Wave function of perturbed Hamiltonian in graphene

Abstract

In this paper, we use the generalized Dirac structure beyond the linear regime of graphene. This is probed using the a deformation of the Dirac structure in graphene by the generalized uncertainty principle. Here, the Planck length is replaced by the graphene lattice spacing. As the graphene sheet is bounded by two boundaries, we analyze this system with suitable boundary conditions. We solve the perturbed Hamiltonian and derive the wave function for this system. We observe that the energy of this system gets corrected due to this deformation. We explicitly calculate these corrections to the energy of this system.