Non-Abelian Currents in Quasi-Relativistic Graphene Model : General Theory

Abstract

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).