Vanishing Zeeman energy in a two-dimensional hole gas

TL;DR

This paper investigates the crossing of Zeeman split states in a strained germanium two-dimensional hole gas, providing a model that links critical magnetic fields to material parameters, aiding quantum device design.

Contribution

It introduces a perturbative model with a closed-form formula for critical magnetic fields, highlighting the role of band differences, strain, and spin-orbit interaction in Zeeman state crossings.

Findings

Zeeman crossing signatures observed in Landau fan diagram

Critical magnetic fields depend on band energy differences and material parameters

Model enables quantification of hole-state parameters from measurements

Abstract

A clear signature of Zeeman split states crossing is observed in Landau fan diagram of strained germanium two-dimensional hole gas. The underlying mechanisms are discussed based on a perturbative model yielding a closed formula for the critical magnetic fields. These fields depend strongly on the energy difference between the top-most and the neighboring valence bands and are sensitive to the quantum well thickness, strain, and spin-orbit-interaction. The latter is a necessary feature for the crossing to occur. This framework enables a straightforward quantification of the hole-state parameters from simple measurements, thus paving the way for its use in design and modelling of hole-based quantum devices.