  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.
