Coupled charge and valley excitations in graphene quantum Hall ferromagnets

TL;DR

This paper investigates charge and valley excitations in graphene quantum Hall ferromagnets, demonstrating the existence of valley skyrmions at fractional fillings through numerical calculations of excitation gaps.

Contribution

It extends quantum Hall ferromagnetism to fractional fillings in graphene and provides numerical evidence for valley skyrmion excitations using DMRG methods.

Findings

Numerical evidence of valley skyrmions in graphene.

Calculated excitation gaps extrapolated to thermodynamic limit.

Criteria established for skyrmion excitations in quantum Hall states.

Abstract

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states realize at integer fillings. Extending the quantum Hall ferromagnetism to the fractional filling case of massless Dirac fermions, we study the elementally charge excitations which couple with the valley degrees of freedom (so-called valley skyrmions). With the use of the density matrix renomalization group (DMRG) method, the excitation gaps are calculated and extrapolated to the thermodynamic limit. These results exhibit numerical evidences and criterions of the skyrmion excitations in graphene.