Semimetals with Fermi Velocity A˙ected by Exchange Interactions: Two Dimensional Majorana Charge Carriers

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 a˙ected 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