Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene

Abstract

Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $\nu =0,\pm 1$. Notably the ground state at $\nu =0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $\nu =\pm 1,0$ by using exact diagonalizations on the spherical geometry. If we neglect anisotropies we confirm the validity of the standard skyrmion picture generalized to four degrees of freedom. For filling factor $\nu =-1$ the hole skyrmion is an infinite-size valley skyrmion with full spin polarization because it does not feel the anisotropies. The electron skyrmion is also always of infinite size. In the F phase it is always fully polarized while in the AF phase it undergoes continuous magnetization under increasing Zeeman energy. In the case of $\nu =0$ the skyrmion is always maximally localized in space both in F and AF phase. In the F phase it is fully polarized while in the AF it has also progressive magnetization with Zeeman energy. The magnetization process is unrelated to the spatial profile of the skyrmions contrary to the SU(2) case. In all cases the skyrmion physics is dominated by the competition between anisotropies and Zeeman effect but not directly by the Coulomb interactions, breaking universal scaling with the ratio Zeeman to Coulomb energy.

14 pages, 9 figures, v2 : comments on experiments added, clarifications. Published version

References in corpus (19)

• Electric Field Effect in Atomically Thin Carbon Films
• Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Theory of integer quantum Hall effect in graphene
• Observation of Quantum Hall Valley Skyrmions
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• SO(5) symmetry in the quantum Hall effect in graphene
• Coupled charge and valley excitations in graphene quantum Hall ferromagnets
• Spin-valley skyrmions in graphene at filling factor $\nu =-1$
• Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach
• A Hartree-Fock study of the $\nu =0$ quantum Hall state of monolayer graphene with short range interactions
• NMR linewidth and Skyrmion localization in quantum Hall ferromagnets

Cited by in corpus (6)

• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Unveiling excitonic properties of magnons in a quantum Hall ferromagnet
• Topological quantum control: Edge currents via Floquet depinning of skyrmions in the $\nu =0$ graphene quantum Hall antiferromagnet
• Spontaneous Breaking of the SU(3) Flavor Symmetry in a Quantum Hall Valley Nematic
• Magnon scattering and transduction in Coulomb-coupled quantum Hall ferromagnets