Berry curvature induced linear electro-optic effect in chiral topological semimetals

Abstract

We studied the linear electro-optic effect of chiral topological semimetals which are characterized by high-fold chiral fermions separated in energy space. We identify that the general second-order conductivity ${\ensuremath{\sigma}}_{xyz}^{(2)}(\ensuremath{\omega})$ includes three sources from the shift current, injection current, and nonlinear anomalous current with frequency $\ensuremath{\omega}$, respectively. The ${\ensuremath{\sigma}}_{xyz}^{(2)}(\ensuremath{\omega})$ contributed by the nonlinear anomalous current is antisymmetric under the exchange of indices $x$ and $y$, and it is proportional to relaxation time and Chern number. We demonstrate that the electro-optic coefficient below 0.65 eV in chiral crystal RhSi is dominated by the nonlinear anomalous current and injection current, and it renders a relatively low half-wave voltage in the order of hundreds of volts. This work classifies how the Berry curvature modifies the linear electro-optic effect in chiral topological semimetals and opens an avenue to design the electro-optic modulator with half-wave voltage compatible with the complementary metal-oxide semiconductor circuit.