Abstract

The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is paid to the equality of the spatial coordinates. We investigate the properties of the obtained nonlinear equation, in order to describe the high-temperature ferromagnetism in graphene without making any assumptions on the key role of defects of the structure in providing the effect. The numerical simulation is carried out for the simple boundary and initial conditions with the Lax–Friedrichs scheme as a result of which information is obtained on the dynamics of the electron density for a number of the simplest initial and boundary conditions.

中文翻译：

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石墨烯的非线性Dirac方程

摘要

考虑了为石墨烯的狄拉克方程引入非线性校正以充分描述集体电子现象的可能性。与该主题的其他论文相比，交互项包括了Spinor分量平方的和而不是它们的差。特别注意空间坐标的相等性。为了描述石墨烯中的高温铁磁性，而未对结构缺陷在提供效果中的关键作用作任何假设，我们研究了所获得的非线性方程的性质。