Nonreciprocal Transport and Optical Phenomena in Quantum Materials

In noncentrosymmetric materials, the responses (for example, electrical and optical) generally depend on the direction of the external stimuli, called nonreciprocal phenomena. In quantum materials, these nonreciprocal responses are governed by the quantum geometric properties and symmetries of the electronic states. In particular, spatial inversion (Formula: see text) and time-reversal (Formula: see text) symmetries play crucial roles, which are also relevant to the geometric Berry phase. Here, we give a comprehensive review of the nonreciprocal transport and optical responses including ( a) the magnetochiral anisotropy, i.e., the nonlinear resistivity with respect to the electric field, in semiconductors and metals, ( b) the nonreciprocal transport in superconductors such as the nonreciprocal paraconductivity and the superconducting diode effect in bulk and Josephson junctions, and ( c) the second-order nonlinear optical effects in the electric field of light, including the geometric shift current in nonmagnetic systems, magnetic systems, and superconductors.