Correlations in twisted double-layer graphene with virtual photons in a microcavity

We analyze the entanglement generation of a system composed of two decoupled rotated graphene layers inside a planar microcavity. By considering the electromagnetic field of the cavity in the vacuum state and using time-dependent perturbation theory it is possible to obtain the range of geometric parameters at which the quantum states of electrons in different layers are entangled. By employing the negativity measure, correlations between layers are obtained for time scales smaller than the light-crossing time of the layers. It is shown that the negativity measure is modulated by the rotation angle between layers, allowing manipulation ofXstates. Finally, an experimental protocol is analyzed in order to detect non-causal effects between layers, by allowing back-voltage switching functions in the two layers with supports that do not overlap in time. By turning off the second-back voltage at a time smaller than the light-crossing time, it is possible to obtain correlations between layers through the independent interaction with virtual photons. The exchange of virtual photons implies that the propagator can be nonzero outside the light cone and this non-causal propagation can create entangled quantum states.