Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session A19: Quantum Hall Effect |
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Sponsoring Units: DCMP Chair: HongWen Jiang, UCLA Room: LACC 406B |
Monday, March 21, 2005 8:00AM - 8:12AM |
A19.00001: Empirical resistivity rule in the second Landau level of a two-dimensional electron system W. Pan, J.S. Xia, C.L. Vicente, E.D. Adams, N.S. Sullivan, H.L. Stormer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin, K.W. West A phenomenological relationship, $R_{xx} \propto B \times dR_ {xy}/dB$, called the resistivity rule, was observed twenty years ago. Yet, today we have only a relatively complex model that addresses the origin of this rule. It remains unclear whether a simpler model, based on some fundamental relationship exists. In recent experiments on ultra-high quality specimens performed in the second Landau level (LL), instead of rising in a stair- like fashion, $R_{xy}$ is found to switch back and forth between FQHE and IQHE values several times as the filling factor varies from $\nu=4$ to $\nu=2$. This non-monotonic $R_ {xy}$ leads to regions of negative $B \times dR_{xy}/dB$, which cannot find an equivalent in $R_{xx}$, a positive definite, thus apparently violating the empirical rule. However, in a more detailed examination, we found, surprisingly, a new resistivity rule in the second LL. The regular, positive parts of $B \times dR_{xy}/dB$ are well reflected in $R_{xx}(+B)$, whereas the irregular negative going sections of $B \times dR_ {xy}/dB$ closely match the inverted $R_{xx}(-B)$ trace, where $- B$ refers to the opposite magnetic field direction of $+B$. It is unclear whether our observations of an expanded resistivity rule reinforces or refutes the present model of its origin. [Preview Abstract] |
Monday, March 21, 2005 8:12AM - 8:24AM |
A19.00002: Spin-dependent resistivity at transitions between integer quantum Hall states Kamran Vakili, Yakov Shkolnikov, Emanuel Tutuc, Nathan Bishop, Etienne De Poortere, Mansour Shayegan The longitudinal resistivity at transitions between integer quantum Hall states is found to depend strongly on the spin orientation of the corresponding partially-filled Landau level in two-dimensional electrons confined to narrow AlAs quantum wells. By tilting the sample with respect to the applied magnetic field, different Landau level spin branches can be brought to and driven past energetic coincidence. The result is a flip of the spin-orientation for the energy level corresponding to a given quantum Hall transition that is accompanied by a change in resistivity. This change can be as much as an order of magnitude. We discuss possible causes and suggest a new explanation for spike-like features, associated with quantum Hall ferromagnetic transitions, observed at the edges of quantum Hall minima. [Preview Abstract] |
Monday, March 21, 2005 8:24AM - 8:36AM |
A19.00003: Landau quantization, Localization, and Insulator-quantum Hall Transition at Low Fields Tsai-Yu Huang, C.-T. Liang, Gil-Ho Kim, C.F. Huang, Chao-Ping Huang, D.A. Ritchie We have performed a magnetotransport study on a two-dimensional gated GaAs electron system containing self-assembled InAs quantum dots. In our system Shubnikov-de Haas (SdH) oscillations are induced by Landau quantization in the low- field insulator, and the system undergoes a direct insulator- quantum Hall ($\nu=4$) transition as the magnetic field is increased. The low-field Landau quantization, in fact, is governed by the SdH theory and can modulate the density of states without causing the formation of a quantum Hall liquid in our system. While the expected property $\rho_{xy} \sim \rho_ {xx}$ may not be valid at direct insulator-quantum Hall transitions, we find that such transitions do occur as the product $\mu B \sim 1$ and hence well-separated Landau bands exist in the energy spectrum. [Preview Abstract] |
Monday, March 21, 2005 8:36AM - 8:48AM |
A19.00004: Symmetries of the Resistance of Mesoscopic Samples in the Quantum Hall Regime Einat Peled, Dan Shahar, Yong Chen, Enrique Diez, Deborah L. Sivco, Alfred Y. Cho We present an experimental study of the symmetries of the resistance of mesoscopic samples in the quantum Hall regime. The samples we use are small Hall-bars, prepared from low-mobility InGaAs/InAlAs wafers. The four-terminal resistances of these samples display large reproducible fluctuations that are unique to the contact configuration used in the measurements. We find that the samples obey new symmetries, in addition to the reciprocity relation, relating the longitudinal and Hall resistances of different contact configurations and magnetic- field ($B$) polarities. These symmetries include the fine details of the resistance fluctuations. The resistances in the vicinity of all integer quantum Hall transitions are found to follow one of two possible sets of symmetries, one on the low-$B$ side and the other on the high- $B$ side of the transitions. [Preview Abstract] |
Monday, March 21, 2005 8:48AM - 9:00AM |
A19.00005: Lifetime of 2D electrons in AlxGa1-xAs-Al0.32Ga0.68As Heterostructures Wanli Li, Daniel Tsui, Loren Pfeiffer, Ken West We have investigated the transport lifetime and the quantum lifetime of 2D electrons confined to the Al$_{x}$Ga$_{1-x}$As-Al$_{0.32}$Ga$_{0.68}$As heterostructures over the range of $x$ from 0 to 0.85{\%}. The transport lifetime is obtained from the mobility measurement, while the quantum lifetime is determined by fitting the temperature and magnetic field dependences of the Shubnikov-de Hass oscillations to the Dingle formula. With $x$ increases from 0 to 0.85{\%}, the transport lifetime is found to decrease from 160ps to 30ps. However the quantum lifetime only changes from 1.71ps to 1.64ps. Since the quantum lifetime is given by the total scattering rate over all directions while the transport lifetime is only affected by the large-angle backscattering rate, our results show that the alloy scattering centers contribute mainly to the short-ranged large-angle scattering. These results demonstrate a powerful way to manipulate the nature of disorder in 2D electron systems and show consistency with the recent scaling experiment of IQHE plateau-to-plateau transitions in Al$_{x}$Ga$_{1-x}$As alloy systems with different $x$. [Preview Abstract] |
Monday, March 21, 2005 9:00AM - 9:12AM |
A19.00006: Interaction effect on quantum magnetooscillations in a two-dimensional electron gas Yury Adamov, Igor' Gornyi, Alexander Mirlin Recently there is considerable experimental interest in the semiconductor systems with apparent quantum phase transition. For this experiments it is important to have independed means of measurements of effective electron mass. This mass can be inferred from quantum magnetic oscillations, and we present a framework for the interpretation of magnetooscillation experiments. We consider the effects of interactions and disorder on the damping of magneto-oscillations in 2D. We study the effect of both long range and short range interaction and point-like disorder in a ballistic ($T\tau\gg1$) and diffusive ($T\tau\ll1$) regime, where $\tau$ is mean scattering time. The dominant effect on the damping comes from interplay of disorder and interaction corrections to to the electron mass. Depending on the nature of interaction we found the corrections to behave like $\ln T$ and $\ln^2T$ in the ballistic and diffusive regime correspondendly. [Preview Abstract] |
Monday, March 21, 2005 9:12AM - 9:24AM |
A19.00007: Measurements of the Spin Susceptibility of 2D GaAs/AlGaAs Heterostructures into the Weak Interacting Region Y.-W. Tan, J. Zhu, H.L. Stormer, L.N. Pfeiffer, K.W. Baldwin, K.W. West We determine the spin susceptibility $\chi$ of a two- dimensional electron system in GaAs/AlGaAs heterostructures using the tilted-field method. The measurements are done on a very high quality heterojunction-insulated gate field-effect transistor (HIGFET) with a mobility as high as $1\times10^{7} cm^{2}/Vs$. We report the $\chi$ measurements on a single HIGFET specimen over a wide range of densities, from $1 \times10^ {10} cm^{-2}$ to $4\times10^{11}cm^{-2}$; deep into the weak interacting regime. The value of $\chi$ decreases monotonically with increasing density. In the low density region, $\chi$ follows an empirical formula proposed by Zhu et al. (\textit {Phys. Rev. Lett.}, \textbf{90}, 056805, 2003), but deviates from it as density increases beyond $6\times10^ {10} cm^{-2}$. After corrections for nonparabolicity of mass and g-factor, our $\chi$ measurements are very close to the most recent theoretical calculation (De Palo et al., cond- mat/0410145) over the whole density range. [Preview Abstract] |
Monday, March 21, 2005 9:24AM - 9:36AM |
A19.00008: Electron interferometer in the integer QH regime F.E. Camino, W. Zhou, V.J. Goldman We report experiments on an electron interferometer fabricated from high mobility, low density GaAs/AlGaAs heterostructure material. In this device, a nearly circular electron island is separated from the 2DES by two nearly open constrictions. In the integer QH regime $f$ = 1 and 2, we observe Aharonov-Bohm-like oscillations of conductance. The interference closed path is comprised by the two edge states circling the island, coupled by tunneling in the constrictions, the radius $r \sim $ 900 nm is determined from the oscillation period. The radius can be tuned by application of a bias V$_{FG}$ to the four front gates. We find approximately linear dependence d$r$/dV$_{FG }$= 0.25 nm/mV. We compare the experimental results to the island B = 0 electron density profile obtained in classical electrostatic models of Gelfand and Halperin, PRB \textbf{49}, 1862 (1994) and Chklovskii el al., PRB \textbf{46}, 4026 (1992). [Preview Abstract] |
Monday, March 21, 2005 9:36AM - 9:48AM |
A19.00009: Bending the quantum Hall effect by 90 degrees: Evidence for a new kind of disordered one-dimensional superconductor M. Grayson, L. Steinke, D. Schuh, M. Bichler, G. Abstreiter, L. Hoeppel, J. Smet, K. von Klitzing, D. Maude Utilizing a recently developed corner-overgrowth technique, we create a two-dimensional (2D) electron system which bends by 90 degrees at an atomically sharp corner. At certain properly oriented magnetic fields, the energetic gap in the two 2D systems confines the motion of electrons along the corner to one dimension, creating a new kind of 1D system. The conductance along this 1D corner shows power-law behavior in temperature and voltage which varies depending on the nature of the gap (integer or fractional quantum Hall effect), and for certain gaps shows a negative power-law exponent indicative of effective attractive interactions between the charges in the wire. This behavior was predicted theoretically for such systems. The 1D systems presented here represent the longest quantum wires ever fabricated, up to several millimeters in length. [Preview Abstract] |
Monday, March 21, 2005 9:48AM - 10:00AM |
A19.00010: Effect of disorder on modulated quantum Hall systems Mikito Koshino, Tsuneya Ando We present a numerical study of the quantum Hall effect in modulated two-dimensional (2D) electron systems in presence of disorder. Theoretically, it is known that a 2D periodic potential in a strong magnetic field gives rise to a recursive subband structure in Landau levels, which is called the Hofstadter butterfly[1]. Recently, the nonmonotonic behavior of the Hall conductivity peculiar to this system was observed in lateral superlattices patterned on GaAs/AlGaAs heterostructures [2,3]. To study how the Hall plateau emerges in those split Landau levels, we numerically calculate the Hall conductivity in a disordered 2D electron system with weak modulations under various magnetic fields. We investigate the scaling property of the Hall conductivity as well as the localization length, to identify the critical energies where the extended states exist. The dependence on the field amplitudes and the Landau levels is also discussed. [1] D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976). [2] C. Albrecht, et al. Phys. Rev. Lett. 86, 147 (2001) [3] M. C. Geisler, et al., Phys. Rev. Lett. 92, 256801 (2004). [Preview Abstract] |
Monday, March 21, 2005 10:00AM - 10:12AM |
A19.00011: Integer Quantum Hall Effect versus Anderson Transition: Numerical Comparison for Eigensolutions Statistics I. Kh. Zharekeshev Two types of the disorder-induced localization transitions, the plateau-to-plateaux transition in the Integer Quantum Hall Effect and the conventional Anderson transition in 3 dimensions are considered by using a comparative analysis. Similarities and differences of critical behavior of the eigenfunctions and eigenvalues statistics for both cases are numerically investigated within the frames of the common self-contained diagonalization technique. Both transitions reveal a number of the same universal features at criticality, including the one-parameter scaling, symmetry dependence of the eigenfucntions distributions, multifractality spectra, non-trivial branching numbers etc. Our results provide a strong support for the quantum-field theoretical description treating the two transitions as a generalized transition, i.e. a unique critical phenomenon. [Preview Abstract] |
Monday, March 21, 2005 10:12AM - 10:24AM |
A19.00012: Symmetry Breaking by Periodic Potentials and Randomness in Quantum Hall Systems Barry Friedman, Ben McCarty The effect of a one dimensional periodic potential on quantum Hall systems is investigated using direct diagonalization and the density matrix renormalization group (dmrg). We find that the phase of the periodic potential (i.e. averaging over the phase) has minimal effect on symmetry breaking, however the addition of a small random potential tends to decrease finite size effects. For certain parameter values, randomness tends to increase symmetry breaking. Preliminary results using dmrg, for larger system sizes, with no randomness, will be presented. [Preview Abstract] |
Monday, March 21, 2005 10:24AM - 10:36AM |
A19.00013: Solitons and Quasielectrons in the Quantum Hall Matrix Model T. Hans Hansson, Janik Kailasvuori, Anders Karlhede, Rikard von Unge We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model. The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons. [Preview Abstract] |
Monday, March 21, 2005 10:36AM - 10:48AM |
A19.00014: Length Scale of Bulk Quantum Hall Effect Michael Bleiweiss, Ming Yin, Jafar Amirzadeh, Timir Datta Quantum hall effects (QHE) are consequences of the condensation of the charge carriers into a novel macroscopic quantum state. Condensation produces steps in the hall resistance (R$_{xy})$ in fundamental units of h/e$^{2}$ (25812.8 Ohms), which correlate with Shubnikov-deHass oscillations in R$_{xx}$ and is represented graphically by the von Klitzing plot; which is a ``double-y'' graph of the hall resistance R$_{xy}$ and magnetoresistance R$_{xx}$ isotherms as functions of B. In two-dimensions electrical resistance per square is scale independent so the steps in R$_{xy}$ are in ohms. QHE condensation occurs in bulk systems as well. However, resistance of three-dimensional conductors depends on the sample geometry and the relevant transport coefficient, resistivity ($\rho _{xy})$, which is dimensionally different from resistance. Hence the QHE plateaus in bulk samples are not directly expressed in ohms. In this case the macroscopic $\rho _{xy}$ can be related to the R$_{xy}$ by a quantum length factor ``L'', we define L such that R$_{xy}$ = L$^{-1}(\rho _{xy). }$By analyzing literature data [Kul'bachinskii, V.A. et al., JETP Let., \textbf{70}, 767, 1999] we determine that for Sb$_{2}$Te$_{3 , }$L is equal to 1.7 nm a remarkable microscopic scale. This factor L is not just the ratio of the macroscopic length to the cross-sectional area of the conductor; instead, it is an effective length associated with the quantum hall states. [Preview Abstract] |
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