Holographic classification of Topological Insulators and its 8-fold periodicity

TL;DR

This paper classifies topological insulators using Clifford algebra properties, reproduces the periodic table holographically, and identifies new candidate Z_2 topological insulators in specific symmetry classes and dimensions.

Contribution

It provides a holographic classification method for topological insulators based on Clifford algebras, avoiding topological invariants and K-theory, and predicts new Z_2 topological insulators.

Findings

Reproduces the periodic table holographically

Identifies candidate Z_2 topological insulators in specific classes and dimensions

Classifies Dirac Hamiltonians with protected zero modes

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.