  Shift current is a photovoltaic current in bulk noncentrosymmetric insulator.
Studies on shift current have so far focused on the extended Bloch waves, such
as in semiconductors and perovskites. In contrast, it is unknown whether the
localized wavefunctions support the dc photocurrent. Here, we show
theoretically that the dc shift current appears in a noncentrosymmetric
disordered one-dimensional insulator with random potential. When the light
illuminates the entire sample, the photocurrent forms in presence of the
electron-phonon coupling. We find this photocurrent remains robustly even when
the energy scale of random potential is larger than the bandwidth. On the other
hand, the photocurrent decays exponentially when the excitation is local, or
the relaxation is only due to the contact with the electrodes. These results
open a route to design high-efficiency solar cells and photodetectors.
