Geodesic
Fundamental solution of the~stationary Dirac equation with a~linear
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 349-367

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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
Mots-clés : graphene, quasiparticle. 
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     author = {I. Bogaevsky},
     title = {Fundamental solution of the~stationary {Dirac} equation with a~linear},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {349--367},
     publisher = {mathdoc},
     volume = {205},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a0/}
}
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I. Bogaevsky. Fundamental solution of the~stationary Dirac equation with a~linear. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 349-367. http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a0/