Effect of wavefunction delocalization on shift current generation

We derive upper bounds on the magnitude of shift photocurrent generation of materials in two limiting cases: the flat-band limit of almost-isolated systems such as molecular crystals, and the wide-band limit of one-dimensional or quasi-one-dimensional materials such as ferroelectric polymers or other materials with chain-like motifs. These bounds relate the magnitudes of the shift current bulk photovoltaic effect to materials parameters. In both cases, we find that ratio of electron hopping amplitudes to the band gap plays a vital role in maximizing the amount of nonlinear response. Furthermore, by using the Wannier function formalism, we quantify the effect of long-range hopping amplitudes, showing how delocalization of electronic states gives rise to larger photocurrents. These results inform the design and selection of new materials for large shift current generation. (paper)