  The Hall conductivity given by the Kubo formula is a linear response of the
quantum transverse transport to a weak electric field. It has been intensively
studied for a quantum system without decoherence, but it is barely explored for
systems subject to decoherence. In this paper, we develop a formalism to deal
with this issue for topological insulators. The Hall conductance for a
topological insulator coupled to an environment is derived, the derivation is
based on a linear response theory of open system. As an application, the Hall
conductance of a two-band topological insulator and a two-dimensional lattice
is presented and discussed.
