# Generalized Dirac structure beyond the linear regime in graphene

## TL;DR

This paper demonstrates that a generalized Dirac structure persists beyond the linear regime in graphene, revealing quantum gravity-like effects and Lorentz violation, which can be experimentally observed through higher-order Hamiltonian corrections.

## Contribution

It introduces a generalized Dirac framework beyond the linear approximation in graphene, linking it to quantum gravity scenarios and providing a method to detect related effects experimentally.

## Key findings

- Generalized Dirac structure survives beyond linear regime
- Emergent field theory mimics quantum gravity scenarios
- Higher-order Hamiltonian reveals observable quantum-gravity-like effects

## Abstract

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a fundamental minimal length (here graphene lattice spacing) and Lorentz violation (here the particle/hole asymmetry, the trigonal warping, etc.) is naturally obtained. We then show that the corresponding emergent field theory is a table-top realization of such scenarios, by explicitly computing the third order Hamiltonian, and giving the general recipe for any order. Remarkably, our results imply that going beyond the low-energy approximation does not spoil the well-known correspondence with analogue massless quantum electrodynamics phenomena (as usually believed), but rather it is a way to obtain experimental signatures of quantum-gravity-like corrections to such phenomena.