  Twisted double bilayer graphene is a compensated semi-metal near the charge
neutrality point with the presence of small electron and hole pockets in its
band structure. We show that strong Coulomb attraction between the electrons
and holes can lead to the formation of indirect excitons. Condensation of these
excitons at low temperature creates an excitonic metal with charge density wave
order for an appropriate range of interaction strength. This has interesting
implications for low-temperature transport in the system as a function of
carrier density and temperature. The reorganization of the single particle
excitations and their density of states in the excitonic metal can lead to
peaks in resistivity as a function of carrier density, recently seen in
experiments at low temperatures. The fluctuations of the Landau damped order
parameter in the quantum critical metal lead to non-Fermi liquid behaviour,
which can explain the sublinear $T^{2/3}$ dependence of the resistance near the
charge neutrality point.
