Weak-coupling theory for partial condensation of mobile excitons

We studied formation of charge density wave between valleys in a system with a double-well-like dispersive valence band relevant for the rhombohedral graphene trilayer. In a regime with 2 Fermi surfaces, electron- and hole-like: one of radius $p_i$, another of $p_o$, an instability in particle-hole channel appears at $q=q_c+\delta q$, where $q_c=p_o-p_i$. In a weak coupling regime ($x/\epsilon_F\ll 1$) presence of an additional energy scale $\propto m q_c\delta q$ gives rise to several regimes with distinct spectrum and transport properties: in a regime with small order parameter $x\lessapprox m p_F \delta q$ 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 different effective exponents $\gamma$ in conductance correction $\sigma\propto \tau_D^\gamma$ where $\tau_D$ is scattering time off disorder and $1\leq\gamma\leq 2$.