Network model for higher-order topological phases

TL;DR

This paper presents a two-dimensional network model that realizes a higher-order topological phase, featuring protected corner states and symmetry-based topological invariants, expanding the understanding of topological phases in network systems.

Contribution

The authors introduce a novel 2D network model that demonstrates higher-order topological phases with protected corner states and symmetry-based topological invariants, contrasting with conventional gapless network models.

Findings

16 protected corner states in the HOTP

Presence of a strong topological phase at maximal coupling

Symmetry-based topological invariants protect the phase

Abstract

We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination of a four-fold rotation, a phase-rotation, and a particle-hole symmetry. In addition, the model exhibits a strong topological phase at a point of maximal coupling. This behavior is in opposition to conventional network models, which are gapless at this point. By introducing the appropriate topological invariants, we show how a point group symmetry can protect a topological phase in a network. Our work provides the basis for the realization of HOTP in alternative experimental platforms implementing the network model.