Abstract

We explicitly express the fundamental solution of the stationary two-dimensional massless Dirac equation with a constant electric field in terms of Fourier transforms of parabolic cylinder functions. This solution describes the flux of quasiparticles in graphene emitted by a pointlike source of electrons that are partially converted into holes (antiparticles). Using our explicit formula, we calculate its semiclassical asymptotic behavior in the hole region.

中文翻译：

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线性势的平稳Dirac方程的基本解

摘要

我们根据抛物柱面函数的傅立叶变换，明确表示具有恒定电场的平稳二维无质量Dirac方程的基本解。该解决方案描述了由点状电子源发射的石墨烯中的准颗粒通量，该电子源已部分转化为空穴（反颗粒）。使用我们的显式公式，我们计算其在孔区域中的半经典渐近行为。