Higher-order topological insulators in antiperovskites

Abstract

We predict that a family of antiperovskite materials realize a higher order topological insulator phase, characterized by a previously introduced ${\mathbb{Z}}_4$ index. A tight binding model and a $k\cdot p$ model are used to capture the physics of the bulk, surface and hinge states of these materials. A phase diagram of the higher order and weak topological invariants is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the crystal to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.

15 pages, 10 figures

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• Band Representations and Topological Quantum Chemistry
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• Floquet second-order topological insulators in non-Hermitian systems
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Helical Liquids in Semiconductors
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Classification of Dirac points with higher-order Fermi arcs
• Topology invisible to eigenvalues in obstructed atomic insulators
• Planar Hall effect with sixfold oscillations in a Dirac antiperovskite
• Perspective: Molecular beam epitaxy of antiperovskite oxides
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Higher order topology in a Creutz ladder
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Higher-order topological insulator in cubic semiconductor quantum wells