Flat Energy Bands within Antiphase and Twin Boundaries and at Open Edges in Topological Materials

TL;DR

This paper introduces a model for topological materials exhibiting flat energy bands and localized states at boundaries and edges, with potential applications in guiding wave propagation in metamaterials.

Contribution

It presents a two-dimensional extension of the SSH model showing flat bands and localized states at boundaries, with analysis of their topological origins and controllability.

Findings

Flat one-dimensional zero-mode energy bands are localized within boundaries.

Localized states' group velocities are tunable by boundary spacing.

Guided wave propagation can be achieved through designed boundary paths.

Abstract

A model for two-dimensional electronic, photonic, and mechanical metamaterial systems is presented, which has flat one-dimensional zero-mode energy bands and stable localized states of a topological origin confined within twin boundaries, antiphase boundaries, and at open edges. Topological origins of these flat bands are analyzed for an electronic system as a specific example, using a two-dimensional extension of the Su-Schrieffer-Heeger Hamiltonian with alternating shift of the chains. It is demonstrated that the slow group velocities of the localized flat band states are sensitively controlled by the distance between the boundaries and the propagation can be guided through designed paths of these boundaries. We also discuss how to realize this model in metamaterials.