Skyrme and Wigner crystals in graphene

Abstract

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime })$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu$ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.

14 pages with 11 figures

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Cited by in corpus (24)

• Electronic Properties of Graphene in a Strong Magnetic Field
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Experimental determination of the energy per particle in partially filled Landau levels
• Contrasting Energy Scales of the Reentrant Integer Quantum Hall States
• Orbital and interlayer Skyrmions crystals in bilayer graphene
• Spin-valley skyrmions in graphene at filling factor $\nu =-1$
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• SU(4) Skyrmions in the $\nu =\pm 1$ Quantum Hall State of Graphene
• Pinning mode resonance of a Skyrme crystal near Landau level filling factor $\nu$=1
• Negative density of states: screening, Einstein relation, and negative diffusion
• Wigner crystal phases in bilayer graphene
• Local density of states of electron-crystal phases in graphene in the quantum Hall regime
• Zeeman coupling and screening corrections to skyrmion excitations in graphene
• Valley-kink in Bilayer Graphene at $\nu =0$: A Charge Density Signature for Quantum Hall Ferromagnetism
• Splitting of critical energies in the $n$=0 Landau level of graphene
• Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide
• Skyrme crystal in bilayer and multilayer graphene
• Collective Edge Modes of a Quantum Hall Ferromagnet in Graphene
• Landau-level composition of bound exciton states in magnetic field
• Wigner crystallization at graphene edges
• Excitation Gap of Fractal Quantum Hall States in Graphene
• Nuclear magnetic resonance line shapes of Wigner crystals in ${}^{13}$C-enriched graphene
• Two-dimensional bound excitons in real space and Landau quantization space: A comparative study