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Excitonic instabilities and spontaneous time-reversal symmetry breaking on the honeycomb lattice

We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher order symmetries. Studies of such pairing instabilites have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fermi liquid excitations. We show that this relationship can be exploited to systematically derive the coupling of the condensate order-parameter to the intraband Fermi liquid particle-hole excitations. Surprisingly, we find that the static susceptibility is negative in the ordered phase when the coupling to the Fermi liquid collective excitations are included, suggesting that a uniform condensate of virtual excitons, with or without time reversal breaking, is an unstable phase at T=0.