Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy.

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.

Band structure asymmetry of bilayer graphene revealed by infrared spectroscopy.

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.

Observation of graphene bubbles and effective mass transport under graphene films.

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.

Temperature-dependent transport in suspended graphene.

The resistivity of ultraclean suspended graphene is strongly temperature (T) dependent for 50.5 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).

Cyclotron resonance in bilayer graphene.

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.

Quantum Hall states near the charge-neutral Dirac point in graphene.

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.

Infrared spectroscopy of Landau levels of graphene.

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 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 (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.

High-frequency magneto-oscillations in GaAs/AlGaAs quantum wells.

We have observed very high-frequency, highly reproducible magneto-oscillations in modulation doped GaAs/AlGaAs quantum well structures. The oscillations are periodic in an inverse magnetic field (1/B) and their amplitude increases with temperature up to T approximately 700 mK. Being initially most pronounced around the filling factor nu=1/2, they move towards lower nu with increasing T. Front and back-gating data imply that these oscillations require a coupling to a parallel conducting layer. A comparison with existing oscillation models renders no explanation.

Room-temperature quantum Hall effect in graphene.

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.

Measurement of scattering rate and minimum conductivity in graphene.

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.

Landau-level splitting in graphene in high magnetic fields.

The quantum Hall (QH) effect in two-dimensional 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, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-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 = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.

Evidence for skyrmion crystallization from NMR relaxation experiments.

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a GaAs/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)As is found to relax much more efficiently with T --> 0 and when a well developed quantum Hall state with R(xx) approximately 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.

Quantization of the diagonal resistance: density gradients and the empirical resistance rule in a 2D system.

We have observed quantization of the diagonal resistance, R(xx), at the edges of several quantum Hall states. Each quantized R(xx) value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R(xy). Peaks in R(xx) occur at different positions in positive and negative magnetic fields. Practically all R(xx) features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R(xx) is determined by R(xy) and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.

Tilt-induced localization and delocalization in the second Landau level.

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 the 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.

Measurements of the density-dependent many-body electron mass in two dimensional GaAs/AlGaAs heterostructures.

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.

Electron correlation in the second Landau level: a competition between many nearly degenerate quantum phases.

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.

Competition between a fractional quantum hall liquid and bubble and Wigner crystal phases in the third Landau level.

Magnetotransport measurements were performed in an ultrahigh mobility GaAs/AlGaAs quantum well of density approximately 3.0 x 10(11) cm(-2). The temperature dependence of the magnetoresistance Rxx was studied in detail in the vicinity of nu=9/2. In particular, we discovered new minima in Rxx at a filling factor nu approximately 41/5 and 44/5, but only at intermediate temperatures 80 approximately less than T approximately less than 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.

Spin susceptibility of an ultra-low-density two-dimensional electron system.

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.

Fractional quantum Hall effect of composite fermions.

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.

Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor.

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.