# Momentum-Space Electromagnetic Induction in Weyl Semimetals

## TL;DR

This paper theoretically investigates how Berry curvature influences nonlinear optical responses in Weyl semimetals, revealing a robust, non-dissipative photocurrent driven by electromagnetic induction in momentum space.

## Contribution

It introduces a semiclassical Boltzmann approach to explain electromagnetic induction-induced photocurrents in Weyl semimetals, highlighting their robustness against decoherence.

## Key findings

- Photocurrent persists with short scattering times.
- Electromagnetic induction explains the nonlinear optical response.
- Second harmonic generation is analyzed under external fields.

## Abstract

We theoretically study the effect of the Berry curvature on the transport properties of Weyl semimetals in the nonadiabatic process, which results in nonlinear optical responses. In the adiabatic process, the Berry curvature, which involves the time derivative of the Bloch states, contributes to the transport properties such as the adiabatic Thouless pump. Although this effect is very weak in usual solids, it is enhanced in Weyl semimetals, where the Berry curvature contributes to observable nonlinear optical responses due to its nodal structure. In this paper, using semiclassical Boltzmann theory, we show that the d.c. photocurrent induced by the Berry curvature robustly persists even in the limit of short scattering time. We also show that the photocurrent is well explained as a consequence of the electromagnetic induction in momentum space. The results indicate that the electromagnetic induction gives rise to a non-dissipative photocurrent that is robust even when decoherence occurs within a time scale shorter than the periodicity of the light. We also discuss the second harmonic response of the a.c. current when the electron distribution is displaced from the ground state by an external field.