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

Takahiro Morimoto,Naoto Nagaosa

doi:10.1038/s41598-018-20539-2

Abstract

In noncentrosymmetric crystals with broken inversion symmetry {boldsymbol{ {mathcal 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.

Highlights

Noncentrosymmetric crystals exhibit a variety of interesting physical phenomena
Based on general symmetry considerations, we show that nonreciprocal current response in crystals generally require two ingredients: (i) dissipation, and (ii) interactions
We show by using gauge invariant formulation of Keldysh Green’s function that nonreciprocal current generally requires some interactions

Summary

Results

Time reversal symmetry constrains nonreciprocal current responses in bulk crystals. Based on general symmetry considerations, we show that nonreciprocal current response in crystals generally require two ingredients: (i) dissipation, and (ii) interactions. We show that dc nonreciprocal current response does not appear when we do not incorporate effects of electron interactions that cause an effective change of the band structure under the applied electric field. KF,i are the Fermi momenta for the band 1 This change of the lesser Green’s function linear in E describes the effect of the applied electric field where the electron occupation is shifted in the momentum space as k → k + τE near the Fermi surface (with τ = 2π/Γ). This coincides with the picture of the semiclassical Boltzmann equation as illustrated in. Our approach may give a good approximation for nonlinear properties of those states, since the nonreciprocal current response is a nonequilibrium property near the ground state under a moderate electric field

Methods

We consider the onsite interaction that is given by

Additional Information