Graphene and Single-walled CNT models with partial degeneracy of the Dirac bands: topological effects in charged carriers transport

H.V. Grushevskaya and G.G. Krylov

Faculty of Physics Belarusian State University


Models of graphene and single-walled carbon nanotubes (SWCNTs) are based on a previously developed theoretical approach to the band theory of two-dimensional semimetals within the self-consistent Dirac Hartree -Fock field approximation [1-3]. Fermi velocity becomes an operator, elementary excitations have been calculated in tight-binding approximation with taking into account of the exchange interactions of (p$_z$)-electron with its three nearest $\pi$(p$_z$)-electrons. These excitations are described by the massless Majorana equation instead of the Dirac one. Squared equation for this field is of a Klein-Gordon-Fock type. Zone-folding and tight-binding calculations of the band structure has been fulfilled with accounting of $\pi$(-electron orbitals. The models admit a Weyl type of charge carriers described by chiral bispinors. Since Weyl fermions in a pair have equal in absolute but opposite in sign values of pseudo- helicity (topological charge), due to the topological charge conservation law the Weyl fermions can decay only in pairs. Therefore, in contrast to the Dirac electrons and holes, Weyl fermions turns out to be long-lived quasiparticles. Stability of the band structure of the 2D materials is stipulated by the coupling of valley currents with pseudospins of chiral Weyl charge carriers. Such features of the band structure of 2D semimetals as appearance of pairs of Weyl-like nodes; partial removal of Dirac cone and replicas degeneration are shown to be naturally explained within the developed formalism. Since the Dirac cone replica are splitted into oppositely directed cones, monolayers of C atoms are 2D materials, in which pairs of Weyl massless fermions can be excited. Simulation of charge transport in these materials and SWCNTs has been performed. [1] Grushevskaya, H.; Krylov, G; Massless Majorana-Like Charged Carriers in Two-Dimensional Semimetals Symmetry, Vol. 8, 60 (2016). [2] Grushevskaya, H. V.; Krylov, G. G.; Low frequency conductivity in monolayer graphene model with partial unfolding of Dirac bands Low frequency conductivity in monolayer graphene model with partial unfolding of Dirac bands Int. J. Mod. Phys., Vol. 30, 1642009 (2016). [3] Grushevskaya, H. V.; Krylov, G . G .; Electronic Structure and Transport in Graphene: QuasiRelativistic Dirac-Hartree-Fock Self-Consistent Field Approximation In: Graphene Science Handbook: Electrical and Optical Properties. Vol. 3, chapter 9. Eds. M. Aliofkhazraei, N. Ali, W.I. Milne, C.S. Ozkan, S. Mitura, J.L. Gervasoni. (Taylor and Francis Group, CRC Press, USA, UK, 2016). Pp. 117-132.