Weak-coupling theory for partial condensation of mobile excitons in a layer with a double-well dispersion

We studied formation of charge density wave between valleys in a system with double-well-like dispersive valence band relevant for the rhombohedral graphene trilayer. In a regime with 2 Fermi surfaces, electron- and hole-like, an instability in particle-hole channel appears at q approximately equal to the difference of their Fermi momentums. In a weak coupling region, presence of an additional energy scale gives rise to several regimes with distinct spectrum and transport properties: in a regime with small order parameter Fermi arcs show up and substantially change conductance. At larger values of the order parameter Fermi arcs are gapped out. Regimes are also distinguished by qualtiatively different dependence of correction to the conductance on scatterring time.