Spin Rotations and Non-Abelian Phases in Quantum Wire Networks

We study quantum transport under the influence of both external magnetic fields and Rashba spin-orbit coupling. We consider two geometries-a straight wire and a ring structure. Our results reveal the precession of spin-polarized modes in the straight wire, and conductance resonances in the ring due to phase shifts from the magnetic field and from the Rashba effect. The conductance resonances arising from the Rashba effect are due to the non-Abelian nature of the phase shifts acquired by electrons propagating around the ring.