Creation of Bielectron of Dirac Cone: The Tachyon Solution in Magnetic Field

DOI: 10.4236/msce.2015.38010   PDF   HTML   XML   2,540 Downloads   2,956 Views   Citations


Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case, the separation of center of mass and relative motion is obtained. Landau quantization ε = ±B/ l for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for bielectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem (ε 2 < 0) is found. The continuum symmetry of Dirac equation allows perfect pairing between electron Fermi spheres when magnetic field is applied in Landau gauge creating a Cooper pair.

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Lokot, L. (2015) Creation of Bielectron of Dirac Cone: The Tachyon Solution in Magnetic Field. Journal of Materials Science and Chemical Engineering, 3, 71-77. doi: 10.4236/msce.2015.38010.

Conflicts of Interest

The authors declare no conflicts of interest.


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