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

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.

arXiv comment5 page main text, 2 page supplemental material

References in corpus (35)

• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Experimental realisation of the topological Haldane model
• Experimental observation of Weyl points
• Observation of topological valley transport of sound in sonic crystals
• Dirac Line Nodes in Inversion Symmetric Crystals
• Quantum spin Hall effect of light
• Topological Boundary Modes in Isostatic Lattices
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Exciton-polariton topological insulator
• The Zak phase and the existence of edge states in graphene
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Topological phonon modes and their role in dynamic instability of microtubules
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Topological Insulators on the Lieb and Perovskite Lattices
• Observation of topological valley modes in an elastic hexagonal lattice
• Topological phases of generalized Su-Schrieffer-Heeger models
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators
• Anderson localisation in tight-binding models with flat bands
• Gapless interface states between topological insulators with opposite Dirac velocities
• Unified bulk-boundary correspondence for band insulators
• Electronic States of Graphene Grain Boundaries
• Polariton condensation in $S$- and $P$-flatbands in a two-dimensional Lieb lattice
• Theory and Experimental Investigation of the Quantum Valley Hall Effect
• Self-organized pseudo-graphene on grain boundaries in topological band insulators
• Zero Modes on Zero-Angle Grain Boundaries in Graphene

Cited by in corpus (6)

• Experimental realization of two-dimensional weak topological insulators
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
• Bismuth antiphase domain wall: A three-dimensional manifestation of the Su-Schrieffer-Heeger model
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Topological aspects in nonlinear optical frequency conversion