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As a new quantum state, topological insulators have become the focus ofcondensed matter and material science. The open system research of topologicalinsulators has aroused the interest of many researchers. Recently, manyaspects, especially experimental aspects, have been developed rapidly, such asprediction and discovery of many novel quantum effects and applications oftopological properties of new materials, but the theoretical research isslightly tough. In this paper, we study the response of topological insulatordriven by momentum-carrying single-mode field. We solve the ground state of thesystem after the addition of a single mode light field with adjustable photonmomentum. Specifically, We show that from the analytical solution of hallconductance compared with the closed system, there is an extra correction term,and hall conductance can no longer be expressed in terms of the chern number orthe weighted sum of the chern number. Furthermore, the topological propertiesare analyzed and discussed through the results of different instance with theirillustration. Such as, the phase transition point of topological phase isrobust to the environment, and the system still has topological phasetransition. It is expected to be realized or controlled by experiments, and ourobservations may contribute to its application and extension in condensedmatter physics and quantum statistical physics.

Response of open two-band systems to a momentum-carrying single-mode quantized field