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Twisted double bilayer graphene is a compensated semi-metal near the chargeneutrality point with the presence of small electron and hole pockets in itsband structure. We show that strong Coulomb attraction between the electronsand holes can lead to the formation of indirect excitons. Condensation of theseexcitons at low temperature creates an excitonic metal with charge density waveorder for an appropriate range of interaction strength. This has interestingimplications for low-temperature transport in the system as a function ofcarrier density and temperature. The reorganization of the single particleexcitations and their density of states in the excitonic metal can lead topeaks in resistivity as a function of carrier density, recently seen inexperiments at low temperatures. The fluctuations of the Landau damped orderparameter in the quantum critical metal lead to non-Fermi liquid behaviour,which can explain the sublinear $T^{2/3}$ dependence of the resistance near thecharge neutrality point.

Excitonic Metal and Non-Fermi Liquid Behaviour in Twisted Double Bilayer Graphene near Charge Neutrality