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

Abstract

a b s t r a c tIn 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.

Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene

“…The conic spectrum of graphene arising from Dirac Hamiltonian is valid only for the low energy region of band structure which describes the isotropic electronic properties of the charge carriers. However, by considering trigonal warp effect [2,18] which extends the continuum approach to the higher energies, the band structure becomes non-linear which yields some anisotropic properties in graphene [19,20]. Even the continuum model of phosphorene was constructed by considering the quadratic wavevectors [21,22], the contributions of higher order wave-vectors that increase the validity of continuum approach for the higher energies have never been discussed before.…”