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Vortex Dynamics of Charge Carriers in the Quasi-Relativistic Graphene Model: High-Energy k · p Approximation

Physics Department, Belarusian State University, 220030 Minsk, Belarus
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Symmetry 2020, 12(2), 261; https://doi.org/10.3390/sym12020261
Received: 6 November 2019 / Revised: 8 January 2020 / Accepted: 14 January 2020 / Published: 8 February 2020
(This article belongs to the Special Issue Vortex, Topology and Singularity in Quantum Systems)
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. View Full-Text
Keywords: graphene; Majorana-like equation; Majorana-like mass term; non-Abelian Zak phase graphene; Majorana-like equation; Majorana-like mass term; non-Abelian Zak phase
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Grushevskaya, H.; Krylov, G. Vortex Dynamics of Charge Carriers in the Quasi-Relativistic Graphene Model: High-Energy k · p Approximation. Symmetry 2020, 12, 261.

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