Nonlinear bulk photocurrent probe Z2 topological phase transition in noncentrosymmetric materials

Detecting topological phase transitions in bulk is challenging due to the limitations of surface-sensitive probes like ARPES. Here, we demonstrate that nonlinear bulk photocurrents, specifically shift and injection currents, serve as effective probes of $Z_2$ topological transitions in noncentrosymmetric materials. These photocurrents show a robust polarity reversal across the $Z_2$ phase transition, offering a direct optical signature that distinguishes strong topological phases from weak or trivial ones. This effect originates from a reorganization of key band geometric quantities, the Berry curvature and shift vector, on time-reversal-invariant momentum planes. Using a low-energy Dirac model, we trace this behavior to a band inversion in the time-reversal-invariant momentum plane that drives the topological transition. We validate these findings through tight-binding model for Bi${}_2$Te${}_3$ and first-principles calculations for ZrTe${}_5$ and BiTeI, where the topological phase can be tuned by pressure or temperature. Our results establish nonlinear photocurrent as a sensitive and broadly applicable alternative probe of $Z_2$ topological phase transitions.