Scaling behavior of charge and spin conductance of a two-dimensional network with Rashba spin-orbit coupling

We study the scaling behavior of a four-terminal square network made of quantum wires with Rashba spin-orbit (SO) coupling in which every node is formed by four wire sections. We numerically calculate the charge and spin-Hall conductance and find that the spin-Hall conductance can be much smaller or greater than the universal value, depending on the number of the input/output channels in every terminal and the strength of the SO coupling, as well as on the strength of the disorder. We also show that the charge conductance is insensitive to the spin-orbit coupling, but depends on the number of the input/output channels and the disorder strength. Furthermore, we study the spatial distribution of local angular momentum, the obtained patterns show fluctuations caused by scattering of the SO interaction and disorder.