Influence of Coulomb interaction on interband photogalvanic effect in semiconductors

The ballistic and shift contributions to the interband linear photogalvanic effect are calculated in the same band structure model of a noncentrosymmetric semiconductor. The calculation uses a two-band generalized Dirac effective Hamiltonian with the off-diagonal components containing $\mathbf{k}$-dependent terms of the first and second order. The developed theory takes into account the Coulomb interaction between the photoexited electron and hole. It is shown that in typical semiconductors the ballistic photocurrent $j^{(\mathrm{b}\mathrm{a}\mathrm{l})}$ significantly exceeds the shift current $j^{(\mathrm{s}\mathrm{h})}$: the ratio $j^{(\mathrm{s}\mathrm{h})}\mathrm{/}{j}^{(\mathrm{b}\mathrm{a}\mathrm{l})}$ has the order of $a_B\mathrm{/}\mathrm{\ell }$, where $a_B$ is the Bohr radius and $\mathrm{\ell }$ is the mean free path of photocarriers due to their quasi-momentum scattering.