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 instabilities 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. © 2014 American Physical Society.