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.

arXiv comment5 pages, 2 figures

References in corpus (36)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological Photonics
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• The Quantum-Mechanical Position Operator in Extended Systems
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Electron Localization in the Insulating State
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Non-perturbative approach to Luttinger's theorem in one dimension
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Many-body approach to non-Hermitian physics in fermionic systems
• Quantum-Mechanical Position Operator and Localization in Extended Systems
• Quantized classical response from spectral winding topology
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions

Cited by in corpus (7)

• Topological Non-Hermitian skin effect
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Electronic polarization in non-Bloch band theory
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• From Hermitian critical to non-Hermitian point-gapped phases