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Nonreciprocal Landau-Zener tunneling

Application of strong dc electric field to an insulator leads to quantum tunneling of electrons from the valence band to the conduction band, which is a famous nonlinear response known as Landau-Zener tunneling. One of the growing interests in recent studies of nonlinear responses is nonreciprocal phenomena where transport toward the left and the right differs. Here, we theoretically study Landau-Zener tunneling in noncentrosymmetric systems, i.e., the crystals without spatial inversion symmetry. A generalized Landau-Zener formula is derived taking into account the geometric nature of the wavefunctions. The obtained formula shows that nonreciprocal tunneling probability originates from the difference in the Berry connections of the Bloch wavefunctions across the band gap, i.e., shift vector. We also discuss application of our formula to tunneling in a one-dimensional model of a ferroelectrics.