Vortex Dynamics of Charge Carriers in the Quasi-Relativistic Graphene Model: High-Energy <inline-formula> <mml:math id="mm400" display="block"> <mml:semantics> <mml:mrow> <mml:mover> <mml:mi>k</mml:mi> <mml:mo stretchy="false">→</mml:mo> </mml:mover> <mml:mo>·</mml:mo> <mml:mover> <mml:mi>p</mml:mi> <mml:mo stretchy="false">→</mml:mo> </mml:mover> </mml:mrow> </mml:semantics> </mml:math> </inline-formula> Approximation

Abstract

Within the earlier developed high-energy- k → · 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 number of flavors N = 3 have been performed in approximations with 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 quasi-relativistic graphene model is the cyclic group Z 12 . This group is deformed into 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 quasi-relativistic model affects the graphene band structure in the following way. Firstly, the inverse symmetry emerges in the graphene model with Majorana-like mass term, and secondly the mass term shifts the location of Weyl nodes and antinodes into the region of higher energies.

Keywords

• graphene
• majorana-like equation
• majorana-like mass term
• non-abelian zak phase