Symmetry protected weak topological phases in a superlattice

TL;DR

This paper investigates weak topological phases in a superlattice Wilson-Dirac model, revealing symmetry-protected edge states sensitive to edge orientation and proposing Z2 indices for topological classification.

Contribution

It introduces a two-dimensional superlattice model exhibiting weak topological insulator phases protected by reflection symmetries, with new topological indices proposed.

Findings

Identification of symmetry-protected gapless edge states

Protection of phases by manifest and hidden reflection symmetries

Proposal of bulk Z2 indices for topological classification

Abstract

We explore novel topological phases realized in a superlattice system based on the Wilson-Dirac model. Our main focus is on a two-dimensional analogue of weak topological insulator phases. We find such phases as those characterized by gapless edge states that are protected by symmetry but sensitive to the orientation of the edge relative to the superlattice structure. We show that manifest and hidden reflection symmetries protect such weak topological phases, and propose bulk Z2 indices responsible for the topological protection of the edge states.