Current-voltage characteristic and shot noise of shift current photovoltaics

We theoretically study the current-voltage relation, $I-V$ characteristic, of the photovoltaics due to the shift current, i.e., the photocurrent generated ${\it without}$ the external dc electric field in noncentrosymmetric crystals through the Berry connection of the Bloch wavefunctions. We find that the $I-V$ characteristic and shot noise are controlled by the difference of group velocities between conduction and valence bands, i.e., $v_{11}-v_{22}$, and the relaxation time $\tau$. Since the shift current itself is independent of these quantities, there are wide possibilities to design it to maximize the energy conversion rate and also to suppress the noise. We propose that the Landau levels in noncentrosymmetric two-dimensional systems are the promising candidate for energy conversion.