This article is cited in 4 papers

Fundamental solution of the stationary Dirac equation with a linear potential

I. Bogaevsky<sup>ab

a</sup> Lomonosov Moscow State University, Moscow, Russia
^b Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow, Russia

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.

Keywords: massless Dirac equation, semiclassical asymptotic behavior, fundamental solution, Green's matrix, parabolic cylinder function, graphene, quasiparticle.

PACS: 03.65.Pm

MSC: 35J08, 81Q20

Received: 15.07.2020
Revised: 15.07.2020

DOI: 10.4213/tmf9958

 English version: Theoretical and Mathematical Physics, 2020, 205:3, 1547–1563

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