Peierls Instability in Hexagonal Lattices
Mathematical Physics
2025-10-30 v1 Materials Science
math.MP
Abstract
We investigate a conventional tight-binding model for graphene, where distortion of the honeycomb lattice is allowed, but penalized by a quadratic energy. We prove that the optimal 3-periodic lattice configuration has Kekul\'e O-type symmetry, and that for a sufficiently small elasticity parameter, the minimizer is not translation-invariant. Conversely, we prove that for a large elasticity parameter the translation-invariant configuration is the unique minimizer.
Keywords
Cite
@article{arxiv.2510.24230,
title = {Peierls Instability in Hexagonal Lattices},
author = {David Gontier and Thaddeus Roussigné and Éric Séré},
journal= {arXiv preprint arXiv:2510.24230},
year = {2025}
}