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We have surveyed the in-plane transport properties of the graphene twistbilayer using (i) a low-energy effective Hamiltonian for the underlyingelectronic structure, (ii) an isotropic elastic phonon model, and (iii) thelinear Boltzmann equation for elastic electron-phonon scattering. We find thattransport in the twist bilayer is profoundly sensitive to the rotation angle ofthe constituent layers. Similar to the electronic structure of the twistbilayer the transport is qualitatively different in three distinct angleregimes. At large angles ($\theta > \,\approx\!\!10^\circ$) and at temperaturesbelow an interlayer Bloch-Gr\"uneisen temperature of $\approx 10$~K theconductivity is independent of the twist angle i.e. the layers are fullydecoupled. Above this temperature the layers, even though decoupled in theground state, are re-coupled by electron-phonon scattering and the transport isdifferent both from single layer graphene as well as the Bernal bilayer. In thesmall angle regime $\theta <\,\approx\!\!2^\circ$ the conductivity drops by twoorders of magnitude and develops a rich energy dependence, reflecting thecomplexity of the underlying topological changes (Lifshitz transitions) of theFermi surface. At intermediate angles the conductivity decreases continuouslyas the twist angle is reduced, while the energy dependence of the conductivitypresents two sharp transitions, that occur at specific angle dependentenergies, and that may be related to (i) the well studied van Hove singularityof the twist bilayer and (ii) a Lifshitz transition that occurs when trigonallyplaced electron pockets decorate the strongly warped Dirac cone. We examine therole of a layer perpendicular electric field finding that it affects theconductivity strongly at low temperatures whereas this effect is washed out byFermi smearing at room temperatures.

Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene