Effect of Rashba parameter on the thermal entanglement of electronic spin and induced subband states in a nanowire

In the present work we use the negativity to study the effect of Rashba parameter on the thermal entanglement of electronic spin and subband states inside a quasi-one-dimensional Rashba nanowire, in a perpendicular uniform magnetic field. We assume that the nanowire is held at a temperature T, so that both spin and subband states, with definite probabilities, are present. The partially transposed density matrix is shown to be block-diagonal, whose eigenvalues are readily obtained. By analyzing these eigenvalues, it is shown that, even at high temperatures there always exist negative eigenvalues, so that the system of electronic spin and subbands inside a Rashba nanowire is never separable. Moreover, we show that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement is maximal strongly depend upon the Rashba parameter. We further present graphs of negativity as functions of temperature for different Rashba parameters, showing that the maximal entanglement occurs at lower temperatures for larger Rashba parameters. The novel results in the present article shows how the behavior of spin-subband thermal entanglement depends upon an externally controllable agent.