Characterization of topological insulators based on the electronic polarization with spiral boundary conditions

Abstract

We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize 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 (the lattice version of the Bernevig-Hughes-Zhang model) in the same way as in one-dimensional systems. Thus the polarization plays the role of "order parameter" to characterize the topological insulating state and enables us to study topological phases in different dimensions in a unified way.

5 pages, 3 figures

References in corpus (4)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Electric polarization in a Chern insulator

Cited by in corpus (9)

• Rigorous Index Theory for One-Dimensional Interacting Topological Insulators
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions
• One-dimensional projection of two-dimensional systems using spiral boundary conditions
• Electronic polarization in non-Bloch band theory
• Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
• Phase diagram of the Kitaev-Heisenberg model using various finite-size clusters
• Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem
• Nontrivial three-sublattice magnetization in the easy-axis spin-1/2 XXZ antiferromagnet on the triangular lattice