Z2 Topological insulator of ultra cold atoms in bichromatic optical lattices

We investigate the effect of a strong bichromatic deformation to the ${\mathbb{Z}}_2$ topological insulator in a fermionic ultracold atomic system proposed by B. B'eri and N. R. Cooper, Phys.Rev.Lett. {\bf 107}, 145301 (2011). Large insulating gap of this system allows for examination of strong perturbations. We consider bichromatic perturbation along all axes on a triangular optical lattice. We find that ${\mathbb{Z}}_2$ topological character of the system is robust up to a certain depth of the deformation. The lowest band can become topologically trivial while the lowest two bands are always protected.