Turning graphene into a lab for noncommutativity

TL;DR

This paper proposes a method to simulate noncommutative geometry in graphene by incorporating lattice structure effects, enabling tabletop experiments to test theories of noncommutativity.

Contribution

It introduces a framework for modeling noncommuting position variables in graphene, extending previous Dirac-like quasiparticle dynamics to include noncommutative phase-space variables.

Findings

Derived the noncommutative parameter $ heta^{ij}$ as proportional to lattice spacing

Provided a general recipe for implementing noncommutative geometry in graphene

Suggested a practical setup for tabletop experiments to test noncommutative theories

Abstract

It was recently shown that taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, $(\vec{X},\vec{P})$, that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting $\vec{X}$, for which $[X^i,X^j] = \mathrm{i} \, \theta^{i j}$ and we find that $\theta^{i j} = \ell^2 \, \epsilon^{i j}$, with $\ell$ the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene.