A crystal without a center of symmetry is like a staircase where all the steps are tilted in the same direction: electrons, given a kick by light, roll predominantly in one direction. This is how a direct current is born — the photogalvanic effect. Until now, theorists could only describe the moment of light absorption, but not what happens next: how electrons collide, lose energy, and eventually form a stable flow.

The new work provides a complete picture. The authors built a method that tracks electrons over time, taking into account all quantum collisions: electrons scatter off lattice vibrations (phonons), transition between bands, and recombine with holes. For barium titanate, a classic piezoelectric, calculations showed that phonons make a significant contribution to the shift current — the current that arises from the displacement of electron clouds upon photon absorption.

The method also explains a puzzle from experiments: with ultrashort laser pulses, the photogalvanic current first flows in one direction, then in the other. It turns out that such a bipolar transient current arises because phonons interfere differently at different stages of the process. First, electrons are accelerated by light, and then the lattice gradually 'adjusts,' changing the direction of the total flow.

The connection between current and the geometry of quantum states, Berry curvature and quantum metric, becomes transparent. These quantities describe how the phase of the wave function changes as one moves through the Brillouin zone, and they determine the magnitude of the photogalvanic response. The practical benefit is obvious: accurate calculation will allow designing materials for solar cells operating on the bulk photogalvanic effect and for terahertz radiation detectors.