Effect of external magnetic field on thermal entanglement of spin-subband states in a Rashba nanowire

In this study the authors use the negativity to study the entanglement of electronic spin and thermally induced subband states inside a quasi-one-dimensional Rashba nanowire (of width in the order of 100 nm), to which a perpendicular uniform magnetic field is applied. To be clearer, it is assumed that the nanowire is held at a temperature T, so that all subband excitations, with definite probabilities, are present. The partially transposed density matrix is shown to be block-diagonal whose eigenvalues are readily obtained. It is shown that at least one of the eigenvalues is always negative, so that the system of electronic spin and subbands inside a Rashba nanowire is never separable. Moreover, it is shown that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement is maximal strongly depend on the magnetic field. The authors further present graphs of negativity, as functions of temperature, for different magnetic fields, indicating how this agent may be used to control the spin-subband entanglement.