Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries

Abstract

We devote this work to the study of the mean-field phase diagram of the $\nu =0$ quantum Hall state in bilayer graphene and the computation of the corresponding neutral collective modes, extending the results of recent works in the literature. Specifically, we provide a detailed classification of the complete orbital-valley-spin structure of the collective modes and show that phase transitions are characterized by singlet modes in orbital pseudospin, which are independent of the Coulomb strength and suffer strong many-body corrections from short-range interactions at low momentum. We describe the symmetry breaking mechanism for phase transitions in terms of the valley-spin structure of the Goldstone modes. For the remaining phase boundaries, we prove that the associated exact $SO(5)$ symmetry existing at zero Zeeman energy and interlayer voltage survives as a weaker mean-field symmetry of the Hartree-Fock equations. We extend the previous results for bilayer graphene to the monolayer scenario. Finally, we show that taking into account Landau level mixing through screening does not modify the physical picture explained above.

44 pages, 10 figures

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Cited by in corpus (11)

• Gapless Spin Wave Transport through a Quantum Canted-Antiferromagnet
• Spin-Valley Coherent Phases of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Scattering of magnons at graphene quantum-Hall-magnet junctions
• Thermal Transport Signatures of Broken-Symmetry Phases in Graphene
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Continuous time crystal from a spontaneous many-body Floquet state
• Simultaneous symmetry breaking in spontaneous Floquet states: temporal Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator
• Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene