Abstract

We study low-energy massless electronic excitations in a graphene monolayer near a pointlike Coulomb impurity. We assume that such excitations are described by the Dirac model. We construct a family of self-adjoint Hamiltonians corresponding to these excitations for any charge of the impurity and perform their spectral analysis. It is shown that in this case, the structure of electron excitation spectra differs qualitatively from the corresponding spectra of massive excitations. The obtained results are used for analyzing the local surface density of electron states in graphene and its dependence of the choice of self-adjoint Hamiltonians.

中文翻译：

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接近库仑杂质的石墨烯中的无质量电子激发

摘要

我们研究了点状库仑杂质附近石墨烯单层中的低能量无质量电子激发。我们假设这种激发是由狄拉克模型描述的。我们为杂质的任何电荷构建了一系列与这些激发相对应的自伴随哈密顿量，并进行光谱分析。结果表明，在这种情况下，电子激发光谱的结构与相应的大量激发光谱有质的不同。所得结果用于分析石墨烯中电子态的局部表面密度及其对自伴随哈密顿量选择的依赖性。