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 $F>\frac{1}{2}$, 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 antichiral edge states. Here, for simplicity, we concentrate on the case $F=\frac{3}{2}$ (which is suitable for ${}^6\mathrm{Li}$ or ${}^2\mathrm{H}$ atoms) but extension to higher spins (such as ${}^{40}\mathrm{K}$ whose ground-state spin is $F=\frac{9}{2}$) is straightforward.

• Received 29 January 2018

DOI:https://doi.org/10.1103/PhysRevB.98.165139