We compute the second-order correction to the electronic dispersion relation of a free electron gas interacting with an effective electron-dislocation potential, derived from a modern quantized theory of dislocations. Our results demonstrate that dislocation patterning induces anisotropic flat bands in the electronic dispersion under specific strain fields and directions, referred to as ``magic'' parameters. These flat bands acquire non-zero curvature as the strain or direction deviates from these magic parameters.
@article{arxiv.2504.07899,
title = {Dislocation Patterning as a Mechanism for Flat Band Formation},
author = {Aziz Fall and Kaushik Dayal},
journal= {arXiv preprint arXiv:2504.07899},
year = {2025}
}