Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators

The precise determination of critical point is the basis to extract various critical properties of phase transitions. We identify that for two-dimensional inversion asymmetric insulators, with and without time-reversal symmetry, when topological phase transitions take place, all nonvanishing components of band-edge shift current tensor will reverse their signs in a singular way, regardless of what realistic value the temperature takes. This remarkable sign-reversal behavior of band-edge shift current tensor thus can be applied to determine the critical points of various topological phase transitions precisely, even for temperature-driven ones. We suggest concrete materials to test our predictions.