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

• URL: http://arxiv.org/abs/2312.17357v3
• Date: Mon, 27 May 2024 17:04:31 GMT
• Title: A note on degeneracy of excited energy levels in massless Dirac fermions
• Authors: Lucas Sourrouille,
• Abstract summary: We construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presence of magnetic flux $Phi$ localized in a restricted region of the plane. We find that the zero and first energy level has the same $N+1$ degeneracy, where $N$ is the integer part of $fracPhi2pi$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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