Shift photocurrent induced by two-quantum transitions

A theory of the shift current induced by direct two-photon and indirect one-photon absorption is developed for noncentrosymmetric crystals. A formula is derived for the microscopic shifts of Bloch electrons induced by two-quantum processes. It is shown that the ratio of the two-photon photocurrent at the photon frequency omega to the photocurrent induced by direct one-photon transitions at the photon frequency 2 omega, as compared to the corresponding absorption-rate ratio, contains a large factor {ie152-1}omega/(2{ie152-2}omega - E (g)), where E (g) is the bandgap; i.e., these photocurrent can be comparable in order of magnitude. For crystals of T (d) symmetry, the photocurrents induced by one- and two-photon absorption are compared in terms of polarization dependence.