Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses

Recent advancements in laser technology have spurred growing interest in nonlinear and nonequilibrium phenomena. Here, we investigate the geometric aspects of quantum tunneling and the nonreciprocal response, particularly focusing on the shift vector, in noncentrosymmetric insulators under a strong DC electric field. In insulators under a strong electric field, electrons undergoing Bloch oscillations interfere with each other by passing through different paths via Landau-Zener tunneling. We found that the interference effect due to multi-tunneling causes the oscillating nonreciprocal response that is significantly amplified with increasing electric field intensity. We also clarified the role of the shift vector in the interference conditions through an analysis of the nonequilibrium steady state. These results will contribute significantly to advancing a systematic understanding of quantum geometric effects in the nonperturbative regime.