High Frequency Conductivity in the Quantum Hall Regime (original) (raw)
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Physica B: Condensed Matter, 1998
The localization/delocalization transitions in the Landau levels (LL) related to the integer quantum Hall eect (QHE) are examined by studying the DC and high-frequency (35 GHz) conductivity r xx of a two-dimensional electron system (2DES) in AlGaAs/GaAs in the temperature range 0.3±4 K. Because of the observed asymmetric shape of r xx (B) between its QHE minima the peak widths are determined separately for the low and high magnetic ®eld side. In the DC data the temperature dependence of the low-®eld width follows a power law with exponents close to those expected from scaling theory, the high-®eld width shows far higher exponents. In the high-frequency data only at the lowest temperatures (hf ) k ) the width becomes temperature independent according to the dynamical scaling theory. Ó 1998 Elsevier Science B.V. All rights reserved.
Anomalous frequency-dependent conductivity near the quantum Hall transition
Physical Review B - PHYS REV B, 1999
The dynamical transport properties near the integer quantum Hall transition are investigated at zero temperature by means of the Dirac fermion approach. These properties have been studied experimentally at low frequency omega and low temperature near the nu=1 filling factor Hall transition, with the observation of an unusual broadening and an overall increase of the longitudinal conductivity Re\{sigmaxx\} as a function of omega. We find in our approach that, unlike for normal metals, the longitudinal conductivity increases as the frequency increases, while the width DeltaB (or Deltanu) of the conductivity peak near the Hall transition increases. These findings are in reasonable quantitative agreement with recent experiments by Engel et al. [Phys. Rev. Lett. 71, 2638 (1993)], as well as with recent numerical work by Avishai and Luck (cond-mat/9609265).
Low-frequency anomalies and scaling of the dynamic conductivity in the quantum Hall effect
Physical Review B, 1996
A numerical study of the dynamic conductivity xx () in the lowest Landau level for a quantum Hall system with short-range and long-range disorder potentials is performed. In the latter case two distinct types of low-frequency anomalies are observed: a scaling regime with an anomalous diffusion exponent of ϭ0.36Ϯ0.06 independent of the potential correlation range and a semiclassical regime giving evidence of the existence of long time tails in the velocity correlation decaying proportional to t Ϫ2. The range of validity of this behavior increases with increasing. The universal value of the critical conductivity is xx c ϭ(0.5Ϯ0.02)e 2 /h for ϭ0 to 2 magnetic lengths. ͓S0163-1829͑96͒00720-5͔ PHYSICAL REVIEW B
Dynamic Conductance in Quantum Hall Systems
1996
In the framework of the edge-channel picture and the scattering approach to conduction, we discuss the low frequency admittance of quantized Hall samples up to second order in frequency. The first-order term gives the leading order phase-shift between current and voltage and is associated with the displacement current. It is determined by the emittance which is a capacitance in a capacitive arrangement of edge channels but which is inductive-like if edge channels predominate which transmit charge between different reservoirs. The second-order term is associated with the charge relaxation. We apply our results to a Corbino disc and to two-and four-terminal quantum Hall bars, and we discuss the symmetry properties of the current response. In particular, we calculate the longitudinal resistance and the Hall resistance as a function of frequency.
Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime
Physical Review B, 2010
Dynamical scaling analysis is theoretically performed for the ac (optical) Hall conductivity σxy(εF , ω) as a function of Fermi energy εF and frequency ω for the two-dimensional electron gas and for graphene. In both systems, results based on exact diagonalization show that σxy(εF , ω) displays a well-defined dynamical scaling, for which the dynamical critical exponent as well as the localization exponent are fitted and plugged in. A crossover from the dc-like bahavior to the ac regime is identified. The dynamical scaling analysis has enabled us to quantify the plateau in the ac Hall conductivity previously obtained, and to predict that the plateaux structure in ac is robust enough to be observed in the THz regime.
Scaling properties of conductance at integer quantum Hall plateau transitions
Physical Review B, 1998
We investigate the scaling properties of zero temperature conductances at integer quantum Hall plateau transitions in the lowest Landau band of a two-dimensional tight-binding model. Scaling is obeyed for all energy and system sizes with critical exponent ν ≈ 7 3 . The arithmetic average of the conductance at the localization-delocalization critical point is found to be < G >c= 0.506 e 2 h , in agreement with the universal longitudinal conductance < σxx >= 1 2 e 2 h predicted by an analytical theory. The probability distribution of the conductance at the critical point is broad with a dip at small G.
Frequency dependent conductivity in the integer quantum Hall effect
1999
Frequency dependent electronic transport is investigated for a two-dimensional disordered system in the presence of a strong perpendicular static magnetic field. The acconductivity is calculated numerically from Kubo's linear response theory using a recursive Green's function technique. In the tail of the lowest Landau band, we find a linear frequency dependence for the imaginary part of σxx(ω) which agrees well with earlier analytical calculations. On the other hand, the frequency dependence of the real part can not be expressed by a simple power law. The broadening of the σxx-peak with frequency in the lowest Landau band is found to exhibit a scaling relation from which the critical exponent can be extracted.
Point-contact conductances at the quantum Hall transition
Physical Review B, 1999
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2|2) symmetry, and postulating a twopoint correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be Xt = 0.640±0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by Xt. Our results demonstrate that multifractality can show up in appropriate transport experiments.
Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system
Journal of Physics: Condensed Matter, 2009
We investigate the relation between the diagonal (σxx) and offdiagonal (σxy) components of the conductivity tensor in the quantum Hall system. We calculate the conductivity components for a short-range impurity potential using the linear response theory, employing an approximation that simply replaces the self-energy by a constant value −i /(2τ ) with τ the scattering time. The approximation is equivalent to assuming that the broadening of a Landau level due to disorder is represented by a Lorentzian with the width Γ = /(2τ ). Analytic formulas are obtained for both σxx and σxy within the framework of this simple approximation at low temperatures. By examining the leading terms in σxx and σxy, we find a proportional relation between dσxy/dB and Bσ 2 xx . The relation, after slight modification to account for the long-range nature of the impurity potential, is shown to be in quantitative agreement with experimental results obtained in the GaAs/AlGaAs two-dimensional electron system at the low magnetic-field regime where spin splitting is negligibly small.