Low-frequency anomalies and scaling of the dynamic conductivity in the quantum Hall effect (original) (raw)
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Scaling of the Static Conductivity in the Quantum Hall Effect
Physical Review Letters, 1994
We performed a numerical study of the static diagonal conductivity o. " in the lowest Landau level for a disordered two-dimensional system in a magnetic field with short range impurity potentials. We find scaling of the conductivity peak at a single critical energy which is governed by both the localization length exponent v = 2.37~0.05 and an exponent g' = 1.63~0.03. %'e argue that q' can be identified with the fractal dimension D(2). For the value of the critical conductivity we obtained (0.5~0.02)e~/h in agreement with the hypothesis of universality.
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).
Universal scaling and diagonal conductivity in the integral quantum Hall effect
Physical Review B, 1998
We perform a numerical finite-size study for the static homogeneous diagonal conductivity xx at the critical filling factor 3/2 for different microscopic realizations of the random impurity potential. The variation of xx with the system size defines a scaling function. It turns out to be independent of the particular realization of disorder and also of the Landau-level index. However, the diagonal conductivity in the second-lowest Landau level varies strongly with disorder. The universal critical conductivity is recovered only asymptotically when the correlation length of the potential is increased.
Activated Conductivity in the Quantum Hall Effect
Physical Review Letters, 1994
Activated dissipative conductivity ¢==o-*~exp(-A/T) and the activated deviation of the Hall conductivity from the precise quanfizafion &r~v=~-ie2/hf~exp(-A/T) are studied in a plateau range of the quantum Hall effect. The prefactors cr*~ and o*~ are calculated for the case of a long-range random potential in the fxa~ework of a classical theory. There is a range of temperatures Tx << T<< T2 where ¢r*~ = e2/h. In this range ~ ~ (e2/h)(T/Ta)S°/21<< o'*~. At large T>> T2. on the other hand, a~ = e2/h and ~ = (ea/h)(Ta/T) I°/ts << a~,. Similar results are valid for a fractional plateau near the lining factor p/q if charge e is replaced by e/q.
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.
Physical Review B, 2007
Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge state, in contrast to the naive expectation that the potential correlation increases it. The effect appears as the sizable shift of quantized conductance plateaus in long wires, where the plateau transitions occur at energies much higher than the Landau band centers. The scale of the shift is of the order of the strength of the random potential and is insensitive to the strength of magnetic fields. Experimental implications are also discussed.
Low-frequency and long-wavelength anomalies of the integral quantum Hall effect
Zeitschrift für Physik B Condensed Matter, 1997
The static, homogeneous, diagonal conductivity for the normal quantum Hall effect at half filling of the lowest Landau level under certain conditions seems to approach the value ¡ £ ¢ £ ¤ ¦ ¥ §. The deviations from this value in dynamical, inhomogeneous situations show anomalies with a nonanalytical behavior of © in and. Existing results concerning this behavior are briefly reviewed and improved, taking screening effects into account. The combination of low-frequency anomalies and screening effects turns out to have dramatic consequences suppressing the low-frequency conductivity very strongly. From our considerations we conclude that it should be possible to observe all these effects.
High Frequency Conductivity in the Quantum Hall Regime
Physical Review Letters, 2001
We have measured the complex conductivity σxx of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that σxx can be scaled to a single function for different frequencies and for all investigated transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length ξ. Even for large filing factor distances δν from the critical point we find ξ ∝ δν −γ with a scaling exponent γ = 2.3.
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.
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.