Topologically Protected Edge States in Triangular Lattices

TL;DR

This paper explores topologically protected edge states in triangular lattices, revealing a new topological phase driven by crystalline symmetries and boundary effects, explaining recent experimental observations.

Contribution

It introduces a novel topological phase in triangular lattices based on crystalline symmetries and boundary conditions, expanding understanding of topological states beyond Berry curvature.

Findings

Identification of boundary-sensitive topological edge states

Explanation of recent bosonic experimental results

Demonstration of a new topological phase in triangular lattices

Abstract

We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the perspective of Berry curvature, but result instead from an interplay between crystalline symmetries and finite boundary effects. Regardless, we show such states are in a distinct topological phase, provided the gauge-dependent symmetries are maintained. Such a model describes a number of recent bosonic experimental demonstrations on triangular lattices, the physics for which has thus far eluded explanation.