Landau levels, response functions and magnetic oscillations from a generalized Onsager relation

TL;DR

This paper explores a generalized semiclassical quantization condition for cyclotron orbits that incorporates higher-order magnetic response functions, enabling new insights into Landau levels, magnetic oscillations, and their analysis in two-dimensional electron systems.

Contribution

It introduces a generalized Onsager relation involving magnetic response functions, providing methods to derive Landau levels from response functions and analyze magnetic oscillations more accurately.

Findings

Derived magnetic response functions from Landau levels.

Reconstructed Landau levels using response functions.

Proposed improved analysis of magnetic oscillations and phase shifts.

Abstract

A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu \cite{Gao}, that goes beyond the Onsager relation \cite{Onsager}. In addition to the integrated density of states, it formally involves magnetic response functions of all orders in the magnetic field. In particular, up to second order, it requires the knowledge of the spontaneous magnetization and the magnetic susceptibility, as was early anticipated by Roth \cite{Roth}. We study three applications of this relation focusing on two-dimensional electrons. First, we obtain magnetic response functions from Landau levels. Second we obtain Landau levels from response functions. Third we study magnetic oscillations in metals and propose a proper way to analyze Landau plots (i.e. the oscillation index $n$ as a function of the inverse magnetic field $1/B$) in order to extract quantities such as a zero-field phase-shift. Whereas the frequency of $1/B$-oscillations depends on the zero-field energy spectrum, the zero-field phase-shift depends on the geometry of the cell-periodic Bloch states via two contributions: the Berry phase and the average orbital magnetic moment on the Fermi surface. We also quantify deviations from linearity in Landau plots (i.e. aperiodic magnetic oscillations), as recently measured in surface states of three-dimensional topological insulators and emphasized by Wright and McKenzie \cite{Wright}.