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

TL;DR

This paper investigates the vortex dynamics of charge carriers in a quasirelativistic graphene model using a high-energy $oldsymbol{koldsymbol{ullet}}$ approximation, revealing topological phase transitions and the effects of Majorana-like modes on band structure.

Contribution

It introduces a high-energy $oldsymbol{koldsymbol{ullet}}$ Hamiltonian approach to analyze non-Abelian Zak phases and band topology in a quasirelativistic graphene model with flavor number N=3.

Findings

Zak-phases form a cyclic group $oldsymbol{Z}_{12}$ deformed to $oldsymbol{Z}_8$ at high momenta

Deconfinement of modes leads to emergence of Weyl nodes and antinodes

Majorana-like mass term shifts Weyl nodes to higher energies and affects symmetry

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.