Order from Disorder in Graphene Quantum Hall Ferromagnet

Abstract

Valley-polarized quantum Hall states in graphene are described by a Heisenberg O(3) ferromagnet model, with the ordering type controlled by the strength and sign of valley anisotropy. A mechanism resulting from electron coupling to strain-induced gauge field, giving leading contribution to the anisotropy, is described in terms of an effective random magnetic field aligned with the ferromagnet z axis. We argue that such random field stabilizes the XY ferromagnet state, which is a coherent equal-weight mixture of the $K$ and $K^{\prime }$ valley states. Other implications such as the Berezinskii-Kosterlitz-Thouless ordering transition and topological defects with half-integer charge are discussed.

4 pages, 2 figures

References in corpus (3)

• Electric Field Effect in Atomically Thin Carbon Films
• Two Dimensional Atomic Crystals
• Observation of Quantum Hall Valley Skyrmions

Cited by in corpus (12)

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• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Charge and Spin Transport at the Quantum Hall Edge of Graphene
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Charge 2e skyrmions in bilayer graphene
• Entanglement Skyrmions in multicomponent quantum Hall systems
• Valley polarization effects on the localization in graphene Landau levels
• Theoretical expectations for a fractional quantum Hall effect in graphene
• Splitting of critical energies in the $n$=0 Landau level of graphene