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Monolayer two-dimensional crystalline systems with broken inversion symmetry have shown unique optical response properties. We calculate the topological non-reciprocal photo-current in the nonlinear response of two-dimensional models involving the Berry connection in the presence of impurity scattering processes. Our results are based on quantum kinetic theory, where we calculate the nonequilibrium distribution function of the valence and conduction bands. We find the significant current peak emerges at the interband absorption threshold in the electron-doped system and the peak is remarkably sensitive to the electron density as well as the effective band masses. The current originates from trigonal warping, and increases when the warping hoping parameter increases as well the band masses . A nonlinear Hall response is equally obtained for certain model Hamiltonian parameters. Our findings provide an alternative platform for nonlinear light-matter interaction engineering.
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