SO(5) symmetry in the quantum Hall effect in graphene

2014/06/30 by Fengcheng Wu, Inti Sodemann, Yasufumi Araki +3 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Coulomb #Electron #Fractional quantum Hall effect #Geometry #Graphene #Graphene research and applications #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Spin (aerodynamics) #Symmetry (geometry) #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.90.235432

published as Phys. Rev. B 90, 235432 (2014) · 12 pages, 4 figures

arxiv created 2014/12/22 · openalex publication_date 2014/12/22 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions, which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants g_z and g_\ensuremath⊥. In this paper, we demonstrate that when g_z=\ensuremath-g_\ensuremath⊥, an exact SO(5) symmetry survives which unifies the N'eel spin order parameter of the antiferromagnetic state and the XY valley order parameter of the Kekul'e distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at \ensuremathν=0 to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor \ensuremathν=0 quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.

Citations

• SO(5)theory of antiferromagnetism and superconductivity
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Exact Realization ofSO(5)Symmetry in Extended Hubbard Models
• Quantum Hall Ferromagnetism in Graphene
• Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics
• Microscopic Electron Models with Exact SO(5) Symmetry
• Two soluble models of an antiferromagnetic chain

Cited by

• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU(N) symmetry
• Phases of one-dimensional SU(N) cold atomic Fermi gases—From molecular Luttinger liquids to topological phases