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 ($x\mathrm{/}{\epsilon }_F\ll 1$) 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 $x⪅m{p}_F\delta q$ 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 $1\le \gamma \le 2$.