Unified theory of the photovoltaic Hall effect by field- and light-induced Berry curvatures

Abstract

Photovoltaic Hall effect, i.e., generation of a photocurrent perpendicular to the bias electric field, is an interesting platform of Berry curvature engineering by external fields. Floquet engineering aims at generation of light-induced Berry curvature associated with topological phase transition in solids, which may manifest itself as a light-induced anomalous Hall effect. However, recent studies have pointed out a larger contribution by momentum asymmetry of photocarriers, termed a field-induced circular photogalvanic effect. Except for numerical studies, the two mechanisms have been described by different theoretical frameworks, hindering a coherent understanding. Here, we develop a unified theory of the photovoltaic Hall effect capable of describing both mechanisms on an equal footing. We reveal that the bias electric field alters the interband transition dipole moment and transition energy, both contributing to the field-induced circular photogalvanic effect in nonmagnetic materials. These effects are governed by an electric field-induced Berry curvature and the shift vector coupled to bias field, respectively. A resonant enhancement of the transverse photocurrent is found in GaAs owing to the topological character of the valence band. We also clearly distinguish the anomalous Hall effect by light-dressed states within the density matrix calculation using the length gauge. Our theory unifies a number of nonlinear optical processes in a physically transparent way and presents a geometric picture of the third-order nonlinear response under light and bias fields, shedding new light on Berry curvature engineering.