Holographic classification of Topological Insulators and its 8-fold periodicity

Abstract

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.

19 pages, 4 Tables

References in corpus (5)

• 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
• 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

Cited by in corpus (4)

• On topological phases of spin chains
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• Electromagnetic and thermal responses of Z topological insulators and superconductors in odd spatial dimensions
• Holographic Wilson Loops, Dielectric Interfaces, and Topological Insulators