X iv :1 70 5. 09 43 0v 1 [ co nd -m at .m es -h al l] 2 6 M ay 2 01 7 Tuning of Fermi Contour Anisotropy in GaAs (001) 2D Holes via Strain Insun Jo, M. A. Mueed, L. N. Pfeiffer, K. W. West, K. W. Baldwin, R. Winkler, Medini Padmanabhan, and M. Shayegan Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA Department of Physics, Northern Illinois University, DeKalb, IL 60115 USA Physical Sciences Department, Rhode Island College, Providence, RI 02908 USA

We study a bilayer GaAs hole system that hosts two distinct many-body phases at low temperatures and high perpendicular magnetic fields. The higher-density (top) layer develops a Fermi sea of composite fermions (CFs) in its half-filled lowest Landau level, while the lower-density (bottom) layer forms a Wigner crystal (WC) as its filling becomes very small. Owing to the interlayer interaction, the CFs in the top layer feel the periodic Coulomb potential of the WC in the bottom layer. We measure the magnetoresistance of the top layer while changing the bottom-layer density. As the WC layer density increases, the resistance peaks separating the adjacent fractional quantum Hall states in the top layer change nonmonotonically and attain maximum values when the cyclotron orbit of the CFs encloses one WC lattice point. These features disappear at T = 275 mK when the WC melts. The observation of such geometric resonance features is unprecedented and surprising as it implies that the CFs retain a well-defined cyclotron orbit and Fermi wave vector even deep in the fractional quantum Hall regime, far from half-filling.

Two-dimensional electron gases in high magnetic fields have proven to be a remarkably rich playground for the study of strongly-correlated quantum many-body systems. In two dimensions with a strong magnetic field, the cyclotron motion of the electrons completely quenches the particle kinetic energy into Landau levels which are macroscopically degenerate–the number of states in a Landau level is equal to the number of flux quanta from the external field that penetrate the sample. This degeneracy is lifted solely by Coulomb interactions (and by weak disorder) making the system automatically strongly correlated. Remarkably, there is a huge zoo of correlated states that occur at different rational values of the fractional filling of the (highest occupied) Landau level. For simple filling fractions like 1/3 and 2/5, the Laughlin liquid states are most stable. For very small filling fractions the potential energy is minimized by placing the electrons into a spatially ordered Wigner crystal. Near filling factor 1/2, it is useful to view the system as consisting of ‘composite fermions’ (CFs are electrons or holes with two quantized flux tubes or vortices attached [1, 2, 3]). At the mean-field level, the flux attachment transformation creates a pseudo magnetic field which cancels the physical magnetic field when the filling factor is precisely one-half. Slightly away from filling factor 1/2, the composite fermions behave as if they are in a weak magnetic field and hence move in cyclotron orbits with relatively large radius (on the micron scale, which is large compared to the mean distance between particles). The dynamics on this new characteristic length scale can be probed with surface acoustic waves [4], but it is challenging to launch phonons with wavelengths on this scale and to continuously vary that wavelength. In a remarkable experiment, Jo et al. use a double quantum well to form a quantum Hall bilayer system (for holes). By means of an intrinsic doping asymmetry in the sample and application of a tunable voltage gradient normal to the plane of the bilayer, they can bias one layer to have low filling factor and the other to have filling factor near 1/2. The holes in the low filling-factor layer form a triangular Wigner crystal which induces a spatially periodic potential on the composite fermions in the other layer. Because of their larger mass

We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of 10−4, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy in situ provides a platform to study the role of anisotropy in phenomena such as the fractional quantum Hall effect and composite fermions in interacting 2D systems.

There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying in situ in-plane strain and measuring their Fermi wave vector anisotropy through commensurability oscillations. For strains on the order of 10^{-4} we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field (α_{CF}) is less than the anisotropy of their low-field hole (fermion) counterparts (α_{F}), and closely follows the relation α_{CF}=sqrt[α_{F}]. The energy gap measured for the ν=2/3 FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to α_{F}∼3.3, the highest anisotropy achieved in our experiments.

We report Shubnikov-de Haas oscillations measurements revealing experimental signatures of an annular Fermi sea that develops near the energy band edge of the excited subband of two-dimensional holes confined in a wide GaAs quantum well. As we increase the hole density, when the Fermi level reaches the excited subband edge, the low-field magnetoresistance traces show a sudden emergence of new oscillations at an unexpectedly large frequency whose value does $\textit{not}$ correspond to the (negligible) density of holes in the excited subband. There is also a sharp and significant increase in zero-field resistance near this onset of subband occupation. Guided by numerical energy dispersion calculations, we associate these observations with the unusual shape of the excited subband dispersion which results in a "ring of extrema" at finite wavevectors and an annular Fermi sea. Such a dispersion and Fermi sea have long been expected from energy band calculations in systems with strong spin-orbit interaction but their experimental signatures have been elusive.

As the isotopic concentration of ultrathin graphite is varied from natural abundance to nearly pure C-13, the thermal conductivity displays a slight dependence on the isotope concentration at temperatures near its maximum similar to 150 K. The strength of phonon-isotope scattering in the high-isotope impurity-concentration regime is found to be well below that given by a commonly used incoherent and independent isotope impurity scattering model. This finding is in agreement with some recent theoretical predictions that coherent multiple scattering of phonons is important in the measured thermal conductivity of low-dimensional materials in the high-isotope impurity-concentration regime.

Thermal transport in suspended graphene samples has been measured in prior works and this work with the use of a suspended electro-thermal micro-bridge method. These measurement results are analyzed here to evaluate and eliminate the errors caused by the extrinsic thermal contact resistance. It is noted that the room-temperature thermal resistance measured in a recent work increases linearly with the suspended length of the single-layer graphene samples synthesized by chemical vapor deposition (CVD), and that such a feature does not reveal the failure of Fourier’s law despite the increase in the reported apparent thermal conductivity with length. The re-analyzed apparent thermal conductivity of a single-layer CVD graphene sample reaches about 1680 ± 180 W m−1 K−1 at room temperature, which is close to the highest value reported for highly oriented pyrolytic graphite. In comparison, the apparent thermal conductivity values measured for two suspended exfoliated bi-layer graphene samples are about 880 ± 60 and 730 ± 60 Wm−1K−1 at room temperature, and approach that of the natural graphite source above room temperature. However, the low-temperature thermal conductivities of these suspended graphene samples are still considerably lower than the graphite values, with the peak thermal conductivities shifted to much higher temperatures. Analysis of the thermal conductivity data reveals that the low temperature behavior is dominated by phonon scattering by polymer residue instead of by the lateral boundary.

We report the in-plane thermal conductivity of suspended exfoliated few-layer molybdenum disulfide (MoS2) samples that were measured by suspended micro-devices with integrated resistance thermometers. The obtained room-temperature thermal conductivity values are (44-50) and (48-52) W m(-1) K-1 for two samples that are 4 and 7 layers thick, respectively. For both samples, the peak thermal conductivity occurs at a temperature close to 120 K, above which the thermal conductivity is dominated by intrinsic phonon-phonon scattering although phonon scattering by surface disorders can still play an important role in these samples especially at low temperatures. (C) 2014 AIP Publishing LLC.

A microdevice was used to measure the in-plane thermoelectric properties of suspended bismuth telluride nanoplates from 9 to 25 nm thick. The results reveal a suppressed Seebeck coefficient together with a general trend of decreasing electrical conductivity and thermal conductivity with decreasing thickness. While the electrical conductivity of the nanoplates is still within the range reported for bulk Bi2Te3, the total thermal conductivity for nanoplates less than 20 nm thick is well below the reported bulk range. These results are explained by the presence of surface band bending and diffuse surface scattering of electrons and phonons in the nanoplates, where pronounced n-type surface band bending can yield suppressed and even negative Seebeck coefficient in unintentionally p-type doped nanoplates.

The thermal conductivity of suspended few-layer hexagonal boron nitride (h-BN) was measured using a microbridge device with built-in resistance thermometers. Based on the measured thermal resistance values of 11-12 atomic layer h-BN samples with suspended lengths ranging between 3 and 7.5 μm, the room-temperature thermal conductivity of a 11-layer sample was found to be about 360 W m(-1) K(-1), approaching the basal plane value reported for bulk h-BN. The presence of a polymer residue layer on the sample surface was found to decrease the thermal conductivity of a 5-layer h-BN sample to be about 250 W m(-1) K(-1) at 300 K. Thermal conductivities for both the 5-layer and the 11-layer samples are suppressed at low temperatures, suggesting increasing scattering of low frequency phonons in thin h-BN samples by polymer residue.

The recent studies of thermal transport in suspended, supported, and encased graphene just began to uncover the richness of two-dimensional phonon physics, which is relevant to the performance and reliability of graphene-based functional materials and devices. Among the outstanding questions are the exact causes of the suppressed basal-plane thermal conductivity measured in graphene in contact with an amorphous material, and the layer thickness needed for supported or embedded multilayer graphene (MLG) to recover the high thermal conductivity of graphite. Here we use sensitive in-plane thermal transport measurements of graphene samples on amorphous silicon dioxide to show that full recovery to the thermal conductivity of the natural graphite source has yet to occur even after the MLG thickness is increased to 34 layers, considerably thicker than previously thought. This seemingly surprising finding is explained by long intrinsic scattering mean free paths of phonons in graphite along both basal-plane and cross-plane directions, as well as partially diffuse scattering of MLG phonons by the MLG-amorphous support interface, which is treated by an interface scattering model developed for highly anisotropic materials. Based on the phonon transmission coefficient calculated from reported experimental thermal interface conductance results, phonons emerging from the interface consist of a large component that is scattered across the interface, making rational choice of the support materials a potential approach to increasing the thermal conductivity of supported MLG.