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

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