Nonlinear Phenomena in Complex Systems, 2018, Vol.21, No.3, pp.278

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2018, Vol.21, No.3, pp.278 - 308

Non-Abelian Currents in Quasi-Relativistic Graphene Model : General Theory
Halina V. Grushevskaya, George Krylov, and Victor A. Gaisyonok

Earlier developed by authors a quasi-relativistic model of graphene is proved to be a 2D ℤ₂ × ℤ₄ topological semimetal model with a number of internal degrees of freedom (flavors) N = 3. Topological non-triviality of the model has been verified by simulation of non-abelian Zak phases accumulated on Wilson loops in the momentum space. Quantum statistical theory of non-abelian currents of Majorana-like charged carriers has been developed. Ohmic contribution to the current has been calculated as well as contributions stipulated by accounting of magnetoelectric effects (resulting in a Hall current) and polarization ones (via Zitterbewegung effect and Klein tunneling).

Key words: graphene, quantum transport, non-abelian currents, quasi-relativistic model, Dirac– Hartree–Fock self-consistent field approximation, Majorana-like equation

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