Magnetic Response Functions in Landau Levels

TL;DR

This paper introduces a new quantization rule linking Landau levels with zero-field magnetic response functions, simplifying calculations and enabling experimental measurement of magnetic properties.

Contribution

It presents a novel quantization rule that connects Landau levels with magnetic response functions, unifying corrections from Berry phase and magnetic moments in a single framework.

Findings

Reproduces Onsager's rule at leading order

Incorporates Berry phase and magnetic moment effects

Allows experimental determination of magnetic responses

Abstract

We propose a new quantization rule which generates Landau levels consistent with the zero-field magnetic response functions from the semiclassical theory. It reproduces the Onsager's rule in the leading order, and re-formulates corrections from the Berry phase and magnetic moment effect in terms of one single magnetic response: the zero-field magnetization. It can yield higher order corrections by including successively magnetic susceptibility and higher order magnetic response functions. In application, it can be easily applied to obtain Landau levels in lattice models. Moreover, it provides an experimental method of measuring different magnetic response functions directly from the measurement of Landau level fan diagram or Hofstadter spectrum.