Speaker: Masaaki Nakamura (Ehime University)

Date & Time: 2pm, Dec. 1, 2021.

Title: Application of the electronic polarization to topological insulators and non-Hermitian systems

Abstract:

The electronic polarization introduced by Resta is known as a good index to characterize the topology of the insulating states in one-dimensional lattice systems. It is also interpreted as an overlap between the ground state and the variational excited state appearing in the Lieb-Schultz-Mattis theorem. In this talk, we consider to apply the polarization to topological insulators and non-Hermitian systems. First, we discuss two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in one-dimensional order. We find that the sign of the polarization changes at topological transition points of the two-dimensional Wilson-Dirac model in the same way as in one-dimensional systems. Next, we discuss an extension to non-Hermitian systems. We point out that there appears a finite region, where the polarization is zero, between two gapped regions and there is a correspondence to the polarization and the generalized winding number which may take half integers. We demonstrate this argument in the non-Hermitian Su-Schrieffer-Heeger model.

References:

[1] M. Nakamura, S. Masuda, and S. Nishimoto, Phys. Rev. B 104, L121114 (2021).

[2] S. Masuda and M. Nakamura, arXiv:2109.10706.