  We study the entanglement harvesting between two identical buckled honeycomb
lattices placed inside a planar microcavity. By applying time dependent
perturbation theory, we obtain quantum correlations between both layers induced
by the cavity field. Considering the vacuum state as the initial state of the
cavity field and tracing out the time-evolved degrees of freedom, we analyze
the entanglement formation using the concurrence measure. We show that the
concurrence depends on the virtual photon exchanged and the positions of the
layer through the interlayer photon propagator. Furthermore, we find that the
formation of entanglement between equal energy electrons tends to be enhanced
when they move in perpendicular directions. Our results indicate that a buckled
honeycomb structure and a large spin-orbit interaction favor the entanglement
harvesting.
