  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.
