of 5.4×1010 electrons/cm2 and lower.

We have succeeded in fabricating a two-dimensional electron gas (2DEG) on the cleaved (110) edge of a GaAs wafer by molecular beam epitaxy (MBE). A (100) wafer previously prepared by MBE growth is reinstalled in the MBE chamber so that an in situ cleave exposes a fresh (110) GaAs edge for further MBE overgrowth. A sequence of Si-doped AlGaAs layers completes the modulation-doped structure at the cleaved edge. Mobilities as high as 6.1×105 cm2/V s are measured in the 2DEG at the cleaved interface.

Low-temperature, electronic transport in Landau levels N>1 of a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of each such Landau level the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. Such anisotropies are absent in the N=0 and N=1 Landau level, which are dominated by the states of the fractional quantum Hall effect. The transport anisotropies may be indicative of a new many particle state, which forms exclusively in higher Landau levels.

We have determined the energy gaps of both prominent sequences of fractional quantum Hall effect of (FQHE) states at filling factor \ensuremath{\nu}=p/(2p\ifmmode\pm\else\textpm\fi{}1) around \ensuremath{\nu}=1/2. The gaps increase linearly with \ensuremath{\Delta}B, the deviation of the magnetic field from half filling. Therefore, the data are indistinguishable from Shubnikov--de Haas oscillations of particles of charge e, effective mass ${\mathit{m}}^{\mathrm{*}}$, and lifetime broadening \ensuremath{\Gamma} exposed to an effective magnetic field \ensuremath{\Delta}B. Our findings are remarkably consistent with recent proposals of composite particles in the FQHE and the existence of a Fermi surface at even-denominator fillings.

According to recent theories, a system of electrons at the half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field. In order to test for these new particles, we have studied transport in antidot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the antidot lattice. At \ensuremath{\nu}=1/2 we observe the same dimensional resonances. This establishes the semiclassical behavior of composite fermions.

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.

Combined magnetotransport and cyclotron-resonance experiments in a two-dimensional hole system at a modulation-doped GaAs-(AlGa)As heterojunction show that the Kramers degeneracy of the lowest subband is lifted for finite $k$ giving rise to two cyclotron masses ${{m}_{1}}^{*}=0.38{m}_{0}$ and ${{m}_{2}}^{*}=0.60{m}_{0}$ at ${E}_{\mathrm{F}}=2.4$ meV. The observation of plateaus in ${\ensuremath{\rho}}_{xy}$ shows that the quantized Hall effect is independent of the details of the host band structure.

Two-dimensional electron systems in a high magnetic field behave very strangely. They exhibit rational fractional quantum numbers and contain exactly fractionally charged particles. Electrons seem to absorb magnetic flux quanta, altering their statistics and consuming the magnetic field. They condense into a manifold of novel ground states of boson and fermion character. These fascinating properties are not characteristic of any individual electron but rather emerge from the highly correlated motion of many.

The zone folding in the acoustic-phonon dispersion curve of GaAs/AlGaAs superlattices is demonstrated using superconducting tunnel junctions as sources and detectors of quasimonochromatic phonons. We present data on selective transmission of high-frequency phonons due to narrow band reflection determined by the superlattice period.

Magnetotransport of two-dimensional electrons and holes was studied in magnetic fields up to 300 kG and temperatures down to 0.5 K. In addition to previously reported structures at Landau-level filling factors $\ensuremath{\nu}=\frac{1}{3} \mathrm{and} \frac{2}{3}$, new structures were resolved at $\ensuremath{\nu}=\frac{4}{3}, \frac{5}{3}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}, \mathrm{and} \frac{2}{7}$. The results suggest that fractional quantization of the Hall effect exists in multiple series, each based on the inverse of an odd integer.

We report the first observation of the modulation doping effect in Si/Ge0.2Si0.8 heterojunctions grown by molecular beam epitaxy. Peak hole mobilities of ∼3300 cm2 V−1 s−1 have been observed at 4.2 K. These values, although nonoptimum, are comparable to the best reported values for holes in Si/SiO2 inversion layers. Low temperature, angular dependent, Shubnikov–de Haas measurements have demonstrated the two-dimensional nature of the hole gas and yield a surface carrier density of 3.5×1011 cm−2. From the temperature dependence of the Shubnikov–de Haas amplitudes a hole effective mass of 0.30±0.02mo has been derived. Identical measurements on n-type heterojunctions having the same Ge content (x=0.2) have failed to show a sustained enhancement of mobility at low temperatures, indicating that ΔEv≫ΔEc.

The polarization of small, disc-shaped regions of two-dimensional electron gas exhibit a well-defined collective resonance. The resonance and its behavior in a magnetic field are accurately described by two-dimensional electrons in a harmonic potential.

Quantization of the Hall effect and concomitantly vanishing magnetoresistance are observed in a GaAs/(AlGa)As superlattice structure whose electronic spectrum exhibits dispersion in all three spatial dimensions.

The density of states of two-dimensional electron systems in GaAs/AlGaAs single-layer and multilayer heterostructures has been determined through measurements of the high-field magnetization. Our results reveal a substantial density of states between Landau levels, even in high-mobility single quantum wells. There is no existing theoretical explanation for this anomaly.

We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observe a significant asymmetry in the optical conductivity upon electrostatic doping of electrons and holes. We show that this finding arises from a marked asymmetry between the valence and conduction bands, which is mainly due to the inequivalence of the two sublattices within the graphene layer and the next-nearest-neighbor interlayer coupling. From the conductivity data, the energy difference of the two sublattices and the interlayer coupling energy are directly determined.

We report ultralow temperature experiments on the obscure fractional quantum Hall effect at Landau level filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2$ in a very high-mobility specimen of $\ensuremath{\mu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.7\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{cm}}^{2}/\mathrm{V}\mathrm{s}$. We achieve an electron temperature as low as $\ensuremath{\sim}4\mathrm{mK}$, where we observe vanishing ${R}_{\mathrm{xx}}$ and, for the first time, a quantized Hall resistance, ${R}_{\mathrm{xy}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}h/(5/2){e}^{2}$ to within 2 ppm. ${R}_{\mathrm{xy}}$ at the neighboring odd-denominator states $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7/3$ and $8/3$ is also quantized. The temperature dependences of the ${R}_{\mathrm{xx}}$ minima at these fractional fillings yield activation energy gaps ${\ensuremath{\Delta}}_{5/2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.11$, ${\ensuremath{\Delta}}_{7/3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.10$, and ${\ensuremath{\Delta}}_{8/3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.055\mathrm{K}$.

At a very low-temperature of 9 mK, electrons in the second Landau level of an extremely high-mobility two-dimensional electron system exhibit a very complex electronic behavior. With a varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed nu=2+2/5 state separated from the even-denominator nu=2+1/2 state by an insulating phase and a nu=2+2/7 and nu=2+1/5 state surrounded by such phases. A developing plateau at nu=2+3/8 points to the existence of other even-denominator states.

The fractional quantum Hall effect is a very counterintuitive physical phenomenon. It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any individual electron. This is not the way things are supposed to be. A collection of objects may assemble to form a bigger object, or the parts may remain their size, but they don’t create anything smaller. If the new particles were doubly charged, it wouldn’t be so paradoxical— electrons could ‘‘just stick together’’ and form pairs. But fractional charges are very bizarre indeed. Not only are they smaller than the charge of any constituent electron, but they are exactly 1/3 or 1/5 or 1/7 etc. of an electronic charge, depending on the conditions under which they have been prepared. And yet we know with certainty that none of these electrons has split up into pieces. Fractional charge is the most puzzling of the observations, but there are others. Quantum numbers—usually integers or half-integers—turn out to be also fractional, such as 2/5, 4/9, and 11/7, or even 5/23. Moreover, bits of magnetic field can get attached to each electron, creating yet other objects. Such composite particles have properties very different from those of the electrons. They sometimes seem to be oblivious to huge magnetic fields and move in straight lines, although any bare electron would orbit on a very tight circle. Their mass is unrelated to the mass of the original electron but arises solely from interactions with their neighbors. More so, the attached magnetic field changes drastically the characteristics of the particles, from fermions to bosons and back to fermions, depending on the field strength. And finally, some of these composites are conjectured to coalesce and form pairs, vaguely similar to the formation of electron pairs in superconductivity. This would provide yet another astounding new state with weird properties. All of these strange phenomena occur in twodimensional electron systems at low temperatures exposed to a high magnetic field—only electrons and a magnetic field. The electrons reside within a solid, at the interface between two slightly different semiconductors. This is presently the smoothest plane we can fabricate to restrict the electrons’ motion to two dimensions. Quantum mechanics does the rest.

We observe a novel transition between distinct fractional quantum Hall states sharing the same filling fraction \ensuremath{\nu}=(8/5. The transition is driven by tilting the two-dimensional electron-gas sample relative to the external magnetic field and is manifested by a sharp change in the dependence of the measured activation energy on tilt angle. After an initial decline, the activation energy abruptly begins to increase as the tilt angle exceeds about 30\ifmmode^\circ\else\textdegree\fi{}. A plausible model for these results implies a transition from a spin-unpolarized quantum fluid at small angles to a polarized one at higher angles.

We report the first observation of the magnetic-field-dependent electronic specific heat in GaAs-GaAs multilayers. With a heat-pulse technique oscillations of the sample temperature on the order of millikelvins were observed. Both intra- and inter-Landau-level contributions could be distinguished. Theoretical fits to the data reveal a density of states consisting of Gaussian peaks on a flat background.

We observed a strong increase in the low temperature electron scattering rate of a 2-dimensional electron gas in a modulation doped GaAs-(AlGa)As heterojunction at the transition from one-subband to two-subband conduction. Our data provide direct evidence for the occurence of intersubband scattering processes. Electron densities as well as mobilities in each subband are determined separately throughout the transition regime. Mobilities of the ground subband considerably exceed those of the excited subband. All features of the calculated density dependence of the mobilities are qualitatively reproduced by our data.

We have studied edge magnetoplasmons (EMP's) created by pulses of 100 ps width in a high-mobility two-dimensional electron gas, using a cryogenic transistor. We find that magnetoplasmon motion along the edge occurs only in the direction expected for negatively charged electrons; there is no hint of propagation in the opposite direction expected for positively charged quasiholes. We also measure the periods and decay rates of the edge modes continuously as a function of the magnetic field. From these characteristics we deduce the width of the EMP boundary layer as well as the magnetic-field-dependent momentum-relaxation time.

We have investigated the influence of an increasing in-plane magnetic field on the states of half filling of Landau levels ( $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11/2$, 9/2, 7/2, and 5/2) of a two-dimensional electron system. In the electrically anisotropic phase at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}9/2$ and 11/2 an in-plane magnetic field of $\ensuremath{\sim}1--2\mathrm{T}$ overcomes its initial pinning to the crystal lattice and reorients this phase. In the initially isotropic phases at $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2$ and 7/2 an in-plane magnetic field induces a strong electrical anisotropy. In all cases, for high in-plane fields the high-resistance axis is parallel to the direction of the in-plane field.

Mechanically exfoliated graphene mounted on a SiO2/Si substrate was subjected to HF/H2O etching or irradiation by energetic protons. In both cases gas was released from the SiO2 and accumulated at the graphene/SiO2 interface resulting in the formation of “bubbles” in the graphene sheet. Formation of these “bubbles” demonstrates the robust nature of single layer graphene membranes, which are capable of containing mesoscopic volumes of gas. In addition, effective mass transport at the graphene/SiO2 interface has been observed.

In a GaAs/AlGaAs quantum well of density 1 x 10(11) cm(-2) we observed a fractional quantum Hall effect (FQHE) at nu = 4/11 and 5/13, and weaker states at nu = 6/17, 4/13, 5/17, and 7/11. These sequences of fractions do not fit into the standard series of integral quantum Hall effects of composite fermions (CF) at nu = p/(2mp +/- 1). They rather can be regarded as the FQHE of CFs attesting to residual interactions between these composite particles. In tilted magnetic fields the nu = 4/11 state remains unchanged, strongly suggesting it to be spin polarized. The weak nu = 7/11 state vanishes quickly with tilt.

The newly discovered even-denominator fractional quantum Hall effect at filling factor $\ensuremath{\nu}=\frac{5}{2}$ is found to collapse rapidly as the magnetic field is tilted away from the normal to the two-dimensional-electron-gas plane. No similar effect has been reported in tilted-field studies of the spin-polarized, odd-denominator effect at $\ensuremath{\nu}=\frac{2}{3} \mathrm{and} \frac{1}{3}$. Since a primary result of such tilting is increased spin splittings, the collapse of the $\ensuremath{\nu}=\frac{5}{2}$ effect strongly suggests that the underlying state is not spin polarized. Condensation into such a quantum liquid must involve substantial spin reversal.

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B=18 T, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow square root[B] for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.

Angular dependent magnetotransport measurements on the fractional quantum Hall (FQHE) states around Landau level filling factor $\ensuremath{\nu}=\frac{3}{2}$ are explained very effectively in terms of composite fermions (CFs) with a spin. The disappearance and reappearance of FQHE states as well as their spin polarization is deduced from a simple "Landau level" fan diagram for CFs. While the "Landau splitting" scales with effective magnetic field, with its origin at $\ensuremath{\nu}=\frac{3}{2}$, the spin-splitting scales with total external magnetic field having its origin at $B=0$. The $g$ factor of a CF is largely the $g$ factor of the electron.

Magnetotransport measurements on a low-density two-dimensional electron system have revealed a re-entrant dependence of the activation energy on magnetic field for the fractional quantum Hall state at 2/3 filling of the lowest Landau level. The data are consistent with a change in the spin structure of the ground state at 2/3 filling, but do not provide a simple picture of the quasiparticle excitation process. As yet we find no similar effect for the \ensuremath{\nu}=2/5 state.

We report magnetotransport measurements on low-density, high-mobility two-dimensional (2D) electron systems in (Al,Ga)As/GaAs heterostructures down to Landau-level filling factors of $v\ensuremath{\sim}\frac{1}{18}$. We observe a striking activated temperature dependence with onset near $v\ensuremath{\sim}\frac{1}{5}$ and continuing to smallest $v$. The activation energy increase is approximately linear with decreasing $v$ and its slope depends monotonically on 2D density. While magnetic-field-induced localization cannot be ruled out, several features of the results are consistent with the formation of a pinned 2D Wigner crystal.

We determine the spin susceptibility in a two-dimensional electron system in GaAs/AlGaAs over a wide range of low densities from 2x10(9) cm(-2) to 4x10(10) cm(-2). Our data can be fitted to an equation that describes the density dependence as well as the polarization dependence of the spin susceptibility. It can account for the anomalous g factors reported recently in GaAs electron and hole systems. The paramagnetic spin susceptibility increases with decreasing density as expected from theoretical calculations.

The introduction of an undoped (AlGa)As spacer enhances significantly the low-temperature mobility in modulation-doped GaAs-(AlGa)As superlattices. Mobilities increase monotonically with spacer thickness. This indicates that ionized impurity scattering can be further suppressed by increasing the separation between carriers and their parent donors. Hall mobilities of 93 000 cm2/V sec were observed for average Hall densities of 4.9×1016 cm−3 at 4.2 K.

The quantum Hall (QH) effect in two-dimensional electron and hole gas is studied in high quality graphene samples. Graphene samples whose lateral size ∼10 μm were fabricated into mesoscopic devices for electrical transport measurement in magnetic fields. In an intermediate field range of up to 10 T, a distinctive half-integer QH effect is discovered with QH plateaus appearing at a filling factor sequence, ν=4(n+1/2), where n is the Landau level (LL) index. As the magnetic field increases to the extreme quantum limit, we observe additional QH plateaus at filling factors ν=0,±1,±4. Further detailed investigations show that the presence of the ν=0,±1 QH states indicates the n=0 LL at the charge neutral Dirac point splits into four sublevels. This lifts both the sublattice and the spin degeneracy, while the QH states at ν=±4 can be attributed to lifting of the spin degeneracy of the LLs. Above 30 T of magnetic field, the large quasiparticle gaps between the n=0 and n=±1 LLs lead to the QH effect that can be observed even at room temperature.

Two classes of artificial semiconductor heterostructures, differing only in the inversion symmetry of their internal quantum wells, are studied via magnetotransport. The samples consist of GaAs/(AlGa) As layered structures containing two-dimensional hole systems. The results reveal a lifting of the spin degeneracy of the lowest hole subband in the samples with inversion asymmetric quantum wells. In those structures with symmetric wells the subband remains doubly degenerate.

The electron mobility of single modulation-doped GaAs-(AlGa)As heterojunctions is strongly dependent on electron density and Al concentration. A low-temperature persistent photoconductive effect is employed to vary the areal electron density continuously within a single sample by nearly a factor of 3. Over this density range the mobility increases monotonically by as much as a factor of 4, quasilinear with density. At equivalent carrier concentrations heterojunctions with lower Al concentration show higher mobilities. At low temperatures a peak mobility of 365 000 cm2/Vs is found at an areal density of 7.0×1011 cm−2 with an interparticle spacing equivalent to a three-dimensional density of 5.9×1017 cm−3.

We have observed a rapid decrease in the rate by which two-dimensional electrons in very high-mobility (\ensuremath{\mu}\ensuremath{\approxeq}${10}^{7}$ ${\mathrm{cm}}^{2}$/V sec) GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures are scattered by acoustic phonons as the temperature approaches T=0. This precipitous drop in scattering rate is caused by strong phase-space restrictions for electron-phonon scattering. The characteristic temperature for this transition is not the Debye temperature of the GaAs host material, but the temperature at which phonons of twice the Fermi wave vector cease to be thermally excited.

We present a spectrum of experimental data on the fractional quantum Hall effect (FQHE) states in the first excited Landau level, obtained in an ultrahigh mobility two-dimensional electron system and at very low temperatures, and report the following results. For the even-denominator FQHE states, the sample dependence of the $\ensuremath{\nu}=5∕2$ state clearly shows that disorder plays an important role in determining the energy gap at $\ensuremath{\nu}=5∕2$. For the developing $\ensuremath{\nu}=19∕8$ FQHE state, the temperature dependence of the ${R}_{xx}$ minimum implies an energy gap of $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. The energy gaps of the odd-denominator FQHE states at $\ensuremath{\nu}=7∕3$ and $8∕3$ also increase with decreasing disorder, similar to the gap at $5∕2$ state. Unexpectedly and contrary to earlier data on lower mobility samples, in this ultrahigh quality specimen, the $\ensuremath{\nu}=13∕5$ state is missing, while its particle-hole conjugate state, the $\ensuremath{\nu}=12∕5$ state, is a fully developed FQHE state. We speculate that this disappearance might indicate a spin polarization of the $\ensuremath{\nu}=13∕5$ state. Finally, the temperature dependence is studied for the two-reentrant integer quantum Hall states around $\ensuremath{\nu}=5∕2$ and is found to show a very narrow temperature range for the transition from quantized to classical value.

We introduce an electrostatic lens for ballistic electrons in two-dimensional (2D) systems and demonstrate its focusing action in very high mobility GaAs-(AlGa)As heterostructures. This is the first refractive element for the control of 2D electrons. It exemplifies the close analogy between ballistic propagation in 2D electron systems and traditional geometrical optics.

Modulation-doped GaAs heterostructures with low-temperature electron mobilities of 5.0×106 cm2/V s at a two-dimensional electron areal density of 1.6×1011 cm−2 have been made. The mobilities are the highest ever observed in a semiconductor. Multiple quantum wells of GaAs prepared by similar methods showed electron mobilities up to 0.54×106 cm2/V s at an areal density of 5.3×1011 cm−2 per layer, which also exceeds any mobility value previously reported for multiple well structures. The structures were grown by molecular beam epitaxy with an atomic-plane sheet-doping technique.

This paper presents a sequence of studies on electronic transport in high-mobility, two-dimensional electron systems in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructures in high magnetic fields at low Landau-level filling factors where the formation of an electron solid has been postulated. It is an extension of our earlier work, summarizes our findings, and compares these findings with the results of other investigations. We observe a thermally activated insulating phase that surrounds the \ensuremath{\nu}=1/5 quantum liquid. This reentrant behavior is now documented for several samples of varying electron density and mobility. This broad universality of the phenomenon suggests an intrinsic mechanism as the cause for the transport features such as electron-solid formation, rather than individual carrier freeze out. Current-voltage measurements in the insulating phase reveal several anomalies. In low-voltage measurements we find nonlinearities similar to earlier results. An analysis of these data, which have been taken as convincing evidence for electron-solid formation, reveals some inconsistencies in the adopted model of charge-density depinning. In high-voltage measurements we observe the strong threshold behavior that also has been attributed, by yet more reports, to depinning of an electron solid. In our analysis we find a strong resemblance of this high-voltage breakdown to the breakdown behavior in the integer quantum Hall regime caused by a temperature runaway. Such a breakdown does not require a many-particle explanation. On the basis of our results, their analysis, and an assessment of the data in the literature, we believe that at the present time, in spite of some circumstantial evidence, there does not exist an experimental study that can positively identify the sought-after electron solid.

We have studied the temperature dependence of the fractional quantum Hall effect at Landaulevel filling factors $\ensuremath{\nu}=\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \frac{5}{3}, \frac{2}{5}, \mathrm{and} \frac{3}{5}$ in magnetic fields up to 28 T to determine the magnitude of the associated energy gaps. The data suggest a single activation energy for $\ensuremath{\nu}=\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \mathrm{and} \frac{3}{5}$. Its magnitude, much smaller than predicted by current theories, vanishes for $B\ensuremath{\lesssim}6$ T and saturates at $B\ensuremath{\gtrsim}18$ T. The data also suggest a single activation energy for $\ensuremath{\nu}=\frac{2}{5} \mathrm{and} \frac{3}{5}$ which is smaller than predicted.

We have made a direct determination of resonant screening (the depolarization field effect) in the collective intersubband excitations of a dense two dimensional electron gas. The effect was observed, for both odd and even parity transitions, in polarized inelastic light scattering spectra of a modulation-doped GaAs-AlGaAs superlattice. We offer a quantitative interpretation in terms of the Coulomb matrix elements for the transitions. Final state, or exciton-like, many-body effects are considered briefly.

When the Fermi level is pinned in the energy gap between two Landau levels of two-dimensional electrons, the response of electrons in the completely filled levels to an electric field is a dissipation-free Hall current perpendicular to the field. Our low-temperature measurements on GaAs-${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterojunctions give an upper limit for the resistance along the current path of ${\ensuremath{\rho}}_{\mathrm{xx}}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ \ensuremath{\Omega}/\ensuremath{\square} which corresponds to a three-dimensional resistivity of $\ensuremath{\rho}&lt;~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ \ensuremath{\Omega} cm. This resistivity is more than one order of magnitude lower than the resistivity of any nonsuperconducting material.

We report results on the fractional quantum Hall effect in GaAs-${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures at fractional Landau-level filling factor $\ensuremath{\nu}=\frac{p}{q}$ obtained with the combination of a dilution refrigerator and the National Magnet Laboratory hybrid magnet. We establish conclusively the quantiztation of the higher-order states $p$ in the series $q$. The Hall resistance is accurately quantized to 2.3 parts in ${10}^{4}$ for the $\frac{2}{5}$ state and 1.3 in ${10}^{3}$ for the $\frac{3}{5}$ state. New structures are observed near $\ensuremath{\nu}=\frac{3}{7}, \frac{4}{7}, \frac{4}{9}, \mathrm{and} \frac{5}{9}$.

We report the first observation of a quantum bound state formed at the junction of two intersecting quantum wells in the shape of a T. The atomically precise T junctions are fabricated by a novel cleaved edge overgrowth process in the AlGaAs/GaAs system. The identification of bound states with energies in excess of 20 meV is made by optical emission and absorption spectroscopy. Such quantum wire states are caused by the unique confinement of the lowest state wave function to the region of the T junction.

We have determined the effective mass of composite fermions in the vicinity of half Landau level filling and observe a mass enhancement by as much as 40% as the filling factor $\ensuremath{\nu}$ approaches $\ensuremath{\nu}=\frac{1}{2}$. These measurements provide the first experimental data for the energetics of this novel fermion system as $\ensuremath{\nu}\ensuremath{\rightarrow}\frac{1}{2}$. The apparently divergent particle mass indicates that the system at exactly $\ensuremath{\nu}=\frac{1}{2}$ is not an ordinary Fermi liquid.

At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu = 2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling-factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follows the series of composite fermion states emanating from nu = 1/6 and nu = 1/8.

A brief review of lateral electronic transport in modulation-doped (AlGa)As-GaAs heterostructures, where mobilities can exceed 106 cm2/V· s, is presented. Importance, strength and temperature dependence of the remaining electron scattering mechanisms are discussed.

We report the observation, by resonant inelastic light scattering, of intersubband excitations of the multilayer two dimensional electron gas, in modulation doped GaAsAlGaAs heterojunction superlattices. These are the first measurements of these transitions by any technique, and furnish intersubband energies in good agreement with calculated values. The spectral bands are broad, and nearly Lorentzian in shape: the implied relaxation rates scale linearly with band energy and are significantly faster than transport relaxation rates. Finally, the polarized spectra reveal differences between spin-flip and non spin-flip excitations which are unique to multilayer two dimensional electron gases.

We determine the density-dependent electron mass m(*) in two-dimensional electron systems of GaAs/AlGaAs heterostructures by performing detailed low-temperature Shubnikov-de Haas measurements. Using very high-quality transistors with tunable electron densities we measure m(*) in single, high mobility specimens over a wide range of r(s) (6 to 0.8). Toward low densities we observe a rapid increase of m(*) by as much as 40%. For 2>r(s)>0.8 the mass values fall approximately 10% below the band mass of GaAs. Numerical calculations are in qualitative agreement with our data but differ considerably in detail.

We report the simultaneous determination of the temperature and mobility of electrons in modulation-doped multiple quantum well GaAs-AlGaAs heterostructures as a function of applied electric field up to 150 V/cm. The decrease of high field mobility with increasing electron temperature is found to be much more rapid than the decrease of the low field mobility with the lattice temperature.

We report a study of the cyclotron resonance (CR) transitions to and from the unusual $n=0$ Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the $n=0$ level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the $n=0$ level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.

We have investigated electric field heating of high mobility electrons in modulation-doped GaAs-AlGaAs heterostructures by simultaneous measurement of luminescence and mobility. We find that hot electrons have a Fermi-Dirac distribution function for fields up to 750 V/cm and that the high field mobility of electrons can be understood in terms of field-induced electron heating and the temperature dependence of low field mobility.

The temperature dependence of the mobility of two-dimensional hole systems at modulation-doped GaAs-(AlGa)As heterojunctions is determined. Its shape follows closely the equivalent curve for high-purity p-type bulk GaAs. Low-temperature mobilities beyond 4×104 cm2/Vs are found for areal hole densities of 5×1011 cm−2. The equivalent scattering times reach those of the best modulation-doped electron systems. In the temperature range where acoustic mode scattering prevails a T−3/4 dependence was observed. Studies under light illumination could not detect any persistent photoconductive effect in two-dimensional holes.

The luminescence line shape of electron-hole drops in germanium is calculated assuming that the final state of the radiative transition is lifetime broadened due to Auger processes in the degenerate bands. This level broadening can account for the existence of the experimentally observed low energy tail in the recombination spectrum. The theoretical line shape is in good agreement with experimental results.

We report on the growth and transport properties of high-mobility two-dimensional electron gases (2DEGs) confined at the AlGaN/GaN interface grown by plasma-assisted molecular-beam epitaxy on GaN templates prepared by hydride vapor phase epitaxy. We have grown samples over a broad range of electron densities ranging from ns=6.9×1011 to 1.1×1013 cm−2, and at T=4.2 K, observe a peak mobility of 53 300 cm2/V s at a density of 2.8×1012 cm−2. Magnetotransport studies on these samples display exceptionally clean signatures of the quantum Hall effect. Our investigation of the dependence of 2DEG mobility on carrier concentration suggests that the low-temperature mobility in our AlGaN/GaN heterostructures is currently limited by the interplay between charged dislocation scattering and interface roughness.

We have been able to fabricate a two-dimensional electron gas containing an atomically precise, lateral Kronig–Penney potential of 102 Å periodicity. The structure was formed by modulation-doped molecular beam epitaxy overgrowth on the cleaved edge of a 71 Å GaAs/31 Å AlGaAs compositional superlattice. Low-temperature magnetotransport reveals clear quantum Hall characteristics. From the onset of the Shubnikov–de Haas oscillations at 0.25 T we deduce a lower limit of the mobility of μ≳40 000 cm2/V s at an electron density of 3.0×1011 cm−2 and infer that the carriers are crossing more than 200 GaAs/AlGaAs interfaces without losing phase coherence.

The edge of a two-dimensional electron system in a magnetic field consists of one-dimensional channels that arise from the confining electric field at the edge of the system. The crossed electric and magnetic fields cause electrons to drift parallel to the sample boundary, creating a chiral current that travels along the edge in only one direction. In an ideal two-dimensional electron system in the quantum Hall regime, all the current flows along the edge. Quantization of the Hall resistance arises from occupation of N one-dimensional edge channels, each contributing a conductance of e2/h. Here we report differential conductance measurements, in the integer quantum Hall regime, of tunnelling between the edges of a pair of two-dimensional electron systems that are separated by an atomically precise, high-quality, tunnel barrier. The resultant interaction between the edge states leads to the formation of new energy gaps and an intriguing dispersion relation for electrons travelling along the barrier: for example, we see a persistent conductance peak at zero bias voltage and an absence of tunnelling features due to electron spin. These features are unexpected and are not consistent with a model of weakly interacting edge states. Remnant disorder along the barrier and charge screening may each play a role, although detailed numerical studies will be required to elucidate these effects.

We analyze the magneto-resistance due to the higher-order fractional quantum Hall effect (FQHE) around v = 12 Landau level filling factor within the standard framework of Shubnikov-deHaas oscillations adopting v = 12 as the new origin for an effective magnetic field, Beff, and find it readily applicable. We deduce ad hoc effective masses, and scattering rates from our analysis. The masses are approximately constant and exceed the electron mass in GaAs by about a factor of 10. Our successful analysis of the FQHE features, in terms of this conventional tool for electron magneto-transport, further strengthens the case for the existence of exotic new particles in the FQHE.

This paper summarizes an extensive study of the temperature dependence of magnetotransport in the fractional quantum Hall effect in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructure devices of varying mobility and density. For devices with electron mobility 400 000\ensuremath{\lesssim}\ensuremath{\mu}\ensuremath{\lesssim}1 000 000 ${\mathrm{cm}}^{2}$/V s, we find a single activation energy, $^{3}/2$, in the longitudinal transport coefficients, ${\ensuremath{\sigma}}_{\mathrm{xx}}$ and ${\ensuremath{\rho}}_{\mathrm{xx}}$, for Landau-level filling factors \ensuremath{\nu}=(1/3, (2/3, (4/3, and (5/3, with a magnetic field dependence which is vanishingly small for B\ensuremath{\lesssim}5.5 T and increases to $^{3}6$.8 K at B=30 T. The observed $^{3}\mathrm{\ensuremath{\Delta}}$ is smaller by more than a factor of 3 than either the unbound quasiparticle-quasihole pair-creation energy gap or the magneto-roton energy gap, calculated for an ideal two-dimensional electron system. Observations for devices of mobility ${\ensuremath{\mu}}_{0}$\ensuremath{\approxeq}300 000 ${\mathrm{cm}}^{2}$/V s yield even smaller $^{3}\mathrm{\ensuremath{\Delta}}$. Adequate fitting of all our results requires inclusion of finite electron layer thickness and disorder, with the effect of decreasing the energy gaps and providing a finite magnetic field threshold. At low temperatures and high magnetic fields, deviations from activated conduction are observed. These deviations are attributed to two-dimensional hopping conduction in a magnetic field. Samples of sufficiently low mobility, ${\ensuremath{\mu}}_{0}$\ensuremath{\lesssim}150 000 ${\mathrm{cm}}^{2}$/V s exhibit no evidence of activated conduction. Rather, the transport is qualitatively consistent with two-dimensional hopping alone. Studies at Landau-level filling factors \ensuremath{\nu}=(2/5 and (3/5 also yield a single activation energy, $^{5}/2$, with a weak magnetic field dependence. Experimentally, we find $^{5}\mathrm{}^{3}$\ensuremath{\Delta}\ensuremath{\sim}0.4, compared with an expected ratio of 0.28 from simple theoretical considerations.

We report on a striking correlation in the electrical transport behavior of very high-quality (${j}_{c}\ensuremath{\sim}3.4\ifmmode\times\else\texttimes\fi{}{10}^{6}$ A/${\mathrm{cm}}^{2}$ at $T=77$ K) epitaxial thin films of high-${T}_{c}$ Y-Ba-Cu-O in the normal state. With increasing superconducting performance, as characterized by the transition temperature, transition-temperature width, and critical current density, the resistivity $\ensuremath{\rho}$, and the Hall coefficient ${R}_{H}$, both assume remarkably simple temperature dependences $\ensuremath{\rho}=\ensuremath{\alpha}T$ and $R_{H}^{\ensuremath{-}1}=\ensuremath{\beta}T$ leading to a Hall mobility ${\ensuremath{\mu}}_{H}\ensuremath{\propto}{T}^{\ensuremath{-}2}$. The magnetoresistance at 10 T is less than $|\frac{\ensuremath{\Delta}\ensuremath{\rho}}{\ensuremath{\rho}}|<{10}^{\ensuremath{-}3}$. We discuss an extreme two-carrier model to assess the $T$ dependence of ${R}_{H}$.

We have measured the De Haas-Van Alphen oscillations in a 2D electron system of GaAs-(AlGa)As superlattices from 0 to 5 T at 1.5 K. The amplitude of the oscillations together with known density distribution implies for the Landau levels a half-width of ∼2 meV. which roughly agrees with the width calculated from the zero field mobility of 19000 cm2V · s. We have observed eddy current relaxation times up to 300 s at T ∼ 0.4 K suggesting the resistivity of the material at a quantized Hall plateau to be as low as ρxx ≈- 10−10 Ω/□ corresponding to a 3D resistivity of ρ ≈ 10−16 Ω cm.

We report a systematic study of the $\frac{2}{3}$ fractional quantum Hall effect at low temperatures (65-770 mK) for a GaAs-${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ sample of very high mobility (${10}^{6}$ ${\mathrm{cm}}^{2}$/V sec). We find the $\frac{2}{3}$ Hall plateau to be accurately quantized. The diagonal and Hall resistivities are observed to be activated at each given filling factor $\ensuremath{\nu}=\frac{\mathrm{nh}}{\mathrm{eB}}$ around $\frac{2}{3}$. The activation energy has a maximum value, ${\ensuremath{\Delta}}_{max}$, at $\ensuremath{\nu}=\frac{2}{3}$ and decreases to each side as $\ensuremath{\nu}$ moves away. By varying the sample mobility and density simultaneously with a backgate bias, we find ${\ensuremath{\Delta}}_{max}$ strongly mobility and magnetic field dependent.

We report the first observation of the oscillatory magnetic moment as a function of the magnetic field (deHaas–van Alphen effect) of a two-dimensional electron gas. The measurements were performed at 1.5 K on a modulation-doped GaAs–(AlGa)As heterostructure using a SQUID magnetometer. The strength of the signal was enhanced by stacking 4000 layers equivalent to an area of 240 cm2. The data are in qualitative agreement with theory but the amplitude of the oscillations is about a factor of 30 weaker than expected. We attribute this discrepancy to sample inhomogeneities. More accurate measurements should allow a direct determination of the electronic density of states.

High purity n-type GaAs grown by molecular beam epitaxy has been characterized using the Hall effect, dye laser excited low-temperature luminescence, and far-infrared magnetospectroscopy. Peak mobilities exceed 105 cm2 V−1 s−1. Carbon is shown to be the dominant background acceptor impurity, whereas silicon and two additional, unidentified donors make up the background donor manifold.

We report the first observation of a two-dimensional hole gas (2DHG) at a semiconductor heterojunction interface (GaAs/AlxGa1−xAs). Low-temperature angular-dependent Shubnikov-de Haas measurements demonstrate the two dimensionality of the system and yield a carrier surface density of 7×1011 cm−2. From the temperature dependence of the magneto oscillations we derive an effective mass of 0.35±0.1m0 for the carriers. Hall measurements establish a He temperature mobility of μ≈1700 cm2/V sec.

We review a new molecular beam epitaxy (MBE) technique we call cleaved edge overgrowth (CEO), which makes possible fabrication of quantum wires or other lower dimensional quantum structures with atomic precision. CEO is accomplished by performing two separate MBE overgrowths separated by an in situ cleave of the substrate sample. We review our development of this novel method and give several examples of new structures recently fabricated using it.

We report on an extensive study of the growth and transport properties of the two-dimensional electron gas (2DEG) confined at the interface of AlGaN/GaN heterostructures grown by molecular beam epitaxy (MBE) on thick, semi-insulating GaN templates prepared by hydride vapor phase epitaxy (HVPE). Thick (∼20 μm) GaN templates are characterized by low threading dislocation densities (∼5×108 cm−2) and by room temperature resistivities of ∼108 Ω cm. We describe sources of parasitic conduction in our structures and how they have been minimized. The growth of low Al containing (x⩽0.05) AlxGa1-xN/GaN heterostructures is investigated. The use of low Al containing heterostructures facilitates the study of the 2DEG transport properties in the previously unexplored regime of carrier density ns⩽2×1012 cm−2. We detail the impact of MBE growth conditions on low temperature mobility. Using an undoped HVPE template that was residually n type at room temperature and characterized an unusually low dislocation density of ∼2×108 cm−2, we have grown an Al0.05Ga0.95N/GaN heterostructure with a record mobility of 75 000 cm2/V s at sheet density of 1.5×1012 cm−2 and T=4.2 K. The same heterostructure design grown on a semi-insulating HVPE template yielded a peak mobility of 62 000 cm2/V s at a density of ns=1.7×1012 cm−2 and T=4.2 K. The observation of the fractional quantum Hall effect at filling factor ν=5/3 in the AlGaN/GaN system is reported. It is also demonstrated that thick semi-insulating GaN templates grown by HVPE are a viable substrate for the growth of high electron mobility transistors. Typical Al0.25Ga0.75N/GaN heterostructures exhibit room temperature density of 1.0×1013 cm−3 and mobility of ∼1500 cm2/V s. The dc and rf characteristics of transistors grown by MBE on a HVPE template are presented.

One-dimensional structures are expected to show unique electronic transport behavior as a consequence of the Coulomb interaction between carriers. A considerable number of theoretical predictions remain largely untested by experiment due to a lack of a suitable one-dimensional wire. Using a new crystal growth technique a unique tube-like structure with a cross section of 25 nm × 25 nm has been created in a semiconductor. The mean free path of the electrons exceeds 10 μm - more than 400 times the confinement dimension. The energy spacing between one-dimensional modes far exceed any random potential fluctuations and is more than 10 times larger than previously achieved by other techniques. The conductance plateaus of these wires deviate significantly from the expected universal values suggesting the relevance of electron-electron interactions.

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a $\mathrm{GaAs}/\mathrm{AlGaAs}$ quantum well. The spin-lattice relaxation rate $(1/{T}_{1})$ was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of $^{75}\mathrm{As}$ is found to relax much more efficiently with $T\ensuremath{\rightarrow}0$ and when a well developed quantum Hall state with ${R}_{xx}\ensuremath{\simeq}0$ occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.

We have observed ballistic electron transport beyond 100 microm in the 2D electron system of an ultra-high mobility GaAs(AlGa)As heterostructure employing a magnetic electron focusing technique through wide point contacts. The amplitude of the characteristic magneto-oscillations is found to depend exponentially on electron propagation distance with a decay length λa = 15 microm. λa differs by about a factor of 2 from the mobility mean free path of 28 microm. This may indicate the determination of a different angular average of scattering events in focusing experiments as compared to standard mobility measurements.

Superconducting films of Ca-Sr-Bi-Cu oxides have been prepared by coevaporation of CaF2, SrF2, Bi, and Cu, followed by post-oxidation in wet O2. The films were characterized by four-probe resistivity measurements, Rutherford backscattering, transmission electron microscopy, x-ray diffraction, and Hall measurements. Zero resistance was achieved at ∼80 K, although evidence of traces of superconductivity at higher temperatures was seen in resistivity and Hall data. The critical current at 4.2 K was 1.0×106 A cm−2. The films were epitaxial on 〈100〉 and 〈110〉 SrTiO3 substrates. The electrical and structural properties of the films were insensitive to film composition over a wide range of stoichiometries.

In selectively doped GaAs-(AlGa)As heterostructures the two-dimensional (2D) electron density is found to be monotonically decreasing with increasing separation (t0) between the mobile carriers and the doped (AlGa)As layer. A quantitative description of this t0 dependence requires the Si dopant to create a deep center in (Al0.3Ga0.7)As. For t0≳60 Å the low-temperature electron mobility, which can be as high as 1.6×106 cm2/Vs, does not show a correlation with t0. Unidentified and as yet uncontrollable impurities in the vicinity of the 2D system are a likely source for the residual electron scattering.

Recent research has uncovered a fascinating quantum liquid made up solely of electrons confined to a plane surface. Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. The excited states of this liquid consist of peculiar particle-like objects that carry an exact fraction of an electron charge. Called quasiparticles, these excitations can themselves condense into new liquid states. Each such liquid is characterized by a fractional quantum number that is directly observable in a simple electrical measurement. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect.

Quantization of the Hall effect is one of the most surprising discoveries in recent experimental solid-state research. At low temperatures and high magnetic fields the ratio of the Hall voltage to the electric current in a two-dimensional system is quantized in units of h/e(2), where h is Planck's constant and e is the electronic charge. Concomitantly, the electrical resistance of the specimen drops to values far below the resistances of the best normal metals.

We report the successful operation of the first p-type, modulation-doped field-effect transistor ( p-MODFET). The channel consists of a two-dimensional hole gas at a GaAs/(AlGa)As heterostructure interface. With a gate length of 2 μm and a source-drain distance of 7 μm we achieve transconductances of 28 mS/mm at 77 K and 44 mS/mm at 4.2 K. This work represents the first demonstration of a p-type transistor that is the complement of the conventional n-MODFET.

We have studied intrinsic optical emission and excitation processes associated with 2D plasmas in modulation-doped GaAs-(AlGa)As quantum-well heterostructures. The emission spectra indicate considerable energy gap renormalizations, assigned to many-body interactions, and large breakdown of the parity selection rule for the optical matrix element in quantum-wells. In spite of the high electron density, in excitation spectra we find evidence of final state electron-hole interactions.

New experiments on the two-dimensional electrons in GaAs-${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As heterostructures at $T\ensuremath{\sim}0.14$ K and $B&lt;~190$ kG demonstrate that the quantum number of the quantized Hall resistance, close to $\frac{1}{3}$ filling of the last Landau level, is $\frac{1}{3}$ to better than 1 part in ${10}^{4}$.

We report the first observation of a two-dimensional electron gas bound to a differentially doped semiconductor heterojunction interface. Low temperature Hall mobilities up to 25 000 cm2 V−1 s−1 are observed. Angular-dependent oscillatory magnetoresistance data demonstrate the two dimensionality of the electronic system and the population of two electronic sub-bands. Cyclotron data establish the carrier mass to be 12% bigger than the conduction band edge mass of GaAs and a scattering time that is in good agreement with the scattering time obtained from the Hall mobility.

We study the scattering properties of an interface between a one-dimensional (1D) wire and a two-dimensional (2D) electron gas. Experiments were conducted in the highly controlled geometry provided by molecular bean epitaxy overgrowth onto the cleaved edge of a high quality GaAs /AlGaAs quantum well. Such structures allow for the creation of variable length 1D-2D coupling sections. We find ballistic 1D electron transport through these interaction regions with a mean free path as long as 6 &mgr;m. Our results explain the origin of the puzzling nonuniversal conductance quantization observed previously in such 1D wires.

A refractive electrostatic prism is used to switch a beam of ballistic electrons between different collectors in the two-dimensional electron gas of an AlGaAs-GaAs heterostructure. This represents a new concept in electronic switching which utilizes the electrostatically controlled refraction of ballistic electrons in high-mobility two-dimensional systems.