Measuring Space Deformation via Graphene under Constraints

TL;DR

This paper models the deformation of graphene under strain using noncommutative geometry, deriving energy spectra similar to magnetic effects, and proposes methods to measure the noncommutative parameter.

Contribution

It introduces a novel noncommutative geometric framework to describe strained graphene and links strain configurations to measurable noncommutative parameters.

Findings

Energy spectrum shows effective Landau levels due to strain.

Certain strain configurations can evaluate the noncommutative parameter.

Framework connects strain effects to noncommutative geometry in graphene.

Abstract

We describe the lattice deformation in graphene under strain effect by considering the spacial-momenta coordinates do not commute. This later can be realized by introducing the star product to end up with a generalized Heisenberg algebra. Within such framework, we build a new model describing Dirac fermions interacting with an external source that noncommutative parameter $\kappa$ dependent. The solutions of the energy spectrum are showing effective Landau levels in similar way to the case of a real magnetic field applied to graphene. We show that some strain configurations would be able to explicitly evaluate $\kappa$ and then offer a piste toward its measurement.