Nonreciprocal Landau\u2013Zener tunneling

Sota Kitamura,Naoto Nagaosa,Takahiro Morimoto

doi:10.1038/s42005-020-0328-0

Sota Kitamura, Naoto Nagaosa + Show 1 more

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https://doi.org/10.1038/s42005-020-0328-0

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Abstract

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.

Highlights

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
We further consider the role of time-reversal symmetry T in the nonreciprocal responses
In the context of magnetochiral anisotropy[17,18,19,20,21], it has been discussed that the nonreciprocal transport requires the broken T in addition to the broken inversion symmetry

Summary

Introduction

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. The quantum mechanical wavefunctions of electrons form the band structure separated by the energy gaps, and the tunneling can occur between these bands when an electric field is applied. This is called Zener tunneling through the energy gap and has been actively studied[1,2,3,4,5,6,7,8,9,10,11,12,13]. P exp À eπ_δE2v; ð2Þ which is essentially singular with respect to E showing the nonperturbative nature of the quantum tunneling

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