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

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We devote this work to the study of the mean-field phase diagram of the ν = 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.
©2017 American Physical Society. We would like to specially thank E. Demler for his collaboration at the beginning the project. We also thank E. Shimsoni, P. Tikhonov, L. Brey, F. Guinea, F. Sols, and T. Stauber for useful discussions. This work has been supported by MINECO (Spain) through grants FIS2010-21372 and FIS2013-41716-P, Comunidad de Madrid through grant MICROSERES-CM (S2009/TIC-1476) and also partially by the Israel Science Foundation