Vortex dynamics of charge carriers in the quasirelativistic graphene model : high-energy $\vec k\cdot \vec p$ approximation

Abstract

Within the earlier developed high-energy-$\vec k\cdot \vec p$-Hamiltonian approach to describe graphene-like materials the simulations of non-Abelian Zak phases and band structure of the quasi-relativistic graphene model with a flavors number $N=3$ have been performed in approximations with %of zero- and non-zero values of and without gauge fields (flavors). It has been shown that a Zak-phases set for non-Abelian Majorana-like excitations (modes) in Dirac valleys of the quasirelativistic graphene model is the cyclic group $\mathbf{Z}_{12}$. This group is deformed into $\mathbf{Z}_8$ at sufficiently high momenta due to deconfinement of the modes. Since the deconfinement removes the degeneracy of the eightfolding valleys, Weyl nodes and antinodes emerge. We offer that a Majorana-like mass term of the quasirelativistic model effects on the graphene band structure in a following way. Firstly the inverse symmetry emerges at "switching on"\ of the mass term, and secondly the mass term shifts the location of Weyl nodes and antinodes into the region of higher energies and accordingly the Majorana-like modes can exist without mixing with the nodes.