Landau-Zener tunneling problem for particles in periodic lattice

The Landau-Zener (LZ) problem plays an important role for the tunneling in nanoscale systems. Conventionally, the LZ formula is widely used for the calculation of the tunneling probability, and this formula is obtained by a linear approximation in the vicinity of the band edges for periodic lattice systems. Therefore, when we take into account the nonlinear effect by the periodic lattice, it is not sufficient for the calculation of the tunneling probability by the LZ formula. In this presentation, we report the LZ tunneling problem for particles bound in the periodic lattice [1]. To this end, we construct the path integral based on the Bloch and Wannier functions in the presence with an external force, and the transition probability is calculated for the Su-Schrieffer-Heeger model with a constant gap. Then, we find that the tunneling probability becomes drastically larger than that by the LZ formula. This enhancement is prominent for small values of the external field or small hopping integral, and comes from the difference between the Dirac and the periodic dispersions. [1] Ryuji Takahashi and Naoyuki Sugimoto, Phys. Rev. B 95, 224302(2017).