A note on degeneracy of excited energy levels in massless Dirac fermions

Abstract

We propose a mechanism to construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presences of magnetic flux $\Phi$ localized in a restricted region of the plane. Using this mechanism we analyze the degeneracy of the existed energy levels. We find that the zero and first energy level has the same $N+1$ degeneracy, where $N$ is the integer part of $\frac{\Phi}{2\pi}$. In addition, and contrary to what is described in the literature regarding graphene, we show that higher energy levels are $N+m$ degenrate, beign $m$ the level of energy. In other words, this implies an indefinite growth of degenerate states as the energy level grows.