Wavefronts Dislocations Measure Topology in Graphene with Defects

TL;DR

This paper introduces a method to identify topological phases in graphene by analyzing dislocation patterns in local electronic density caused by defects, linking these patterns to topological invariants.

Contribution

The authors demonstrate that dislocation patterns in electronic density reveal topological invariants in graphene with defects, providing a new diagnostic tool for topological materials.

Findings

Dislocation patterns encode topological invariants like Chern and winding numbers.

Topological defects produce distinct interference patterns in electronic density.

Non-topological defects, such as adatoms, do not produce these patterns due to Friedel oscillations.

Abstract

We present a general method to identify topological materials by studying the local electronic density $\delta \rho \left(\boldsymbol{r}\right)$. More specifically, certain types of defects or spatial textures such as vacancies, turn graphene into a topological material characterised by invariant Chern or winding numbers. We show that these numbers are directly accessible from a dislocation pattern of $\delta \rho \left(\boldsymbol{r}\right)$, resulting from an interference effect induced by topological defects. For non topological defects such as adatoms, this pattern is scrambled by Friedel oscillations absent in topological cases. A Kekule distortion is discussed and shown to be equivalent to a vacancy.