Transverse circular photogalvanic effect associated with Lorentz-violating Weyl fermions

Nonlinear optical responses of quantum materials have recently undergone dramatic developments to unveil nontrivial geometry and topology. A remarkable example is the quantized longitudinal circular photogalvanic effect (CPGE) associated with the Chern number of Weyl fermions, while the physics of transverse CPGE in Weyl semimetals remains exclusive. Here, we show that the transverse CPGE of Lorentz invariant Weyl fermions is forced to be zero. We find that the transverse photocurrents of Weyl fermions are associated not only with the Chern numbers but also with the degree of Lorentz-symmetry breaking in condensed matter systems. Based on the generic two-band model analysis, we provide a new powerful equation to calculate the transverse CPGE based on the tilting and warping terms of Weyl fermions. Our results are more capable in designing large transverse CPGE of Weyl semimetals in experiments and are applied to more than tens of Weyl materials to estimate their photocurrents. Our method paves the way to study the CPGE of massless or massive quasiparticles to design next-generation quantum optoelectronics.