Theory of the bulk photovoltaic effect in pure crystals

A theory is presented for the intrinisic anomalous bulk photovoltaic effect observed in noncentrosymmetric crystals, e.g., BaTi${\mathrm{O}}_{3}$. An exact formula is derived for the calculation of the short-circuit photovoltaic current in a pure crystal in terms of its Bloch states and energy bands. Unlike a conventional field or diffusion current, the photovoltaic current is essentially determined by the change of wave functions upon photoexcitation of an electron from the valence to the conduction band. Our theory also reveals that the bulk photovoltaic effect can occur even in pure nonpyroelectric piezoelectric crystals, e.g., Te and GaP, which have no polar axis and therefore no a priori direction for the photovoltaic current.