Topological states in a dimerized system with staggered magnetic fluxes

TL;DR

This paper explores novel topological states in a two-dimensional dimerized lattice with staggered magnetic fluxes, revealing anomalous bulk-boundary correspondence and unique edge and corner states that differ from conventional topological insulators.

Contribution

It introduces new topological phases with anomalous bulk-boundary relations in a dimerized lattice with staggered flux, expanding understanding of topological matter.

Findings

Isolated corner states with no fractional charge at half-filling

Metallic near-edge states in Chern insulator states

Robust edge states bypassing corners in quarter-filling topological state

Abstract

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.