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 appropiate gate voltages.

中文翻译：

---

微腔中扭曲双层石墨烯的有效相互作用

在这项工作中，获得了微腔内两个旋转石墨烯层之间有效相互作用的推导。假设电磁波顺时针极化，沿 z 轴传播并应用 Schrieffer-Wolff 变换，获得不同石墨烯层中电子之间的显式相互作用，其中相互作用强度取决于层间距离、腔光子频率和图层的旋转角度。投射到低能量部分，每个石墨烯层的有效哈密顿量会在费米速度中引入共振，并通过引入带隙来修改狄拉克点附近的色散关系。在双层石墨烯的子空间中，有效的相互作用适合开发具有适当栅极电压的双量子位器件。