Dissipative non-adiabatic topological pumping in an open Floquet system

Motivated by recent experimental realizations of topological charge pumping in cold atoms, we theoretically study the Rice-Mele model with spatiotemporal disorder coupled to two leads using the Floquet Keldysh green’s function approach. The temporal disorder characterizes random motion of electrons due to a bath, with diffusive, sub-diffusive, or white noise as special cases. We obtain the pumped charge in the full range of drive frequency away from the adiabatic limit for different strengths of disorder, and for different temporal disorders. We quantify and discuss localization-delocalization transitions in the Floquet spectrum and their effect on the topological pumped charge.