Topological Number of Edge States
arXiv:1602.05577 · doi:10.1103/PhysRevB.93.195166
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.
13 pages, 2 figures
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- Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
- Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry
- Gauge interactions and topological phases of matter
- Models for the BPS Berry Connection
- Instantons and Berry's connections on quantum graph
- Boundary Condition Analysis of First and Second Order Topological Insulators