Thermal entanglement of electronic spin–subband in a Rashba isotropic two-dimensional nanodot

• Thermal electronic spin–subband entanglement in a Rashba 2D nanodot is investigated.
• Introducing a Casimir operator, eigenstates of the total Hamiltonian are obtained.
• The combined system is entangled at zero temperature.
• Rising temperature, the entanglement suddenly dips and then increases.
• Rashba and magnetic fields strongly influence the entanglement at any temperature.

In the present report the thermal entanglement between electronic spin and subband states in a Rashba isotropic nanodot, under the action of a perpendicular magnetic field, is investigated. The nanodot is assumed to be in thermal equilibrium with a heat reservoir so that all electronic micro states (subbands plus spin states) with definite probabilities participate into the entanglement. Introducing a Casimir operator, C^, which commutes with the total Hamiltonian, it is shown that the Hamiltonian is block-diagonal, each of dimensions 2Ne+12Ne+1, where NeNe is an eigenvalue of C^. We then proceed to diagonalize each block so that the thermal (Gibb’s) density matrix, written in the bases of the total Hamiltonian, becomes block-diagonal as well. Consequently, a simple procedure to calculate the negativity, as a measure of thermal entanglement is developed. Our calculations show that the ground state of the combined system is an entangled one whose degree depends upon the externally controllable magnetic field and the Bychkov–Rashba (BR) parameter. Moreover, the thermal spin–subband entanglement exhibits a local minimum followed by a local maximum and asymptotically vanishes as the temperature is increased. The variation of the extrema as well as the rate at which the entanglement approaches zero, with the magnetic field and BR parameter are also discussed.