Topological Insulators and Superconductors from String Theory

Abstract

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and supercondutors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K-theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K-theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the $\theta$-term in various dimensions. This sheds light on topological insulators and superconductors beyond non-interacting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).

13 pages, 3 figures;references updated

References in corpus (20)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• On the $Z_2$ classification of Quantum Spin Hall Models
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Interaction effects and quantum phase transitions in topological insulators
• Gravity Dual of a Quantum Hall Plateau Transition
• ABJM with Flavors and FQHE
• Electric-Magnetic Duality and Topological Insulators
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Three-dimensional topological phase on the diamond lattice
• A Fractionalized Quantum Spin Hall Effect
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect