Entanglement between electronic states in silicene and photons

• Time evolution of entanglement between π-electrons and photons in silicene is reported.
• Intrinsic spin–orbit coupling (ISOC) and buckling effect (BE) are taken into account.
• Initial states with ISOC and BE of opposite signs show quantum phase transitions.
• Quantum phase transitions spontaneously occur when ISOC is equal to BE.
• Periodic plateaus of maximal entanglement are observed for high photonic excitations.

Temporal behavior of entanglement between electrons in silicene and single mode radiations is reported. We show that the corresponding total Hamiltonian and time evolution operators are block diagonal. Initial states are divided into two categories for which buckling and the intrinsic spin–orbit effects are either of opposite or the same signs. Negativity shows that π-electrons and photons periodically become entangled for both categories. The entanglement spontaneously shows abrupt variations when buckling and the spin–orbit effects are equal but opposite in sign, leading to quantum phase transitions. As photonic excitations increase, the entanglement exhibits plateaus of constant durations for such initial states.