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

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 $g_{\perp }$. In this paper we demonstrate that when $g_z=-g_{\perp }$ an exact SO(5) symmetry survives which unifies the Néel spin order parameter of the antiferromagnetic state and the $XY$ valley order parameter of the Kekulé distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at $\nu =0$ 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 $\nu =0$ 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.

12 pages, 4 figures

References in corpus (11)

• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Interactions and phase transitions on graphene's honeycomb lattice
• Multicomponent fractional quantum Hall effect in graphene
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Interplay of Coulomb and electron-phonon interactions in graphene
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at $\nu =0$ in High Magnetic Fields
• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry

Cited by in corpus (14)

• Composite fermion duality for half-filled multicomponent Landau Levels
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• SU(N) fractional quantum Hall effects in topological flat bands
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Spin-valley entangled quantum Hall states in graphene
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Moiré Assisted Fractional Quantum Hall State Spectroscopy
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Two-component parton fractional quantum Hall state in graphene
• Uniquely identifying quantum Hall phases in charge neutral graphene