Hall conductance for open two-band system beyond rotating-wave approximation

The response of the open two-band system to external fields would in general be different from that of a strictly isolated one. In this paper, we systematically study the Hall conductance of a two-band model under the influence of its environment by treating the system and its environment on equal footing. In order to clarify some well-established conclusions about the Hall conductance, we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. Specifically, we first derive the ground state of the whole system (the system plus the environment) beyond the RWA, then calculate an analytical expression for Hall conductance of this open system in the ground state. We apply the expression to two examples, including a magnetic semiconductor with Rashba-type spin-orbit coupling and an electron gas on a square two-dimensional lattice. The calculations show that the transition points of topological phase are robust against the environment. Our results suggest a way to the controlling of the whole system response, which has potential applications for condensed matter physics and quantum statistical mechanics.