Precision of Quantization of the Hall Conductivity in a Sample of Finite Size: Power Law

TL;DR

This paper presents a microscopic analysis of the quantization precision in the integer quantum Hall effect, revealing a power-law dependence on sample size and a linear relation with potential amplitude, supported by experimental comparisons.

Contribution

It introduces a new scaling parameter and provides a detailed microscopic calculation of quantization precision in finite-sized samples.

Findings

Quantization precision follows a power-law with sample size.

Precision linearly depends on the ratio of chaotic potential amplitude to cyclotron energy.

Results align with magnetotransport measurements in mesoscopic samples.

Abstract

A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) regime is carried out. The problem of precision of quantization is analyzed for samples of finite size. It is demonstrated that the precision of quantization shows a power-law dependence on the sample size. A new scaling parameter describing a dependence of this kind is introduced. It is also demonstrated that the precision of quantization linearly depends on the ratio between the amplitude of the chaotic potential and the cyclotron energy. The results obtained are compared with the magnetotransport measurements in mesoscopic samples.