Impact of spin--orbit coupling on orbital diamagnetism in a narrow-gap semiconductor $\mathrm{Pb}_{1-x}\mathrm{Sn}_x\mathrm{Te}$

TL;DR

This study investigates how spin--orbit coupling influences orbital diamagnetism in narrow-gap semiconductor $ ext{Pb}_{1-x} ext{Sn}_x ext{Te}$, revealing SOC's role in enhancing diamagnetism via interband effects.

Contribution

It introduces a detailed analysis of SOC's impact on orbital magnetism in $ ext{Pb}_{1-x} ext{Sn}_x ext{Te}$, including a new free--Zeeman--Dirac model to explain the mechanisms.

Findings

Diamagnetism is observed for both $x=0$ and $x=0.35$, with stronger response at smaller gaps.

Diamagnetism magnitude increases monotonically with SOC strength, especially in strong magnetic fields.

SOC enhances Dirac-type interband contributions, increasing diamagnetism.

Abstract

We study the influence of spin--orbit coupling (SOC) on orbital magnetism in $\mathrm{Pb}_{1-x}\mathrm{Sn}_x\mathrm{Te}$, a narrow-gap semiconductor. Using the $\pi$-matrix method, we calculate material-specific Landau levels and evaluate the magnetization, fully including interband effects. The system exhibits diamagnetism for both $x = 0$ and $x = 0.35$, with the latter showing a stronger response due to its smaller gap. The magnitude of diamagnetism increases monotonically with SOC strength, particularly in strong magnetic fields. To clarify the underlying mechanism, we introduce the free--Zeeman--Dirac (fZD) model and fit its parameters to the calculated Landau levels. The analysis reveals that SOC enhances the Dirac-type interband contribution relative to the Zeeman term, leading to increased diamagnetism. These results demonstrate that SOC can play a key role in orbital magnetism through interband effects.