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arXiv · 2312.17357

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

Lucas Sourrouille
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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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Lucas Sourrouille. 2023-12-28. A note on degeneracy of excited energy levels in massless Dirac fermions. https://doi.org/10.1016/j.physleta.2024.129659

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