Effective interactions in twisted double-layer graphene in a microcavity

In this work a derivation of the effective interactions between two rotated graphene layers inside a microcavity is obtained. Assuming an electromagnetic wave clockwise-polarized, propagating along the z-axis and applying the Schrieffer-Wolff transformation, an explicit interaction between electrons in different graphene layers is obtained, where the interaction strength depends on the distance between layers, the cavity photon frequency and the rotation angle of the layers. Projecting over the low-energy sector, an effective Hamiltonian for each graphene layer introduces a resonance in the Fermi velocities and modify the dispersion relation near the Dirac point by introducing a bandgap. In the subspace of the double-layer graphene, the effective interaction is suitable to develop two-qubit devices with appropriate gate voltages.