A topological principle for photovoltaics

To realize an efficient solar cell without inhomogeneous doping, one would like to maximize the shift component of the bulk photovoltaic current, in noncentric semiconductors with wide band gaps. I achieve this maximization for a new class of topological insulators whose band topology is only compatible with a polar crystal class.  For such insulators, it is impossible to continuously tune the k-dependent electron-hole separation (or `shift vector') to zero throughout the Brillouin zone. Averaging the shift vector over high-symmetry cross-sections of the Brillouin zone gives exactly a rational multiple of a Bravais lattice vector.  Even with wide band gaps, the frequency-integrated shift conductivity greatly exceeds e^3/h^2, and is at least three orders of magnitude larger than the conductivity of  the prototypical ferroelectric BaTiO₃, challenging a widely-held expectation that small band gaps are necessary for large shift currents in topological materials.