  As a new quantum state, topological insulators have become the focus of
condensed matter and material science. The open system research of topological
insulators has aroused the interest of many researchers. Recently, many
aspects, especially experimental aspects, have been developed rapidly, such as
prediction and discovery of many novel quantum effects and applications of
topological properties of new materials, but the theoretical research is
slightly tough. In this paper, we study the response of topological insulator
driven by momentum-carrying single-mode field. We solve the ground state of the
system after the addition of a single mode light field with adjustable photon
momentum. Specifically, We show that from the analytical solution of hall
conductance 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 or
the weighted sum of the chern number. Furthermore, the topological properties
are analyzed and discussed through the results of different instance with their
illustration. Such as, the phase transition point of topological phase is
robust to the environment, and the system still has topological phase
transition. It is expected to be realized or controlled by experiments, and our
observations may contribute to its application and extension in condensed
matter physics and quantum statistical physics.
