Symmetry-adapted models for multifold fermions with spin-orbit coupling

TL;DR

This paper develops symmetry-adapted effective models for multifold fermions with spin-orbit coupling, enabling detailed analysis of their responses to external fields and revealing phenomena like magnetic monopole pair annihilation.

Contribution

It introduces comprehensive $oldsymbol{k} oldsymbol{ ext{p}}$ and tight-binding models for multifold fermions, incorporating external fields and spin-orbit coupling, advancing theoretical understanding of their responses.

Findings

Magnetic field induces pair annihilation of magnetic monopoles.

Constructed $oldsymbol{k} oldsymbol{ ext{p}}$ models for threefold and eightfold fermions.

Revealed coupling effects of external fields on multifold fermions.

Abstract

Multifold fermions, quasiparticles with multiple degeneracy protected by crystalline symmetries, exhibit a variety of intriguing phenomena stemming from their large topological charges and unique band structures. A comprehensive understanding of their response to external stimuli remains challenging, especially for types protected by nonsymmorphic symmetries where various degrees of freedom are intricately coupled. Here, we systematically construct effective models for multifold fermions that incorporate external fields based on crystalline symmetry. Specifically, we develop a $\boldsymbol{k} \cdot \boldsymbol{p}$ model for the threefold fermion protected by space group I2$_1$3 (No.~199) in the presence of spin--orbit coupling, and derive the terms for external fields. By complementing this with a tight-binding model, we investigate the magnetic field response and reveal the pair annihilation of magnetic monopoles. Furthermore, we construct a $\boldsymbol{k} \cdot \boldsymbol{p}$ model for the eightfold fermion in space group P$\bar{4}3n1'$ (No.~218), including its coupling to external fields. This work provides a robust theoretical foundation for advancing the study of external field responses and transport phenomena in multifold fermions, opening new avenues to explore their rich physics.