Fundamental limits of nonlinear optical processes in semiconductors: shift photocurrents and second harmonic generation

Second harmonic generation and shift currents are nonlinear optical effects occurring in noncentrosymmetric materials. The shift current is responsible for the generation of photocurrents in the bulk of single-phase materials, resulting in advantages over traditional photovoltaics, such as above-band gap photovoltages, and bulk photocurrent generation without the need for interface engineering. Despite numerous theoretical and experimental research efforts into these nonlinear optical effects, there has been no systematic investigation into their maximum attainable magnitude in solid-state materials. In this talk, we present analytic upper bounds on the second-order optical conductivities of noncentrosymmetric semiconductors. We show that this bound depends on the band gap, band width, and geometrical properties of the material in question, but do not involve its polarization. As a proof of principle, we perform first-principles calculations of the response tensors of a wide variety of materials, finding that the materials in our database do not yet saturate the upper bound. This suggests that new materials with large nonlinear responses will likely be discovered by future materials research guided by the factors mentioned in this work.