Measuring Space Deformation via Graphene under Constraints

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.