The fate of Z$_2$ topological insulator in optical lattices with disorder

Topological insulator is considered to be very robust against any perturbation which Doesn't break time-reversal invariant and there are now many proposal about creating such systems in cold atom area which one can have very good control for tuning it. Here we investigate the effect of disorder in the TI Z$_2$ system proposed in B. Beri and N. R. Cooper PRL 107, 145301 (2011) We show that under a strong disorder the system undergoes a topological phase transition.