The bulk-dislocation correspondence for weak topological insulators on screw-dislocated lattices

TL;DR

This paper rigorously proves that weak topological insulators in three dimensions host protected gapless modes along screw dislocations using C*-algebra K-theory and coarse index theory.

Contribution

It provides a mathematical proof of the bulk-dislocation correspondence for weak topological insulators employing advanced operator algebra techniques.

Findings

Proof of the topological protected gapless mode along screw dislocations

Application of C*-algebra K-theory to topological insulators

Use of coarse index theory in topological physics

Abstract

A weak topological insulator in dimension $3$ is known to have a topologically protected gapless mode along the screw dislocation. In this paper we formulate and prove this fact with the language of C*-algebra K-theory. The proof is based on the coarse index theory of the helical surface.