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:1807.10778v2 [cond-mat.mes-hall]

Two-dimensional weak-type topological insulators in inversion symmetric crystals

“…where k 1 = k ⋅ a 1 and k 2 = k ⋅ a 2 are dimensionless lattice momenta. In good agreement with the ZPA results [18], the energy bands are calculated as fully gapped at (e, d x , d y ) = (1 3, 0, 1 3) and (e, d x , d y ) = (−1 3, 1 3, 0). Topological phase diagrams -Topological phase diagrams in d-space are calculated using the inversionsymmetry indicators (ν 0 ; ν 1 ,ν 2 ).…”

“…and 1D flat-band DW states -We argue that the ZPA 1D boundary modes are a physical manifestation of the DPs that wind the BZ. ZPA have shown that the DWs of the 2D SSH chain host the one-dimensional flat bands [18], which we reproduce in Fig. 4.…”

“…The advent of magic angle twisted bilayer graphene has renewed the interest in the realization of flat bands in diverse systems [15][16][17]. Notable examples include the recent study by Zhu, Prodan, and Ahn (ZPA) [18]. Utilizing the two-dimensional (2D) array of the Su-Schrieffer-Heeger (SSH) chains [19][20][21], ZPA have shown that one-dimensional (1D) flat bands can arise, being stabilized via the formation of topological domain walls (DWs).…”

A Lattice Litany for Transition Metal Oxides

“…This results in locally metallic filaments in a semiconducting host. In fact, the TB can be considered a 2D Dirac metal with flat electronic bands of edge states [39]. WOx provides an excellent example of quasi-periodic patterns of shear planes [40,41], and intriguingly, in a certain x regime, it is also a high-temperature superconductor, with the superconductivity probably strongest on the shear planes-recall the comments on possible filamentary superconductivity above, since dopant (polaronic) charges will preferentially decorate shear planes (and TBs).…”

Observation of Phase Controllable Majorana-like Bound States in Metamaterial-based Kitaev Chain Analogues

“…One of the two topological gapped phases, hosting mid-gap MZMs, occurs at |µ| < 2|ω| and ∆ > 0 and the other at |µ| < 2|ω| and ∆ < 0, while nontopological gapped phases arise at |µ| > 2|ω|. Mechanical systems of magnetically coupled spinners [43][44][45][46] have recently been used to simulate a number of electronic tight-binding Hamiltonians. The spinner ladder system pictured in Fig.…”