Linear Magnetoelectric Electro-Optic Effect

In this work, we derive a generalized constitutive relation describing the current response to external electromagnetic fields in electrically biased quantum materials. While our semiclassical Boltzmann approach reveals the existence of electro-optic effects induced by the Berry curvature dipole of Bloch electrons, we also find a wealth of alternative electro-optic effects originating from the interplay between Berry curvature and magnetic moment. In particular, our symmetry analysis indicates the existence of a magnetoelectric electro-optic effect, derived from the simultaneous presence of Berry curvature and magnetic moment, that requires either time-reversal or inversion symmetry breaking. The revealed conductivity coefficients are explicitly written and we derive the tensor shape describing such alternative electromagnetic responses for chiral materials pertaining to space groups 152 and 198.