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Excitonic effects in twisted bilayer graphene

In the present work, we consider the excitonic effects in the twisted bilayer graphene (tBLG) within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interactions have been considered and the half-filling condition is imposed for the electronic densities is both layers of the bilayer. We calculate the excitonic pairing gap parameter and the chemical potential for different twist angles and different values of the interlayer Coulomb interaction parameter. Furthermore, we show the appearance of the electronic flat bands in the electronic band structure, mediated by the excitonic effects. We show that there is a doubling effect of the Dirac's $K$-point at the low interaction limit and one of Dirac's nodes is stable and the other one changes its position as a function of rotation angle. At the large twist angle limit, there appear two additional Dirac-like nodes at the $M$-point in the Brillouin zone. We show the excitonic red-shift effect of the principal Dirac's point $K$, in the low interaction limit, while, at the strong interactions, we get also the blue-shift effect at the $M$-point. Apart from the mentioned effects, the theory evaluated here predicts a metal-semiconductor transition in the tBLG system when augmenting the interlayer Coulomb interaction parameter.