Spin-Orbit Coupling and Topological States in $F=\frac{3}{2}$ Cold Fermi Gas

TL;DR

This paper explores the emergence of topological insulators in high-spin 2D cold fermion systems, demonstrating how spin-orbit coupling and magnetic fields induce mirror-symmetry-protected edge states, with potential for various atomic species.

Contribution

It introduces a method to realize topological insulators in high-spin cold fermion gases via engineered spin-orbit coupling and magnetic fields, highlighting the role of mirror symmetries and extending to higher spins.

Findings

Topological insulators can be realized in high-spin cold fermion systems.

Spin-orbit coupling is induced by polarized laser beam arrangements.

Mirror symmetry leads to positive and negative mirror Chern numbers.

Abstract

In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>\tfrac{1}{2}$, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin $\frac{1}{2}$. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively corresponding to chiral and anti-chiral edge states. Here, for simplicity, we concentrate on the case $F=\tfrac{3}{2}$ (which is suitable for $^{6}$Li or $^2$H atoms) but extension to higher spins (such as $^{40}$K whose ground-state spin is $F=\tfrac{9}{2}$), is straightforward.