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 Number of Edge States
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abstract
We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
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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.