Peak values of the longitudinal conductivity under integer quantum Hall effect conditions for sharp and smooth chaotic p
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PROPERTIES OF SOLIDS
Peak Values of the Longitudinal Conductivity under Integer Quantum Hall Effect Conditions for Sharp and Smooth Chaotic Potentials A. A. Greshnov, G. G. Zegrya, and É. N. Kolesnikova Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia e-mail: [email protected] Received October 9, 2007
Abstract—The problem of the peak values of the longitudinal conductivity under integer quantum Hall effect conditions is studied. The limiting cases of sharp and smooth chaotic potentials are considered. In the case of (0)
a sharp chaotic potential, the first longitudinal conductivity peak ( σ xx ) obtained by the extrapolation of numerical data to an infinite sample size L ∞ is (0.55 ± 0.03)e2/h. In the case of a smooth chaotic potential, the peak values of the longitudinal conductivity are independent of the Landau level number and decrease as the chaotic-potential correlation length λ increases. The results obtained for sharp and smooth chaotic potentials agree with the reported experimental and numerically calculated data. PACS numbers: 73.43.-f DOI: 10.1134/S1063776108090161
1. INTRODUCTION The problem of the peak values of the longitudinal conductivity under integer quantum Hall effect conditions is of particular interest due to the statement about the universal behavior of the conductivity tensor components that follows from the Pruisken–Khmel’nitskiœ theory [1, 2]. According to this theory, the conductivity tensor components σxx and σxy obey renormalization (n)
group equations that demonstrate that peak values σ xx are independent of the Landau level number n to which a given longitudinal conductivity peak is related. This result was obtained in terms of a nonlinear σ model for noninteracting electrons with a sharp chaotic potential (white noise) placed in a magnetic field [3], and it was then generalized to the case of a system of interacting carriers [4]. The estimate of this universal (independent ( ) of n) value of σ * obtained in terms of the nonlinear σ xx
model [5] is 0.88e2/h, which is in poor agreement with the experimental data [6–8]. However, a direct comparison of this estimate with the experimental data, in which the Coulomb interaction plays a key role, is not completely correct, since this estimate was obtained in a noninteracting-electron model. The authors of [9] ( ) estimated σ * using an approach based on the Chern– xx
Simons topological quantum field theory, which
neglects the effect of a chaotic potential on carriers, and found that ( )
σ xx* = 0.5e /h. 2
(1)
In [10], the same value was obtained in terms of a phenomenological two-phase model. In structures with a sharp chaotic potential (e.g., quantum wells based on solid solutions such as InGaAs/AlGaAs), Eq. (1) is approximately valid for the ground Landau level (n = 0; the integer quantum Hall effect–insulator transition is usually studied under these conditions), and it is difficult to experimentally check excited Landau levels (n ≥ 1) because of stron
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