Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems

Abstract

We discuss an extension of the Resta's electronic polarization to non-Hermitian systems with periodic boundary conditions. We introduce the ``electronic polarization'' as an expectation value of the exponential of the position operator in terms of the biorthogonal basis. We found that there appears a finite region where the polarization is zero between two topologically distinguished regions, and there is one-to-one correspondence between the polarization and the winding number which takes half-odd integers as well as integers. We demonstrate this argument in the non-Hermitian Su-Schrieffer-Heeger model.

5 pages, 2 figures

References in corpus (4)

• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Origin of Non-Hermitian Skin Effects
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions

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• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• From Hermitian critical to non-Hermitian point-gapped phases