Semiclassical analysis and the magnetization of the Hofstadter model

TL;DR

This paper analyzes the magnetization and de Haas-van Alphen oscillations of Bloch electrons near commensurate magnetic fluxes, emphasizing the roles of Berry's phase and Wilkinson's phase in the quantization of mixed systems.

Contribution

It introduces a semiclassical analysis of the Hofstadter model incorporating Berry's phase and Wilkinson's phase effects on magnetization.

Findings

Identification of Berry's phase influence on magnetization

Discovery of Wilkinson's phase role in quantization

Quantitative predictions of oscillation behaviors

Abstract

The magnetization and the de Haas-van Alphen oscillations of Bloch electrons are calculated near commensurate magnetic fluxes. Two phases that appear in the quantization of mixed systems--the Berry's phase and a phase first discovered by Wilkinson--play a key role in the theory.