Effect of the Landau level broadening on the quantum Hall conductance (original) (raw)
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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.
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
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.
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.
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.
Scaling of the anomalous Hall effect in lower conductivity regimes
EPL (Europhysics Letters), 2016
PACS 73.50.-h-Electronic transport phenomena in thin films PACS 73.61.Jc-Amorphous semiconductors; glasses PACS 73.50.Jt-Galvanomagnetic and other magnetotransport effects (including thermomagnetic effects) Abstract-The scaling of the anomalous Hall effect (AHE) was investigated using amorphous and epitaxial FexSi1−x (0.43 <x<0.71) magnetic thin films by varying the longitudinal conductivity (σxx) using two different approaches: modifying the carrier mean free path (l) with chemical or structural disorder while holding the carrier concentration (n h) constant or varying n h and keeping l constant. The anomalous Hall conductivity (σxy), when suitably normalized by magnetization and n h , is shown to be independent of σxx for all samples. This observation suggests a primary dependence on an intrinsic mechanism, unsurprising for the epitaxial high conductivity films where the Berry phase curvature mechanism is expected, but remarkable for the amorphous samples. That the amorphous samples show this scaling indicates a local atomic level description of a Berry phase, resulting in an intrinsic AHE in a system that lacks lattice periodicity.
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.
Journal of Geometry and Physics, 1984
We consider a particle in a 2 dimensional plane in a periodic potential and a homogeneous magnetic field perpendicular to the plane. Kubo 's expression for conductivity of the Hall current is an integer. This result of Thouless, Kohomoto, Nightingale and den Ni/s is interpreted geometrically. 1. THE EXPERIMENT OF V. KLITZING, DORDA AND PAPPER in 1980 v. Klitzing, Dorda and Pepper published an article entitled <> [1]. They measured the conductivity UH of the Hall-current in the twodimensional boundary layer of a Silicon-Siliconoxide transistor with the magnetic field perpendicular to the layer. The magnetic field had the order of magnitude 100 Kilogauss and the temperature was about l.5°K. In latter experiments [e.g.2], a 11 was measured as function of the magnetic field. The qualitative behavior of conductivity is represented by the graph in fig. 1.
World Journal of Condensed Matter Physics, 2015
We develop a model Hamiltonian to treat intrinsic anomalous Hall conductivity in dilute magnetic semiconductor (DMS) of type (III, Mn, V) and obtain the Berry potential and Berry curvature which are responsible for intrinsic anomalous Hall conductivity in Ga1−xMnxAs DMS. Based on Kubo formalism, we establish the relation between Berry curvature and intrinsic anomalous Hall conductivity. We find that for strong spin-orbit interaction intrinsic anomalous Hall conductivity is quantized which is in agreement with recent experimental observation. In addition, we show that the intrinsic anomalous Hall conductivity (AHC) can be controlled by changing concentration of magnetic impurities as well as exchange field. Since Berry curvature related contribution of anomalous Hall conductivity is believed to be dissipationless, our result is a significant step toward achieving dissipationless electron transport in technologically relevant conditions in emerging of spintronics.
Philosophical Magazine B, 1998
The quantized Hall insulator is characterized by vanishing conductivities and a quantized Hall resistance. For low mobility samples, the quantized Hall insulator is obtained when the magnetic field is increased well above the ν=1 quantum Hall state. For higher mobility samples, a similar quantization is observed when the magnetic field is increased above the ν = 1/3 fractional quantum Hall states. This quantization, throughout the quantum Hall liquid-to-insulator transition, leads to a perfect semicircle relation for the diagonal and Hall conductivities. The measurements were performed in Ge/SiGe quantum Wells and in n-type InP/InGaAs and GaAs/AlGaAs heterostuctures.