Linear response of twisted bilayer graphene: Continuum versus tight-binding models

We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [Stauber, Phys. Rev. Lett. 120, 046801 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.046801] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous counterflow around the neutrality point, better interpreted as a paramagnetic response. We have addressed the differences between Drude and equilibrium response, and we showed that orbital paramagnetism is the equilibrium response to a parallel magnetic field over a substantial doping region around the neutrality point. Chirality also causes the equilibrium response to exhibit a nontrivial current structure associated with the nonvertical character of interlayer bonds in the tight-binding calculation.