Non-Bloch bands in two-dimensional non-Hermitian systems

The non-Bloch band theory can describe energy bands in a one-dimensional (1D) non-Hermitian system. On the other hand, whether be extended to higher-dimensional systems is nontrivial. In this work, we construct two classes of two-dimensional by reducing problem that for 1D model. these systems, get generalized Brillouin zone complex wave vector and investigate topological properties. model Chern insulator, as an example, show bulk-edge correspondence between number defined from appearance edge states.