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

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.