Turning graphene into a lab for noncommutativity

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 $[X^i,X^j]=\mathrm{i}\hat{I}{¸}^{ij}$ and we find that $\hat{I}{¸}^{ij}={\ell }^2\hat{I}{\mu }^{ij}$, 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.

8 pages, no figures. Added new Section and references. It matches the published version