Explanation for the isotropy of the Dirac cone in graphene

TL;DR

This paper demonstrates that Dirac cones in interacting electrons on a honeycomb lattice are inherently isotropic at low energies due to symmetry considerations, with implications for symmetry-breaking effects.

Contribution

It reveals that the isotropy of Dirac cones arises from the $Z_3$ subgroup of the $D_3$ symmetry group in the absence of spontaneous symmetry breaking.

Findings

Dirac cones are isotropic at low energies without symmetry breaking.

The isotropy is due to the $Z_3$ subgroup of $D_3$ symmetry.

Violations of $Z_3$ or sublattice symmetry affect cone isotropy.

Abstract

It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the $Z_3$ subgroup of the $D_3$ symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the $Z_3$ or the sublattice symmetry are discussed.