Nonlinear Phenomena in Complex Systems, 2015, Vol.18, No.2, pp.266-283

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2015, Vol.18, No.2, pp.266-283

Semimetals with Fermi Velocity Affected by Exchange Interactions: Two Dimensional Majorana Charge Carriers
Halina V. Grushevskaya and George Krylov

A theoretical approach to the band theory of two-dimensional (2D) semimetals within the self-consistent Dirac–Hartree–Fock field approximation has been developed. It reveals partially breaking symmetry of Dirac cone affected by quasi-relativistic exchange interactions for 2D crystals with hexagonal symmetry. Fermi velocity becomes an operator within this approach, elementary excitations are three-particle fermionic excitons described by Majorana rather than Dirac equation. Such features of the band structure of 2D semimetals as appearance of 4 pairs of Weyl-like nodes and Dirac cone replicas is shown to be naturally explained with the developed formalism.

Key words: two dimensional semimetals, Dirac–Hartree–Fock self-consistent field approximation, Fermi velocity operator, Dirac bands, Weyl-like nodes, Majorana charge carriers

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