Anomalous bulk photovoltaic effect in ferroelectrics: A quadratic response theory

We present a phenomenological description and a quantum-mechanical theory of electron transport in the anomalous bulk photovoltaic effect (ABPVE) in ferroelectrics. Our theory is based on a quadratic response formalism which leads to an exact expression for the short-circuit photovoltaic current (SCPVC). This theory indicates the existence of an ABPVE even in a system of pure Bloch states. We demonstrate the capability of our theory by performing an explicit calculation of the SCPVC for a one-dimensional model of independent impurities. From these results we conclude that sign changes of the SCPVC, as observed in BaTi${\mathrm{O}}_3$, are either due to impurities which have a bound excited state, or to Bloch states with two or more overlapping valence or conduction bands. There is evidence for both mechanisms.