Random walks and magnetic oscillations in compensated metals

TL;DR

This paper investigates quantum oscillations in a two-dimensional compensated metal with a complex Fermi surface, showing that the first harmonic follows the Lifshits-Kosevich formula while the second harmonic exhibits non-trivial behavior.

Contribution

It introduces a novel approach using random walks on the orbit network to accurately evaluate the first harmonic amplitude in quantum oscillations.

Findings

First harmonic amplitude matches LK formula predictions.

Second harmonic vanishes at a critical field-to-temperature ratio.

Behavior depends on the relative effective masses of electrons and holes.

Abstract

The field- and temperature-dependent de Haas-van Alphen oscillations spectrum is studied for an ideal two-dimensional compensated metal whose Fermi surface is made of a linear chain of successive orbits with electron and hole character, coupled by magnetic breakdown. We show that the first harmonics amplitude can be accurately evaluated on the basis of the Lifshits-Kosevich (LK) formula by considering a set of random walks on the orbit network, in agreement with the numerical resolution of semi-classical equations. Oppositely, the second harmonics amplitude does not follow the LK behavior and vanishes at a critical value of the field-to-temperature ratio which depends explicitly on the relative value between the hole and electron effective masses.