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In a mean-field-theory treatment the ground state of a graphene bilayer spontaneously breaks inversion symmetry for arbitrarily weak electron-electron interactions when trigonal-warping terms in the band structure are ignored. We report on a perturbative renormalization-group calculation, which assesses the robustness of this instability, comparing with the closely related case of the charge-density-wave instability incorrectly predicted by mean-field theory in a one-dimensional electron gas. We conclude that spontaneous inversion symmetry breaking in graphene is not suppressed by quantum fluctuations but that, because of trigonal warping, it may occur only in high quality suspended bilayers.
Zhang et al. (Mon,) studied this question.