  We investigate the shift current bulk photovoltaic response of materials
close to a band inversion topological phase transition. We find that the bulk
photocurrent reverses direction across the band inversion transition, and that
its magnitude is enhanced in the vicinity of the phase transition. These
results are demonstrated with first principles DFT calculations of BiTeI and
CsPbI$_3$ under hydrostatic pressure, and explained with an analytical model,
suggesting that this phenomenon remains robust across disparate material
systems.
