Band spectrum is D-brane

Abstract

We show that band spectrum of topological insulators can be identified as the shape of D-branes in string theory. The identification is based on a relation between the Berry connection associated with the band structure and the ADHM/Nahm construction of solitons whose geometric realization is available with D-branes. We also show that chiral and helical edge states are identified as D-branes representing a noncommutative monopole.

1+32 pages; 7 figures

References in corpus (8)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• The electronic properties of bilayer graphene
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Topological Insulators and Superconductors from String Theory
• Conic D-branes

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• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Gauge interactions and topological phases of matter
• Domain-wall, overlap, and topological insulators
• Dynamical characterization of topological phases beyond the minimal models
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Topological invariant of multilayer Haldane models with irregular stackings