The study of quantum transport in mesoscopic scale structures is today the subject of intense research. At these length scales the wave nature of the carriers is a fundamental physical component. The transport problem then necessarily needs to be studied in light of the full quantum mechanical theory which, for all but the most simple systems, can be hopelessly complex. However, by studying the symmetry properties of the system, the possible solution space can be greatly reduced. Such studies have been undertaken to derive analytical constraints on the spin resolved transmission amplitudes and polarisation vector in electron [1] and hole [2] waveguides. It was shown that the possibility to produce spin polarised current in these systems is determined by general symmetry relations independent of the particular details of the system. In order to illustrate these constraints, we will here present a study of quantum spin transport by electron and holes in the presence of randomly distributed scatterers, two-component magnetic fields produced by nano-scale magnetic elements, and with both Rashba and Dresselhaus spin-orbit interaction. To this end, we will employ an exact numerical method [3,4] to calculate the spin-resolved conductances, spin-polarisation of the transmitted flux, spin accumulations and zitterbewegung [5] in typical nanoscale waveguides of arbitrary scattering potential distributions. These examples will show the existence of reciprocal relations in the spin resolved conductances as well as spin polarisation vector under reversal of the non-uniform magnetic field distribution. We will further show that under certain symmetries the spin polarisation vanishes in arbitrarily complex structures. In particular, under time-reversal symmetry the spin polarisation vanishes identically, for both electrons and holes, whenever the outgoing lead from an arbitrary structure only supports a single spin degenerate channel.
[1] F. Zhai and H. Q. Xu, Phys. Rev. Lett. 94, 246601 (2005).
[2] P. Brusheim and H. Q. Xu, Phys. Rev. B 74, 233306 (2006).
[3] L. Zhang, P. Brusheim, and H. Q. Xu, Phys. Rev. B 72, 045347 (2005).
[4] L. Zhang, F. Zhai, and H. Q. Xu, Phys. Rev. B 74, 195332 (2006).
[5] P. Brusheim and H. Q. Xu, Phys. Rev. B 74, 205307 (2006). |