Hidden topology in flat-band topological insulators: Strong, weak and square-root topological states

TL;DR

This paper uncovers a new class of topological states in flat-band insulators protected by hidden local chiral symmetries, deriving their invariants and revealing complex end modes including the first square-root topological insulator.

Contribution

It introduces hidden local chiral symmetries in topological insulators, derives their invariants, and demonstrates their role in protecting diverse end modes, including the novel square-root topological states.

Findings

Identification of hidden local chiral symmetries protecting topological states

Derivation of topological invariants for these hidden symmetries

Discovery of a square-root topological insulator as its own parent

Abstract

In this Letter, we study a previously unexplored class of topological states protected by hidden chiral symmetries that are local, that is, that protect against any off-diagonal disorder. We derive their related topological invariant for the first time, and show that these previously unidentified symmetries can act together with standard chiral symmetries to increase the protection of the end modes, using the Creutz ladder as an example. Finally, thanks to local hidden symmetries, we show that the diamond necklace chain can have three different types of topological end modes: strong, weak or square-root, with some of the states inheriting their topology from others. This marks the first time a square-root topological insulator is identified as its own parent.