The hierarchical spectral flow of Bloch electron

TL;DR

This paper investigates the hierarchical spectral flow of Hall conductivity in a two-dimensional electron gas under magnetic fields, revealing quantization phenomena and contributions beyond classical models.

Contribution

It introduces a new theoretical framework for understanding the hierarchical spectral flow of Hall conductivity, emphasizing quantum effects and quantization in the Hall effect.

Findings

Hall conductivity expressed as classical and quantum contributions

Quantization of Hall conductance when Fermi energy is in a gap

Hierarchical spectral flow elucidated in the quantum Hall regime

Abstract

The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field. The Hall conductivity is expressed as a sum of two contributions: one corresponding to the classical Drude-Zener formula, and a second which has no classical analogy. The developed theory is applied to the Hall effect. The Kobo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. We examine the hierarchical spectral flow of Hall conductivity.