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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 Schrodinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. 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.

We have achieved mobilities in excess of 200,000 cm^2/Vs at electron densities of ~2*10^11 cm^-2 by suspending single layer graphene. Suspension ~150 nm above a Si/SiO_2 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, non-suspended devices. This advance should allow for accessing the intrinsic transport properties of graphene., 4 pages, 3 figures, references updated

We have investigated the electron transport in graphene at different carrier densities. Single layer graphene was fabricated into Hall bar shaped devices by mechanical extraction onto a silicon oxide/silicon substrate followed by standard microfabrication techniques. From magnetoresistance and Hall measurements, we measure the carrier density and mobility at different gate voltages. Different temperature dependent resistivity behaviors are found in samples with high and low mobilities.

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.

We have studied the quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples in strong magnetic fields up to 45 T. A distinctive half-integer QH effect is discovered at high magnetic fields, with QH plateaus appearing at filling factors ν = ±4(|n| + 1/2), where n is the Landau level (LL) index. This finding is consistent with theoretical predictions. In addition, in the extreme magnetic quantum limit with magnetic fields up to 45 T, we observe LL splittings in graphene at filling factors ν = 0,±1,±4. Further detailed investigation shows 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, lifting 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 n = ±1 LLS.

Recent experiments have shown that two-dimensional electron systems with an externally applied magnetic field are an extremely rich ground for many-body physics. In particular, when only two of the Landau levels (LL) are filled an intricate magnetoresistance is found. This result stems from an interesting competition of electronic phases such as fractional quantum Hall liquids, reentrant integer Hall states, and unique quantized states at even denominator LL filling factors. We present a brief review of the transport properties of these electronic phases and discuss in detail the effects of an added in-plane magnetic field.

In this paper, we review low temperature electronic transport results in high quality two-dimensional electron systems. We discuss the quantization of the diagonal resistance, R x x , at the edges of several quantum Hall states. Each quantized R x x value turns out to be close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R x y . Moreover, peaks in R x x occur at different positions in positive and negative magnetic fields. All three R x x features can be explained quantitatively by a ∼1% cm electron density gradient. Furthermore, based on this observation, the well known but still enigmatic resistivity rule, relating R x x to d R x y / d B , finds a simple interpretation in terms of this gradient. In another sample, at 1.2 K, R x x we observe a strongly linear magnetic field dependence. Surprisingly, this linear magnetoresistance also originates from the density gradient. Our findings throw an unexpected light on the relationship between the experimentally measured R x x and the diagonal resistivity ρ x x .

We determined the spin susceptibility Χ and the effective mass m* towards the high density limit. Using a tunable GaAs/AlGaAs heterostructure, we can vary the 2D electron density from n = 1 x 10 10 cm -2 to 4 x 10" cm -2 . From ∼5 x 10 10 cm -2 to our highest densities the mass values fall ∼10% below the band mass of GaAs. The enhancement of Χ decreases monotonically from a factor of 3 to 0.88 with increasing density. It continues to follow a previously observed power law, which leads to an unphysical limit for n → oo. Band structure effects affecting mass and g-factor become appreciable for large n and, when taken into account, lead to the correct limiting behavior of Χ. Numerical calculations are in qualitative agreement with our data but differ in detail.

With certainty scaling in silicon is going to hit a wall – technologically or economically. While we do not know exactly when this is going to happen, “approximately a decade from now” is a pretty common guess. Hence it is prudent to imagine and investigate alternative ways to create electronic systems that may have a chance to lead us “beyond silicon”. At present there is no clear path at all. Only open-minded and imaginative research has a chance to overcome the foreseeable impasse.

We determine the spin susceptibility in a variable-density two-dimensional electron system in GaAs/AlGaAs. Our measurements extend over a wide range of low densities from 2×10 9 to 4×10 10 cm −2 . Our data can be well described by an empirical equation which incorporates both the density dependence and the magnetic field dependence of the spin susceptibility. It can explain the anomalous g -factors reported recently in GaAs electron and hole systems. The extrapolated paramagnetic spin susceptibility increases with decreasing density as expected from theoretical calculations.

In the second Landau level around v = 5/2 filling of an extremely high quality 2D electron system and at temperatures T down to 9 mK we observe a very strong even-denominator fractional quantum Hall effect at Landau level filling v = 5/2 and its energy gap is large and Δ ∼ 0.45K. A clear FQHE state is seen at v = 2 + 2/5, with well-quantized R xy . A novel, even-denominator FQHE state at v = 2 + 3/8 seems to develop, as deduced from the T-dependence of dR xy /dB. In addition, four fully developed re-entrant integral quantum Hall effect (RIQHE) states are also observed. At low temperatures, the wide RIQHE plateau around at v = 2 + 2/7 is interrupted by a dip, indicating an additional reentrance. Finally, the tilted magnetic field experiment at an ultra-low temperature of 10 mK was carried out to examine the spin-polarization of the v = 5/2 FQHE state.

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 (∼20μm) GaN templates are characterized by low threading dislocation densities (∼5×10 ⁸cm ⁻²) and by room temperature resistivities of ∼10 ⁸cm. We describe sources of parasitic conduction in our structures and how they have been minimized. The growth of low Al containing (x≤0.05) Al ₓGa ₁₋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 n s≤2×10 ¹²cm ⁻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 ∼2×10 ⁸cm ⁻², we have grown an Al ₀.₀₅Ga ₀.₉₅N/GaN heterostructure with a record mobility of 75000cm ²/Vs at sheet density of 1.5×10 ¹²cm ⁻² and T=4.2K. The same heterostructure design grown on a semi-insulating HVPE template yielded a peak mobility of 62000cm ²/Vs at a density of n s=1.7×10 ¹²cm ⁻² and T=4.2K. 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 Al ₀.₂₅Ga ₀.₇₅N/GaN heterostructures exhibit room temperature density of 1.0×10 ¹³cm ⁻³ and mobility of ∼1500cm ²/Vs. The dc and rf characteristics of transistors grown by MBE on a HVPE template are presented. © 2002 American Institute of Physics.

This paper presents some recent results on the anisotropic electronic transport at half-filling factors in the second and third Landau levels. In the third Landau level at ν= 9 2 and 11 2 , the electronic transport is already strongly anisotropic in perpendicular magnetic field. This anisotropic phase is believed to be due to the formation of a unidirectional charge density wave. Applying an in-plane field overcomes the initial pinning and reorients the direction of this anisotropy. In the second Landau level, the even-denominator fractional quantum Hall state at ν= 5 2 and 7 2 is destroyed and transformed into an anisotropic phase by an in-plane magnetic field. This result provides additional evidence that the ground state at ν= 5 2 and 7 2 is spin-polarized.

We report the results of 3 terminal measurements on a one-dimensional (1D) wire. By utilizing cleaved-edge overgrowth, we were able to vary the coupling between a 1D conductor and an adjacent two-dimensional electron gas (2DEG) strip attached to the central part of the wire. We study the 1D-2DEG coupling by controlling the width of the 2DEG strip. Ballistic transport along the wire persists for interaction regions as long as 6 μm . Thus, with our shortest interaction region (narrowest strip) of 2 μm , the wire remains almost undisturbed by the presence of the nearby 2DEG allowing a true 3 terminal measurement on a clean wire. Our observations also explain the origin of the non-universal conductance quantization of such 1D wires.

Experimental data on the sequence of fractional quantum Hall effects (FQHE) states around Landau level filling factor ν =1/2 are well explained within the framework of the composite fermion model. Around other even-denominator fractions the situation is less clear, experimentally as well as theoretically. In this paper we report experimental studies at even-denominator fillings at ν=1/4, 3/4,5/2 , etc. We show that the composite fermion picture can be applied successfully to the fractions at ν =1/4 and 3/4. Their effective mass, when normalized to B 1/2 (where B is the magnetic field) and their effective g factor are very similar to the composite fermions at ν =1/2 and 3/2. Our ultra-low-temperature study at ν =5/2 shows that this fraction is a true FQHE state, showing vanishing R xx and a Hall resistance R xy precisely quantized to h /(5/2 e 2 ).

We have measured magnetotransport at half-filled high Landau levels in a quantum well with two occupied electric subbands. We find resistivities that are {\em isotropic} in perpendicular magnetic field but become strongly {\em anisotropic} at $\nu$ = 9/2 and 11/2 on tilting the field. The anisotropy appears at an in-plane field, $B_{ip} \sim$ 2.5T, with the easy-current direction {\em parallel} to $B_{ip}$ but rotates by 90$^{\circ}$ at $B_{ip} \sim$ 10T and points now in the same direction as in single-subband samples. This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model., Comment: 4 pages, 4 figures

We present experimental data showing unambiguously an even-denominator fractional quantum Hall effect (FQHE) state at ν=52. At a bath temperature Tb=8 mK, we observe a Hall plateau quantized to a value of 2h/5e2 with an uncertainty smaller than 2 parts in 106 and a vanishing Rxx (Rxx=1.7±1.7Ω). The thermal activation energy gaps Δ at Landau level filling factors ν=52,73, and 83 are 0.11, 0.10, and 0.055 K, respectively. Adding a disorder broadening (typically ∼2 K) to these values, we deduce that all three FQHE states have probably very similar energy gaps. The electron heating experiment shows that the 2D electrons are efficiently cooled to the bath temperature for Tb⩾8 mK. We also explore the density dependence of the activation gap at ν=52. Preliminary results at Tb⩾25 mK show that the 52 state is very sensitive to disorder.

Recent experiments (Yacoby et al., Phys. Rev. Lett. 77 (1996) 4612; Solid State Commun. 101 (1997) 77; M. Rother et al., ICPS-24, Th-P137) have shown non-universal conductance quantization in one-dimensional wires that are fabricated using the cleaved edge overgrowth technique (L.N. Pfeiffer et al., Microelectronics J. 28 (1997) 817). In one of the papers (Yacoby et al., Phys. Rev. Lett. 77 (1996) 4612), it was speculated that the origin of the reduced conductance lies in the interface between the one-dimensional wire and the two-dimensional electron gas regions, which serve as ohmic contacts and thermal reservoirs. Here we report the results of a systematic study of such 2D–1D interfaces. By embedding a 2D–1D interaction section region of controllable length inside an otherwise isolated wire, we were able to study the properties of the coupling between these two subsystems. Our results show that 2D–1D interface is in fact the origin of the non-universal conductance.

Low-temperature, electronic transport in higher Landau levels (N>1) in a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of such Landau levels ( ν= 9 2 , 11 2 , 13 2 , 15 2 , etc.) the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. The anisotropic axis can be reoriented by applying an in-plane magnetic field of ∼1–2 T strength. The magnetoresistance at ν= 5 2 and ν= 7 2 (N=1) is initially isotropic but an in-plane field induces a strong anisotropy. Our observations are strong evidence for a new many-electron phase in higher Landau levels, which forms spontaneously or can be induced by an in-plane field.

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.

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 investigate the properties of composite fermions with four attached flux quanta through tilted field experiments near Landau level filling factor nu = 3/4. The observed collapse of fractional quantum Hall gaps in the vicinity of this quarter-filling state can be comprehensively understood in terms of composite fermions with mass and spin. Remarkably, the effective mass and g-factor of these four flux quanta composite fermions around nu = 3/4 are very similar to those of two flux quanta composite fermions around nu = 3/2., Comment: 4 pages, 1 table, 3 postscript figures

A short review of recent developments in the area of the fractional quantum Hall effect is presented. The article attempts to develop some intuitive images of the highly-correlated electron behavior. It emphasizes the new states at half-filled landau levels and their composite fermion quasiparticles. Recent theoretical calculations promise yet more bizarre electronic states to be discovered by experiment.

Graphene, which consists of a single atomic sheet of graphene, possesses high electronic mobility, and excellent mechanical properties, making it an ideal candidate for nanoelectromechanical (NEMS) applications, including sensing and signal processing. Toward these applications, we have measured the mechanical properties of graphene sheets and demonstrated fabrication and electrical readout of monolayer graphene NEMS that show vibrational resonances in the MHz range. The dependence of the resonant frequency on applied gate voltage yields the mass density and built-in strain. Upon addition of mass, we observe changes in both the density and the strain, indicating that adsorbates impart tension to the graphene. The quality factor increases monotonically with decreasing temperature and reaches ∼104 at 5 K.

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 non-monotonic 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 limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. {\bf 123}, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure., 4 pages, 4 figures. Version 2, edited for publication. Includes a number of edits for clarity; also added a paragraph contrasting our work w/ previous CR expts. in 2D Si and GaAs

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 approximately 1 x 10(4) 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.

We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observed 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. From the conductivity data, the energy difference of the two sublattices is determined., Comment: 4 pages, 3 figures

With certainty, scaling in silicon is going to hit a wall - technologically or economically. While we do not know exactly when this is going to happen, "approximately a decade from now" is a pretty common guess. Hence it is prudent to contemplate and investigate alternative ways to create electronic systems that may have a chance to lead us "beyond silicon". At present, there is no clear path at all. Only open-minded and imaginative research has a chance to overcome the foreseeable impasse.

Mechanically exfoliated graphene mounted on a SiO2/Si substrate was subjected to HF/H(2)O 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.

The resistivity of ultraclean suspended graphene is strongly temperature ($T$) dependent for $5lTl240\text{ }\text{ }\mathrm{K}$. At $T\ensuremath{\sim}5\text{ }\text{ }\mathrm{K}$ transport is near-ballistic in a device of $\ensuremath{\sim}2\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ dimension and a mobility $\ensuremath{\sim}170\text{ }000\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{V}\text{ }\mathrm{s}$. At large carrier density, $ng0.5\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$, the resistivity increases with increasing $T$ and is linear above 50 K, suggesting carrier scattering from acoustic phonons. At $T=240\text{ }\text{ }\mathrm{K}$ the mobility is $\ensuremath{\sim}120\text{ }000\text{ }\text{ }{\mathrm{cm}}^{2}/\mathrm{V}\text{ }\mathrm{s}$, 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 $l{10}^{8}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$.

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 \sqrt{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., Comment: to appear in Phys. Rev. Lett. Updated version with two added references and minor text editing

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 (2DES) and at very low temperatures and report the following results: For the even-denominator FQHE states, the sample dependence of the nu=5/2 state clearly shows that disorder plays an important role in determining the energy gap at nu=5/2. For the developing nu=19/8 FQHE state the temperature dependence of the Rxx minimum implies an energy gap of ~5mK.The energy gaps of the odd-denominator FQHE states at 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 ultra-high quality specimen, the nu=13/5 state is missing, while its particle-hole conjugate state, the nu=12/5 state, is a fully developed FQHE state. We speculate that this disappearance might indicate a spin polarization of the nu=13/5 state. Finally, the temperature dependence is studied for the two-reentrant integer quantum Hall states around nu=5/2 and is found to show a very narrow temperature range for the transition from quantized to classical value., to be published

In the high-magnetic-field low-disorder limit the ground state at v=1/5 Landau-level filling is an incompressible quantum limit. This is determined by observing vanishing resistivity p xx as the temperature T→0. At filling factors below v=1/5 as well as in a narrow region above v=1/5, p xx diverges exponentially as T→0. This contrasts the T dependence at any higher v. The quantum limit at v=1/5 is surrounded by a different phase. In as much as the exponential divergencies are indicative of an electron solid this solid phase is reentrant in a narrow region above v=1/5

Neutral spin texture ST excitations at nu=1/3 are directly observed for the first time by resonant inelastic light scattering. They are determined to involve two simultaneous spin- flips. At low magnetic fields, the ST energy is below that of the magneto-roton minimum. With increasing in-plane magnetic field these modes energies cross at a critical ratio of the Zeeman and Coulomb energies of eta_c=0.020 +- 0.001. Surprisingly, the intensity of the ST mode grows with temperature in the range in which the magneto-roton modes collapse. The temperature dependence is interpreted in terms of a competition between coexisting phases supporting different excitations. We consider the role of the ST excitations in activated transport at nu=1/3., 5 pages, 4 color figs

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 $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}1$ 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 $\ensuremath{\nu}=1$ suggests a many-body origin. We therefore propose that the $\ensuremath{\nu}=0$ and $\ifmmode\pm\else\textpm\fi{}1$ states arise from the lifting of the spin and sublattice degeneracy of the $n=0$ Landau level, respectively.

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show \textit{in situ} half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 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 $\tilde{c}\approx1.1\times10^6$ m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies., Comment: 4 pages, 3 figures, to appear in Phys. Rev. Lett

The conductivity of graphene samples with various levels of disorder is investigated for a set of specimens with mobility in the range of $1-20\times10^3$ cm$^2$/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 $2-15\times 10^{11}$ cm$^{-2}$. In the low carrier density limit, the conductivity exhibits values in the range of $2-12e^2/h$, 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., Comment: 4 pages 4 figures

The quantum Hall effect (QHE), one example of a quantum phenomenon that occur on a truly macroscopic scale, has been attracting 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 could only have been observed at liquid-helium temperatures. Here, we show that in graphene - a single atomic layer of carbon - the QHE can reliably be measured even at room temperature, which is not only surprising and inspirational but also promises QHE resistance standards becoming available to a broader community, outside a few national institutions., Comment: Published in Science online 15 February 2007

We perform a direct study of the magnitude of the anomalous splitting in the cyclotron resonance (CR) of a two-dimensional electron system (2DES) as a function of sample disorder. In a series of AlGaAs/GaAs quantum wells, identical except for a range of carbon doping in the well, we find the CR splitting to vanish at high sample mobilities but to increase dramatically with increasing impurity density and electron scattering rates. This observation lends strong support to the conjecture that the non-zero wavevector, roton-like minimum in the dispersion of 2D magnetoplasmons comes into resonance with the CR, with the two modes being coupled via disorder., accepted to PRB Rapid Comm

We determine the spin susceptibility $\ensuremath{\chi}$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure. The band structure effects, modifying mass and $g$-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime. When properly normalized, $\ensuremath{\chi}$ decreases monotonically from 3 to 1.1 with increasing density over our experimental range from 0.1 to $4\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. In the high density limit, $\ensuremath{\chi}$ tends correctly towards $\ensuremath{\chi}\ensuremath{\rightarrow}1$ and compare well with recent theory.

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., Comment: 11 pages including 4 figures, to appear in PRL

We report on a magnetic resonance study in the electron solid phase of a low-disorder $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ sample at very high magnetic fields using a resistively detected NMR technique. An anomalous dispersivelike line shape is observed at the onset of the electron solid in the vicinity of the Landau filling $\ensuremath{\nu}=\frac{2}{9},\frac{1}{5}$ fractional quantum Hall state, reminiscent of the line shape observed near filling factor $\ensuremath{\nu}\ensuremath{\sim}1$. In contrast to this filling factor region, the spin-lattice relaxation time ${T}_{1}$ in the electron solid is found to be very long, and does not correlate with either ${R}_{xx}$ or the Landau filling factor. The dispersivelike line shapes observed in this regime suggests that the intricate interplay between the nuclear spin and the electronic transport may be modified by the formation of the electron solid.

Magnetotransport measurements were performed in a ultra-high mobility GaAs/AlGaAs quantum well of density $\sim 3.0 \times 10^{11}$ $cm^{-2}$. The temperature dependence of the magnetoresistance $R_{xx}$ was studied in detail in the vicinity of $\nu={9/2}$. In particular, we discovered new minima in $R_{xx}$ at filling factor $\nu\simeq 4{1/5}$ and $4{4/5}$, but only at intermediate temperatures $80\lesssim T\lesssim 120$ mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0., Comment: Phys. Rev. Lett.93 266804 (2004)

We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at $\nu=$2+1/5 and 2+4/5 and the solid phases at $\nu=$2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.

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 $\ensuremath{\nu}=2+2/5$ state separated from the even-denominator $\ensuremath{\nu}=2+1/2$ state by an insulating phase and a $\ensuremath{\nu}=2+2/7$ and $\ensuremath{\nu}=2+1/5$ state surrounded by such phases. A developing plateau at $\ensuremath{\nu}=2+3/8$ points to the existence of other even-denominator states.

Ever since its first demonstration in 1953 [1], cyclotron resonance (CR) has become the most widely used technique to determine effective masses of carriers in semiconductors and their heterojunctions. In the presence of an external magnetic field, B, electrons of charge e are set into cyclotron motion whose frequency is given by ωc = eB/m ∗ c. An RF or far infra-red source is swept which generates a single absorption line at ωc, from which the effective mass m ∗ is deduced. CR has also been instrumental in detecting other excitations of the solid via their interaction with CR. They often take on the shape of a level anti-crossing from which the energy of the new excitation and its coupling to CR can be inferred. These are well-established, textbook phenomena, which make CR one of the best-understood tools in solid state research [2]. Yet, in our experiments on the comparatively new AlGaN/GaN heterostructures we observe huge splittings in the CR line, indicating a strong interaction with an excitation whose origin remains unknown. Our results provide a fundamental challenge to our apparently thorough understanding of CR in solids. For AlGaN/GaN heterostructures there exist only few CR data [3, 4, 5, 6]. Our study of CR in two-dimensional electron systems (2DESs) in a sequence of high-quality AlGaN/GaN structures with a wide range of carrier densities (1 - 4×10 12 cm −2 ) reveals splittings in the CR line reminiscent of level anti-crossings, reaching 20% of the resonance energy. While their origin is not established, they resemble splittings seen previously in the CR of AlGaAs/GaAs and Si systems. Our data do not support a universal ad-hoc model put forward in the AlGaAs/GaAs work and points to the lack of a theoretical understanding of this phenomenon, now seen in three different 2D systems.

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.

Using cyclotron resonance, we measure the effective mass, $m$*, of electrons in AlGaN/GaN heterostructures with densities, $n_{2D}\sim 1-6\times10^{12}$cm$^{-2}$. From our extensive data, we extrapolate a band edge mass of $(0.208\pm0.002) m_e$. By comparing our $m$* data with the results of a multi-band \textbf{k.p} calculation we infer that the effect of remote bands is essential in explaining the observed conduction band non-parabolicity (NP). Our calculation of polaron mass corrections -- including finite width and screening - suggests those to be negligible. It implies that the behavior of $m*(n_{2D})$ can be understood solely in terms of NP. Finally, using our NP and polaron corrections, we are able to reduce the large scatter in the published band edge mass values.

A rotator, made from polycarbonate and operated hydraulically using liquid helium, has been developed at the High B/T Facility of the National High Magnetic Field Laboratory (NHMFL) in Gainesville, It can be tilted more than 90 degrees by applying a pressure of several bars. The frictional heating was found to be negligible down to 8.0 mK. The sintered silver powder heat exchangers, specially designed for the cooling of the two-dimensional electron gas (2DEG) system in the fractional quantum Hall effect (FQHE) experiment,1,2 are also attached to the rotator. We have conducted an angular-dependent study of the even-denominator FQHE state at ν = 5/2. Our preliminary data showed that the rotator performed well at ultra-low temperatures and high magnetic fields. This technique should be applicable for other transport measurements at such extreme experimental conditions.

At very large tilt of the magnetic (B) field with respect to the plane of a two-dimensional electron system the transport in the integer quantum Hall regime at $\nu$ = 4, 6, and 8 becomes strongly anisotropic. At these filling factors the usual {\em deep minima} in the magneto-resistance occur for the current flowing {\em perpendicular} to the in-plane B field direction but develop into {\em strong maxima} for the current flowing {\em parallel} to the in-plane B field. The origin of this anisotropy is unknown but resembles the recently observed anisotropy at half-filled Landau levels., Comment: 4 pages, 4 figures