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Marginal Fermi liquid in twisted bilayer graphene

Linear resistivity at low temperatures is a prominent feature of high-T$_c$ superconductors which has also been found recently in twisted bilayer graphene. We show that due to an extended van Hove singularity (vHS), the $T$-linear resistivity can be obtained from a microscopic tight-binding model for filling factors close to the vHS. The linear behavior is shown to be related to the linear energy dependence of the electron quasiparticle decay rate which implies the low-energy logarithmic attenuation of the quasiparticle weight. These are distinctive features of a marginal Fermi liquid, which we also see reflected in the respective low-temperature logarithmic corrections of the heat capacity and the thermal conductivity, leading to the consequent violation of the Wiedemann-Franz law. We also show that there is a crossover at $T \sim 6$ K from the marginal Fermi liquid regime to a regime dominated by excitations on the Dirac cone right above the vHS that also yields a linear resistivity albeit with smaller slope, in agreement with experimental observations.