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.

在绝缘体上施加强直流电场会导致电子从价带到导带的量子隧穿，这是著名的非线性响应，称为Landau-Zener隧穿。在非线性响应的最新研究中，越来越多的兴趣之一是不可逆现象，其中向左和向右的传输不同。在这里，我们从理论上研究非中心对称系统中的Landau-Zener隧穿，即没有空间反演对称性的晶体。考虑到波函数的几何性质，得出了一个广义的Landau-Zener公式。所获得的公式表明，不可逆的隧穿概率起源于跨越带隙的Bloch波函数的Berry连接的差，即位移矢量。