Fully consistent ab initio calculation of the shift current at steady state

The bulk photovoltaic effect (BPVE) is a process through which a homogeneous sample of a noncentrosymmetric material can generate a photocurrent. The effect is usually described in terms of two mechanisms: the ballistic current, where asymmetric scattering leads to unequal carrier generation rates at opposite momenta, and the shift current, where carrier excitation is accompanied by a net displacement in real space. However, the story does not stop there: after excitation, photoexcited carriers relax and recombine, forming a kinetic cycle at steady state. The relaxation and recombination processes are also predicted to produce photocurrent through a shift current mechanism, but so far, they have only been calculated in model systems. Thus, it is difficult to know the relative magnitude of the relaxation currents in comparison to the more commonly calculated excitation currents. To address this gap, we model photocurrents from the remainder of the kinetic cycle from first principles. In conjunction with existing ab initio descriptions of excitation shift and ballistic current, this allows us to make direct comparisons between different photocurrent contributions in real materials under realistic experimental conditions.