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.
@article{arxiv.2507.01530,
title = {Defects Potentials for Two-Dimensional Topological Materials},
author = {Yuval Abulafia and Amit Goft and Nadav Orion and Eric Akkermans},
journal= {arXiv preprint arXiv:2507.01530},
year = {2025}
}