Excitonic metal and non-Fermi liquid behaviour in twisted double bilayer graphene*

We show that twisted double bilayer graphene, whose band structure shows low energy electron and hole pockets, forms an excitonic metal near the charge neutrality point at very low temperatures ~ a few K. This leads to interesting implications for low-temperature transport in the system as a function of carrier density. Above the transition temperature, the density fluctuations in this critical metal lead to non-Fermi liquid features, which can also be seen in the temperature dependence of transport in the system. Similar features are also observed in recent experiments on these systems.