Entanglement formation in two-dimensional materials within microcavity

Abstract: In this work, the entanglement generation between two hexagonal-lattice layers embedded in a microcavity is studied, accounting for both electromagnetic coupling and intrinsic spin-orbit interaction (SOI). Utilizing a short-time dynamical approach, we perform a perturbative Taylor expansion of the reduced density matrix to characterize the bipartite quantum correlations between the hexagonal layers. We demonstrate that the system undergoes a rapid transition from a localized product state in the conduction bands at t = 0 to a coherent superposition of valence and conduction band states. Our results indicate that the degree of entanglement is highly sensitive to the interlayer photon propagator, which contains the geometric ratios of the layer positions and the height cavity, and the specific Fermi energy and SOI signatures of the respective layers. We show the emergence of spacelike-separated quantum correlations in the ultra-short evolution regime, suggesting that heterostructures in cavities may be suitable to develop experiments for a deep understanding of spacelike-separated quantum effects.