We show that the Bardeen-Cooper-Schrieffer state (BCS) and the Bose-Einstein condensation (BEC) sides of the BCS-BEC crossover can be rigorously distinguished from each other by the extrema of the spectrum of the fermionic excitations. Moreover, we d
emonstrate that this formal distinction is realized as a non-equilibrium phase transition under radio frequency radiation. The BEC phase remains translationally invariant, whereas the BCS phase transforms into the supersolid phase. For a two-dimensional system this effect occurs at arbitrary small amplitude of the radiation field.
We derive the renormalization group equations describing all the short-range interactions in bilayer graphene allowed by symmetry and the long range Coulomb interaction. For certain range of parameters, we predict the first order phase transition to
the uniaxially deformed gapless state accompanied by the change of the topology of the electron spectrum.
