Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system (original) (raw)
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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.
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
Physical Review B, 2008
We determine wave number q and frequency ω dependent spin Hall conductivity σ s yx (q, ω) for a disordered two dimensional electron system with Rashba spin orbit interaction when q is transverse to the electric field. Both the conventional definition of spin current and its new definition which takes care of the conservation of spins, have been considered. The spin Hall conductivitivities for both of these definitions are qualitatively similar. σ s yx (q, ω) is zero at q = 0, ω = 0 and is maximum at q = 0 and at small but finite ω whose value depends on different parameters of the system. Interestingly for ω → 0, σ s yx (q) resonates when Λ ≃ Lso which are the wavelength (Λ = 2π/q) of the electric field's spatial variation and the length for one cycle of spin precession respectively. The sign of the out-of-plane component of the electrons' spin flips when the sign of electric field changes due to its spatial variation along transverse direction. It changes the mode of spin precession from clockwise to anticlockwise or vice versa and consequently a finite spin Hall current flows in the bulk of the system.
Longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
Physical Review B, 2004
We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte et al, Phys. Rev. Lett. 92, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.
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.
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.
Non-ohmic out-of-plane conductance in a multilayered quantum Hall system
Physica B: Condensed Matter, 2000
Out-of-plane transport in a GaAs/AlGaAs superlattice in the quantum Hall regime exhibits a strong non-ohmicity. At low temperatures and low current bias, the out-of-plane conductance G XX scales with the sample perimeter. These are signatures of the chiral surface state. At higher temperatures or higher current bias, G XX becomes scaled with the sample area, suggesting a crossover to bulk transport.
Effect of the Landau level broadening on the quantum Hall conductance
Il Nuovo Cimento D, 1991
In a previous paper, Kliros et al. presented a model calculation of the Hall conductivity as a function of the Landau level broadening F for finite temperatures. In this paper, the effect of Landau-level broadening on the structure of the Hall conductivity is investigated. The experimental data regarding the Si-MOSFET and GaAs-heterostructure experiments are reproduced including a functional dependence of F on the magnetic field. The influence of the effective g-factor is considered as well. PACS 72.20.My-Galvanomagnetic and other magnetotransport effects. PACS 73.20.Dx-Electron states in low-dimensional structures (including quantum wells, superlattices, layer structures, and intercalation compounds).
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.