  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.
