Nonreciprocal current from electron interactions in noncentrosymmetric crystals: roles of time reversal symmetry and dissipation

In noncentrosymmetric crystals with broken inversion symmetry I, the I-V (I: current, V: voltage) characteristic is generally expected to depend on the direction of I, which is known as nonreciprocal response and, for example, found in p-n junction. However, it is a highly nontrivial issue in translationally invariant systems since the time-reversal symmetry T plays an essential role, where the two states at crystal momenta k and -k are connected in the band structure. Therefore, it has been considered that the external magnetic field (B) or the magnetic order which breaks the T-symmetry is necessary to realize the nonreciprocal I-V characteristics, i.e., magnetochiral anisotropy. Here we theoretically show that the electron correlation in T-broken multi-band systems can induce nonreciprocal I-V characteristics without T-breaking. An analog of Onsager's relation shows that nonreciprocal current response without T -breaking generally requires two effects: dissipation and interactions. By using nonequilibrium Green's functions, we derive general formula of the nonreciprocal response for two-band systems with onsite interaction. The formula is applied to Rice-Mele model, a representative 1D model with inversion breaking, and some candidate materials are discussed. This finding offers a coherent understanding of the origin of nonreciprocal I-V characteristics, and will pave a way to design it.