Derives dispersion relations for edge and hinge states from boundary conditions on Dirac lattice models and shows that nontrivial topology of a gapped edge state ensures a gapless hinge state.
Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
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abstract
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two topological invariants are defined. One is defined for the gapped bulk and edge Hamiltonians, and the non-triviality of the other means that the corner Hamiltonian is gapless. A correspondence between these two invariants is proved. Such gapped Hamiltonians can be constructed from Hamiltonians of 2-D type A and 1-D type AIII topological insulators, and its corner topological invariant is the product of topological invariants of these two phases.
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cond-mat.mes-hall 1years
2022 1verdicts
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Boundary Condition Analysis of First and Second Order Topological Insulators
Derives dispersion relations for edge and hinge states from boundary conditions on Dirac lattice models and shows that nontrivial topology of a gapped edge state ensures a gapless hinge state.