Anisotropic resistivity of the monolayer graphene in the trigonal warping and connected Fermi curve regimes

TL;DR

This study investigates the anisotropic resistivity of monolayer graphene across different energy regimes, revealing the roles of band structure and scattering effects in causing anisotropy beyond the Dirac point approximation.

Contribution

It provides a detailed analysis of how anisotropic resistivity in graphene depends on Fermi energy, highlighting the influence of trigonal warping and scattering matrix effects at various energy levels.

Findings

Anisotropic resistivity near Dirac points is minimal due to isotropic band energy.

Trigonal warping causes significant anisotropy at intermediate energies.

Scattering matrix effects dominate anisotropy at high energies.

Abstract

In the present study, the anisotropic resistivity of the monolayer graphene has been obtained in semiclassical regime beyond the Dirac point approximation. In particular, detailed investigations were made on the dependence of conductivity on the Fermi energy. At low energies, in the vicinity of the Dirac points, band energy of the monolayer graphene is isotropic at the Fermi level. Meanwhile, at the intermediate Fermi energies anisotropic effects such as trigonal warping is expected to be the origin of the anisotropic resistivity. However, besides the band anisotropy there also exists an other source of anisotropic resistivity which was introduced by scattering matrix. At high energies it was shown that the band anisotropy is less effective than the anisotropy generated by the scattering matrix. It was also shown that there exist two distinct regimes of anisotropic resistivity corresponding the trigonal warping and connected Fermi curve at intermediate and high energies respectively.