Session F51: 2DEG and Quantum Hall Effect

Reorientation of quantum Hall stripes within a partially filled Landau level

We investigate the effect of the filling factor on transport anisotropies, known as stripes, in high Landau levels of a two-dimensional electron gas. We find that at certain in-plane magnetic fields, the stripes orientation is sensitive to the filling factor within a given Landau level. This sensitivity gives rise to the emergence of stripes away from half-filling while orthogonally-oriented, native stripes reside at half-filling. We attribute this switching of the anisotropy axes within a single Landau level to a strong dependence of the native symmetry breaking potential on the filling factor.   

Magnetic Response Functions in Landau Levels

We propose a new quantization scheme which generates Landau levels consistent with the zero-field magnetic response functions from the semiclassical theory. It reproduces the Onsager's rule in the leading order, and re-formulates corrections to the Onsager's rule from the Berry phase and magnetic moment effect in terms of one single magnetic response: the zero-field magnetization. It can yield higher order corrections by including successively magnetic susceptibility and higher order magnetic response functions. In application, it can be easily applied to obtain Landau levels in lattice models. Moreover, it provides an experimental method of measuring different magnetic response functions directly from the measurement of Landau level fan diagram or Hofstadter spectrum.   

Hall Potential Distribution in Anti-Hall bar Geometry

A high quality system has been fabricated in an Anti-Hall bar geometry, by opening a 1.4 x 2.0 mm rectangular window using wet etching in the middle of a 2.4 x 3.0 mm two-dimensional high-mobility ($\mu = 2.6\times$10$^6$ cm$^2$/(V$\cdot$s)) hole system confined in a 20 nm wide (100) GaAs quantum well. Topologically this system is equivalent to a normal Hall bar even though there is an extra set of edges in the center. This configuration allows us to probe the Hall potential distribution in relation to the formation of edge channels. The Quantum Hall measurements at 30 mK show a standard behavior of the outer edges. At each Hall plateau the inner edge becomes an equipotential and the Hall voltage between the inner and outer edges exhibits a drastic asymmetry for the upper and lower arms of the sample. At various integer fillings, depending on the chirality, the voltage drop across one of the arms measures 0 while the drop across the other one is equal to the Hall voltage. This behavior will be explained in terms of the dynamical process of forming the edge channels which also will account for the more irregular behavior of the Hall potential in more disordered systems.   

Finite-wavevector Electromagnetic Response in Quantum Hall Systems: Lattice Corrections and Signatures of Hall Viscosity

It has recently been shown that the electromagnetic response of a quantum Hall fluid at finite wavevector includes a dependence on the Hall viscosity, raising the possibility of measuring this quantity in an experiment. We present a new, quantum mechanical derivation of this relationship and extend the result to include lattice corrections, which may be significant in a real sample. We find that these corrections have a universal structure whose form depends only on the symmetries of the underlying lattice, and provide numerical estimates for cases of experimental interest. Finally, we consider the Hall viscosity of lattice models more generally and discuss our results in this broader context.   

Insulating States in the Integer Quantum Hall Regime

Quantum Hall measurements are performed at temperatures 20-300 mK in high quality $p$-type GaAs quantum well systems having mobility $\mu=4\times10^{6}$ cm$^2$/V$\cdot$s for density $5\times10^{10}$ cm$^{-2}$. We report a series of insulating phases appearing at or near integer filling factors $\nu \geq 1$. The DC resistance demonstrates a maximum of 25M$\Omega$, much larger than the quantum resistance $h/e^2$, with threshold transport behavior at low currents around 10 pA at low temperatures. The threshold diminishes upon heating up to 200 mK, consistent with a finite temperature melting of bubble phases or Wigner crystal. Additionally, these peaks have a complex electrical impedance for AC signals, with large phase shifts down to 1Hz. In this regime, the ac impedance of the two chiral edges show distinct correlated characteristics.   

Geometry of Landau Level without Galilean or Rotational Symmetry

The integer quantum Hall effect is usually modeled using Galilean-invariant or rotationally-invariant Landau levels. However, these are not generic symmetries of electrons moving in a crystalline background. We explicitly break both symmetries by considering a inversion-symmetric Hamiltonian with quartic terms. We carry out exact diagonalization numerically with a truncated Hilbert space, and define an emergent metric $g^n_{ab}$ for each Landau level as the expectation value of a bilinear form in momentum. With an appropriate choice of the guiding center coherent state, the Landau level wavefunctions are holomorphic functions of $z^*$ times a Gaussian (this is distinct from a well-known property of rotationally-invariant lowest-Landau-level wavefunctions). We show that the zeroes of the wavefunction define a ``topological spin $s_n$'', with its original definition as an ``intrinsic angular momentum'' no longer valid without rotational symmetry. This is now related to the number of zeroes $n$ encircled by the classical orbit by $s_n=n+\frac{1}{2}$. Finally we introduce a mass tensor $m^n_{ab}$ for each Landau level using a Lagrangian formalism. We conclude that topological and geometric information can be extracted without resort to Galilean or Rotational symmetries.   

Quantum Hall states in strained InAs heterostructures

In a recent development it was realized that non-Abelian quasiparticles, parafermion zero-modes emerge at an interface between a superconductor and two dimensional electron system (2DES) in the quantum Hall regime. [1]. Unlike widely used GaAs systems, surface level pinning in InAs could allow for fabrication of transparent contacts to superconductors. However, no fractional quantum Hall state has been observed in InAs quantum wells so far. Whether this is due to the type of disorder present in the quantum well is not clear. In this work, we study the transport and dingle mobility of 2DESs confined to strained InAs quantum wells as a function of electron density and spacer thickness to the surface. We compare our results to early observation of fractional quantum Hall states in GaAs. [1] R. S. K. Mong, et al. Phys. Rev. X 4, 011036 (2014)   

Universal response of quantum hall states to lattice curvature

In this talk I shall present general results for the response of quantum Hall states to points of singular real-space curvature. The salient results are that (i) points of singular curvature bind an excess fractional charge and (ii) bound states appear in the inter-Landau level energy gap whose energies are universal functions of bulk parameters and the curvature. Time permitting, I will comment on the implications of these results.   

Microwave Spectroscopic Observation of Multiple Phase Transitions of Bilayer Electron Solids in a Wide Quantum Well

For a single-layer two dimensional electron system, the fractional quantum Hall effect (FQHE) series terminates to form an insulating phase (IP) for Landau filling factor $\nu < 1/5$. In a wide quantum well the charge distribution can separate into two layers as density increases resulting in a modification of the IP onset to $\nu < 1/2$ [1]. The IP is understood as an electron solid pinned by residual disorder. The solid exhibits a microwave pinning mode resonance, which is due to pieces of the solid oscillating within the disorder potential. We have previously observed that the microwave pinning mode spectra reveal phase transitions between different types of solid within the terminating IP [2]. In this talk we extend our studies of microwave spectroscopic measurements of a wide quantum well by investigating these phase transitions in the presence of an in-plane magnetic field. Applying an in-plane field forces the system to be more bilayer-like and for small tilt angles we find that the transitions move to higher $\nu$. However, at sufficiently high angles the resonance onset extends above $\nu=1/2$ and the $\nu$ of the transitions saturate. [1] Manoharan et al., Phys. Rev. Lett. 77, 1813 (1996). [2] A. T. Hatke et al., Nature Commun. 6, 7071 (2015).   

Dicke Model for Quantum Hall Systems

Quantum Hall (QH) systems comprise of many-body electron spins and nuclear spins. They are weakly coupled with nuclear spins through the hyperfine interaction so that electron spin dynamics is scarcely affected by the nuclear spins. The dynamics of the QH systems, however, may drastically change when the nuclear spins interact with low energy collective excitation modes of the electron spins. In connection with this, the nuclear spin relaxation measurement have revealed novel behaviors in the canted antiferromagnetic phase in the total filling factor two bilayer QH systems [1,2]. Here, we theoretically study the interaction between the nuclear spins and the linear dispersing Nambu-Goldstone mode mediated by the hyperfine interaction. We show that such interaction is effectively represented by the Dicke model, and predict that collective spin phenomena realized in quantum optical systems are also observed in the QH systems [3]. References: [1] N. Kumada et al., Science 313, 329 (2006). [2] M. H. Fauzi et al., Phys. Rev. B 90, 235308 (2014). [3] Y. Hama et al., arXiv:1510.04792v1.   

Large-filling-factor giant Shubnikov-de Haas oscillations in the ultrahigh-mobility two-dimensional GaAs/AlGaAs electron system

The observation of microwave-induced zero-resistance states (ZRS) produced new interest in transport studies of very high filling factors in the high mobility GaAs/AlGaAs 2D electron system. In particular, there has been interest in the study of the overlap of such ZRS with high filling factor quantum Hall effect.[1] Ref. 1 reported different phase relations between oscillatory resistances at high filling factors. In an effort to clarify the observations, we examine the influence of a dc current bias on the lineshape of oscillatory resistances in the ultrahigh-mobility two-dimensional GaAs/AlGaAs electron system. With increasing dc current bias, a change is also observed in the characteristic lineshape of the SdH oscillations. To quantify the change, we carry out lineshape fits of the oscillatory resistance obtained at different dc bias. In this talk, we will summarize the results of the study. [1] R. G. Mani, W. B. Johnson, V. Umansky, V. Narayanamurti, and K. Ploog, Phys. Rev. B 79, 205320 (2009).   

Landau-level mixing, floating-up extended states, and scaling behavior in a GaAs-based two-dimensional electron system containing self-assembled InAs dots

Temperature-driven flow lines corresponding to Landau level filling factor $\nu=2 \sim 4$ were studied in the $\sigma_{xx}-\sigma_{xy}$ plane in a GaAs-based two-dimensional electron system with self-assembled InAs dots. In the insulator-quantum Hall (I-QH) transition resulting from the floating-up extended states, the flow diagram showed the validity of the scaling and we observed the expected semicircle. On the other hand, the curve $\sigma_{xx}(\sigma_{xy})$ in the low-field insulator demonstrated the existence of Landau-level mixing. By decreasing the effective disorder, we found that such flow lines can leave the I-QH regime and follow the scaling for the plateau transition between $\nu =4$ and 2. The semicircle in the observed I-QH transition, in fact, originated from the distortion on the plateau-transition curve due to Landau-level mixing. Our study showed the importance of the level-mixing effects to the scaling and semicircle law as the extended states float up.   

Probing the excited subband dispersion of holes confined to GaAs wide quantum wells

Owing to the strong spin-orbit coupling and their large effective mass, the two-dimensional (2D) holes in modulation-doped GaAs quantum wells provide a fertile test bed to study the rich physics of low-dimensional systems. In a wide quantum well, even at moderate 2D densities, the holes start to occupy the excited subband, a subband whose dispersion is very unusual and has a non-monotonic dependence on the wave vector. Here, we study a 2D hole system confined to a 40-nm-thick (001) GaAs quantum well and demonstrate that, via the application of both front and back gates, the density can be tuned in a wide range, between \textasciitilde 1 and 2 \texttimes 10$^{\mathrm{11}}$ cm$^{\mathrm{-2}}$. Using Fourier analysis of the low-field Shubnikov-de Haas oscillations, we investigate the population of holes and the spin-orbit interaction induced spin-splitting in different subbands. We discuss the results in light of self-consistent quantum calculations of magneto-oscillations.   

Formation of a helical channel in a 2D system in a quantum Hall regime

A two-dimensional system with reconfigurable network of one-dimensional p-wave superconducting channels is a perfect platform to perform braiding of non-Abelian excitations. Such channels can be realized in CdTe:Mn quantum wells in a quantum Hall effect regime, where counterpropagaring edge states with opposite spin polarization can be formed by electrostatic gating. These edges form helical channels similar to the edges of 2D topological insulators and, coupled to a superconductor, should support non-Abelian excitations. While long channels are localized at low temperatures, we found that resistance in short (<6 $\mu$m) helical channels remains finite at low temperatures. Transport data and resistance scaling with channel length will be presented.   

Enhanced thermopower of gate-induced ZnO two-dimensional electron gas

Control of dimensionality has proven to be an effective way to manipulate the electronic properties of materials, thereby enabling exotic quantum phenomena, such as superconductivity\footnote{Q. Y. Wang {\it et al.}, Chinese Phys. Lett. {\bf 29}, 037402 (2012).}, quantum Hall effects, and valleytronic effects\footnote{K. F. Mak {\it et al.}, Science {\bf 344}, 1489 (2014).}. Another example is thermoelectricity, which has been proposed to be favorably controllable by reducing the dimensionality\footnote{L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B {\bf 47}, 12727 (1993).}. We report the thermopower in a gate-induced two-dimensional electron gas (2DEG) formed at the surface of ZnO. Combining electric double layer transistor experiments and realistic tight-binding calculations, it is shown that, for a wide range of carrier densities, the 2DEG channel comprises a single subband, and its effective thickness can be reduced to several nanometers at sufficiently high gate biases. We demonstrate that the thermopower of the 2DEG region is significantly higher than that of bulk ZnO. Our approach opens up a novel route to exploit the peculiar behavior of 2DEG electronic states and realize thermoelectric devices with advanced functionalities.