Session X11: Integer Quantum Hall Effect

Imaging quantum Hall Coulomb islands inside a quantum ring

In the quantum Hall regime near integer filling factors, electrons are transmitted through edge states confined at the borders of the device. In mesoscopic samples, however, edge states may be sufficiently close to allow electrons to tunnel, or to be transmitted through localized states (``Coulomb islands'') [1]. Here, we use the biased tip of a low temperature scanning gate microscope to alter tunneling through quantum Hall Coulomb islands localized inside a quantum ring patterned in an InGaAs/InAlAs heterostructure. Simultaneously, we map the quantum ring resistance and observe different sets of concentric resistance fringes, due to charging/discharging of each Coulomb island. Tuning the magnetic field and the tip voltage, we reveal the rich and complex behaviour of these fringes [2].\\[4pt] [1] B. Rosenow and B. I. Halperin, PRL 98, 106801 (2007).\\[0pt] [2] B. Hackens et al., Nature Communications 1, 39 (2010).   

Emergent Dissipation in the $\nu=1$ Quantum Hall Bilayer

Disorder is known to be central to the $\nu=1$ bilayer [1]. Building on our previous study of the bilayer $\nu=1$ system in a periodic potential [2] to capture the nonperturbative effects of disorder, we construct a $T=0$ effective theory, in which the $XY$ angle is coupled to an emergent Ising spin. We uncover a $z=2$ quantum phase transition with emergent dissipation. Calculations of the interlayer tunnelling conductance and counterflow conductivity will be presented. \\[4pt] [1] H. A. Fertig and G. Murthy, Phys. Rev. Lett. {\bf 95}, 156802 (2005). \\[0pt] [2] J. Sun, G. Murthy, H. A. Fertig, and N. Bray-Ali, Phys. Rev. B, {\bf 81}, 195314 (2010).   

Microwave induced electron heating in the regime of radiation-induced magnetoresistance oscillations in the GaAs/AlGaAs system

We examine the influence of microwave photoexcitation on the amplitude of Shubnikov-de Haas (SdH) oscillations at large filling factors in a two dimensional GaAs/AlGaAs electron system. A SdH lineshape analysis indicates that increasing the incident microwave power has a weak effect on the amplitude of the SdH oscillations, in comparison to the influence of modest temperature changes at liquid Helium temperatures on the dark-specimen SdH effect. The results indicate negligible electron heating under modest microwave photoexcitation, in good agreement with theoretical predictions for this regime.   

Transport study under microwave photoexcitation in epitaxial graphene

Single layers of carbon known as graphene are a promising new electronic material with potential for high frequency applications. For electronics, top-gated graphene field-effect transistors fabricated on large area epitaxial graphene wafers have already indicated switching cutoff frequencies up to 100 GHz [1]. Microwave and terahertz radiation-sensing constitutes another area of interest. Hence, we examine the electrical photo-response of graphene devices in the microwave band, and report transport measurements under microwave photo-excitation (f $<$ 120 GHz) carried out on micron sized Hall bars at liquid Helium temperatures. \\[4pt] [1] Y-M Lin et al., Science 327, 662 (2010).   

Quantized Anomalous Hall Insulator in a Nanopatterned Two-Dimensional Electron Gas

We propose that a quantum anomalous Hall insulator (QAHI) can be realized in a nanopatterned two-dimensional electron gas (2DEG) with an in-plane magnetic field. The Berry curvatures originating from the in-plane magnetic field and Rashba and Dresselhaus spin-orbit coupling, in combination with a nanoscale honeycomb lattice potential modulation, lead to topologically nontrivial insulating states in the 2DEG. In the bulk insulating gaps, the anomalous Hall conductivity is quantized -e$^{2}$/h, corresponding to a finite Chern number -1. There exists one gapless chiral edge state on each edge of a finite size 2DEG.   

Remote sensing of transport in microwave photo-excited GaAs/AlGaAs heterostructure devices

The GaAs/AlGaAs two dimensional electron system (2DES) exhibits magnetoresistance oscillations under microwave and terahertz photo-excitation at liquid Helium temperatures. Such oscillations are understood in terms of the displacement and inelastic models for photo-excited transport in this system. In order to identify the relative physical contributions, we report on transport measurements and concurrent ``remote'' sensing of the 2DES. Hence, measurements under microwave photo-excitation were carried out on Hall bars fabricated from high mobility GaAs/AlGaAs single heterostructures, as a sensor above the specimen served to look for concurrent changes in response. We report here on the observed noticeable changes in the remote sensor and correlate the observations with the observed transport response of the photo-excited 2DES.   

Microscopic conductivity imaging of the quantum Hall edge states by a microwave impedance microscope

Spatially resolved studies of the quantum Hall edge channels are usually challenging because most high mobility two-dimensional electron gas (2DEG) systems are buried underneath the surface. Using a cryogenic microwave impedance microscope, we demonstrate the conductivity mapping of the bulk and edge states in a GaAs/AlGaAs 2DEG. Narrow strips with either metallic or insulating screening properties are observed along edges of the 2DEG. The sizes and positions of these strips as a function of the magnetic fields agree with the self-consistent electrostatic picture. The quantitative local conductivity information provides a complete microscopic description of the evolution through the bulk filling factor $\nu $ = 2. The imaging was performed without DC electrodes, vividly manifesting that the quantum Hall edges are equilibrium states and do not depend on externally supplied currents.   

Study of integer quantum Hall transition in long-ranged potentials

We present results of a numerical study of a two-dimensional system of noninteracting electrons in a random correlated potential in the lowest Landau level in the presence of a perpendicular magnetic field. We use spatially uncorrelated and unbiased random gaussian potentials as well as potentials $V(r) $ with long-range, power-law correlations $\langle V(0)V(r) \rangle \propto r^{-\alpha}$ for different exponents $\alpha$ as models of disorder. We compute the Hall conductance $\sigma_{xy} $ as well as the Thouless conductance as a function of size $L$ of the sample, and use finite size scaling to determine the exponent $\nu$ characterizing the divergence of the localization length $\xi$ at the quantum Hall transition. We also study the scaling of the diagonal conductivity as a function of $L$ and compare our results to those obtained previously through different methods.   

High-Resolution Tunneling Spectroscopy of 2D Holes in the Quantum Hall Regime

We use Time-Domain Capacitance Spectroscopy (TDCS){[}1{]}, a method for extracting precise, high-resolution tunneling spectra, to determine the single-particle spectrum of the 2D hole system (2DHS) in the presence of high magnetic fields. The 2DHS has a variable density from zero to $3\times10^{11}\,\mathrm{cm^{-2}}$ and $T=100\,\mathrm{mK}$. Owing to the heavy mass of holes in GaAs quantum wells, much higher values of $r_{s}$ are attainable compared to 2D electron systems(2DES). Basic structure in the spectra appear very different from those observed in the 2DES{[}1{]}. For instance, a magnetic-field-induced Coulomb gap {[}1{]} appearing about the Fermi energy has a strong dependence on electron density (with a larger gap at low densities) that is not present for the 2DES. In addition, structure created by the exchange enhancement of spin splittings has an entirely different appearance from that seen in the 2DES. Ultimately, at lower temperatures, a high-resolution TDCS study of the 2DHS may show features related to the 2D metal-insulator transition. \\[4pt] [1] O.E. Dial et al, Nature 448, 176-179 (2007).   

High quality two-dimensional hole system on hydrogen terminated silicon (111) surfaces

We have previously developed a novel field effect transistor structure, in which high mobility two-dimensional electrons are induced at a hydrogen-terminated Si(111) surface by a positive gate voltage through an encapsulated vacuum dielectric [1]. In this talk, we will demonstrate that a similar structure can also be used to define a high quality two-dimensional hole system (2DHS) at the H-Si(111) surface with a negative gate voltage. Hole concentrations up to $7.1\times 10^{11}$ cm$^{-2}$ are obtained. The longitudinal and Hall resistivities are measured as functions of magnetic fields up to 12 T. Preliminary data show Shubnikov-de Haas (SdH) oscillations at B $>$ 3 T at T= 5 K. Until now the studies on 2DHSs on Si(111) surfaces are limited, primarily due to the lack of high quality 2DHSs on them. The high quality 2DHS here can provide some new opportunities.\\[4pt] [1] K. Eng, R. N. McFarland, and B. E. Kane, Appl. Phys. Lett. 87, 052106 (2005).   

Microwave photo-voltaic oscillations in the GaAs/AlGaAs system

Microwave photo-excitation of the GaAs/AlGaAs system produces oscillations in the diagonal resistance that lead into novel zero-resistance states in the low temperature limit. Such photo-excitation also produces concomitant photo-voltage oscillations. Here, we examine this microwave photo-voltaic effect and correlate the results with observed magneto-transport over the frequency range $30 \le f \le 120 GHz$ in Hall bars fabricatedfrom material characterized by n = 2x $10^{11} cm^{-2}$.   

Terahertz Coherent Control of Cyclotron Resonance in the Quantum Hall Regime

We report on the creation and coherent control of a superposition of many-electron quantum states (or a qubit) in a Landau-quantized GaAs two-dimensional electron gas (2DEG) using a sequence of coherent terahertz (THz) pulses. The first pulse excites electrons from the highest-filled Landau level (LL) to the lowest-unfilled LL, creating a superposition of the two LLs which re-emits a coherent THz wave. We found that the second THz pulse incident within the decoherence time stops or enhances the THz re-emission depending on its arrival phase. These results show that an arbitrary coherent control of the LL qubit is possible using THz pulses. We also performed a simulation within the framework of single-particle optical Bloch equations, which reproduced the experimental results surprisingly well. This agreement shows that the 2DEG behaves in the same way as a single-electron two-level system despite the fact that it contains a large density of interacting electrons. This finding extends the Kohn's theorem to a more general level of coherent dynamics.   

THz quantum Hall conductivity in a two dimensional electron gas

We investigate the THz Hall conductivity through measurement of the Faraday effect at 84 cm$^{-1}$ near the cyclotron resonance (CR) in a two dimensional electron gas formed at a GaAs/(AlGa)As interface. Motivated by predictions of novel step-like features in the optical Hall conductivity ($\sigma _{xy})$ by Morimoto et.al. (Phys. Rev. Lett. 2009), we measure the THz $\sigma _{xy}$ as a function of filling factor and temperature using polarization modulation techniques (Grayson, Phys. Rev. Lett. 2002). We observe plateaus in the Faraday rotation near integer filling factors of 1, 2 and 3 which we attribute to the THz integer quantum Hall effect. In electron density dependent studies, we observe a slight non-monotonic shift of the plateaus as a function of filling factor at magnetic fields above CR. A comparison of this effect with the shift in temperature shows that this cannot be explained by a simple electronic heating effect. This research was funded through NSF-DMR1006078.   

Superconducting Transport Mediated by Quantum Hall Edge Modes

We report transport measurements between superconducting leads separated by a small gap consisting of quantum Hall edge modes. The NbTi superconducting layer is grown in-situ on top of the semiconducting heterostructure to allow good contact. The samples are then fabricated into Hall bars with narrow gaps between the superconducting leads. Differential resistance and IV characteristics are measured in two and four terminal setups at 300mK both on and off quantum Hall plateaus. We will show that in the smallest gaps when we are on a plateau, we see a chiral supercurrent the direction of which is controlled by the field. With larger gaps we see either a zero bias resistance minimum or maximum. Data taken on and off plateaus show marked differences, indicating that quantum Hall modes are crucial. Results for samples with different heterostructures will also be shown.   

In-plane Field Tuned Subband Quantum Hall Ferromagnetism

Motivated by the recent experimental work of Guo \textit{et al.} (Phys. Rev. B 78, 233305 (2008)), we study the effects of an in-plane magnetic field on quantum Hall states in which subband, Landau level, and spin degrees of freedom compete. We find that the phase diagram identified by these authors can be explained qualitatively by using only single-electron properties, whereas the energy gap behavior can be explained only by considering electron-electron interactions. We predict a series of in-plane field tuned first order phase transitions in high-mobility samples.