Nonvanishing sub-gap photocurrent as a probe of lifetime effects
For semiconductors and insulators, it is commonly believed that in-gap transitions into non-localized states are smoothly suppressed in the clean limit, i.e. at zero temperature their contribution vanishes due to the unavailability of states. We present a novel type of sub-gap response which shows that this intuition does not generalize beyond linear response. Namely, we find that the dc current due to the bulk photovoltaic effect can be finite and mostly temperature independent in an allowed window of sub-gap transitions. We expect that a moderate range of excitation energies lies between the bulk energy gap and the mobility edge where this effect is observable. Using a simplified relaxation time model for the band broadening, we find the sub-gap dc-current to be temperature-independent for non-interacting systems but temperature-dependent for strongly interacting systems. Thus, the sub-gap response may be used to distinguish whether a state is single-particle localized or many-body localized.