Polarization in Quasirelativistic Graphene Model with Topologically Non-Trivial Charge Carriers

Halina Grushevskaya,George Krylov

doi:10.3390/quantum4010001

Abstract

Within the earlier developed high-energy-k→·p→-Hamiltonian approach to describe graphene-like materials, the simulations of band structure, non-Abelian Zak phases and the complex conductivity of graphene have been performed. The quasi-relativistic graphene model with a number of flavors (gauge fields) NF=3 in two approximations (with and without a pseudo-Majorana mass term) has been utilized as a ground for the simulations. It has been shown that Zak-phases set for the non-Abelian Majorana-like excitations (modes) in graphene represent the cyclic Z12 and this group is deformed into a smaller one Z8 at sufficiently high momenta due to a deconfinement of the modes. Simulations of complex longitudinal low-frequency conductivity have been performed with a focus on effects of spatial dispersion. A spatial periodic polarization in the graphene models with the pseudo Majorana charge carriers is offered.

Highlights

Revolutionary progress in low dimensional physics is stipulated primarily by the discovery of graphene and related materials
The experimental facts [1] testify that the Fermi velocity vF in valleys K(K ) (Dirac points) of a monolayergraphene Brillouin zone is renormalized in the process of the Coulomb electron-electron interactions, and because of the weak screening the suspended-graphene dielectric constant G remains moderate: G ≈ 2.2 and 5 for the small and large charge concentrations n ∼ 109 and 1012 cm−2, respectively
The band structure of graphene within the quasirelativistic model with pseudo Majorana charge carriers hosts vortex and antivortex whose cores are in the graphene valleys K and K of the Brillouin zone, respectively

Summary

Introduction

Revolutionary progress in low dimensional physics is stipulated primarily by the discovery of graphene and related materials. The experimental facts [1] testify that the Fermi velocity vF in valleys K(K ) (Dirac points) of a monolayergraphene Brillouin zone is renormalized in the process of the Coulomb electron-electron interactions, and because of the weak screening the suspended-graphene dielectric constant G remains moderate: G ≈ 2.2 and 5 for the small and large charge concentrations n ∼ 109 and 1012 cm−2, respectively. A filling-dependent band flattening caused by the strong interactions between electrons in the bilayer graphene has been detected [6]. The fact that this phenomenon occurs at the rotation angles, well above the superconductivity magic angle, indicates the occurrence of the dielectric-polarization process, both in weak and strong screening regimes. The screening of the Coulomb electron-electron interactions calculated using a massless pseudoDirac fermion Hamiltonian within the Hartree-Fock approximation favors the graphene superconductivity [7,8]

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Conclusion