Anomalous frequency-dependent conductivity near the quantum Hall transition (original) (raw)
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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.
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.
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.
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
A new transport regime in the quantum Hall effect
Solid State Communications, 1998
Our evolving understanding of the dramatic features of charge-transport in the quantum Hall (QH) regime has its roots in the more general problem of the metal-insulator transition. Conversely, the set of conductivity transitions observed in the QH regime provides a fertile experimental ground for studying many aspects of the metal-insulator transition. While earlier works tend to concentrate on transitions between adjacent QH liquid states, more recent works focus on the transition from the last QH state to the high-magnetic-field insulator. Here we report on measurements that identified a novel transport regime which is distinct from both, the fully developed QH liquid, and the critical scaling regime believed to exist asymptotically close to the transition at very low temperatures (T 's).
Novel Finite Temperature Conductivity in Quantum Hall Systems
1995
We study quantum Hall systems (mainly the integer case) at finite temperatures and show that there is a novel temperature dependence even for a pure system, thanks to the 'anomalous' nature of generators of translation. The deviation of Hall conductivity from its zero temperature value is controlled by a parameter T 0 = πρ/m * N which is sample specific and hence the universality of quantization is lost at finite temperatures.
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.
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.