Defects Potentials for Two-Dimensional Topological Materials

TL;DR

This paper introduces a method to design defect potentials in two-dimensional materials like graphene to induce topological properties, providing a systematic way to generate and analyze topological zero-energy modes.

Contribution

It presents a novel approach to construct potential matrices that induce non-zero topological invariants, bridging continuum models and tight-binding descriptions for 2D materials.

Findings

Method successfully distinguishes topological from non-topological zero modes.

Application to graphene demonstrates defect-induced topological states.

Provides analytical tools for defect design in 2D topological materials.

Abstract

For non-topological quantum materials, introducing defects can significantly alter their properties by modifying symmetry and generating a nonzero analytical index, thus transforming the material into a topological one. We present a method to construct the potential matrix configuration with the purpose of obtaining a non-zero analytical index, akin to a topological invariant like a winding or Chern number. We establish systematic connections between these potentials, expressed in the continuum limit, and their initial tight-binding model description. We apply our method to graphene with an adatom, a vacancy, and both as key examples illustrating our comprehensive description. This method enables analytical differentiation between topological and non-topological zero-energy modes and allows for the construction of defects that induce topology.