  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.
