Abstract:

Topological insulators are characterized by topological numbers of the fermion wave function, and provide gapless edge modes which result from the topological number. Here we demonstrate that a certain choice of the boundary condition of the topological insulators will give rise to Nahm construction of BPS monopoles, and the band structure of the fermion is found to be identical to the shape of D-branes which have topological charges. We generalize the notion of topological charge of the bulk to that of the edge states, and further found some examples where the edge state topological charges are given by nonAbelian monopoles. We describe generic boundary conditions of the topological insulators and discuss possible implication of the classification of the boundary conditions. The talk is based on a collaboration with Dr. Taro Kimura, arXiv:1602.05577 and arXiv:1509.04676.