Non-Abelian Aharonov-Casher Phase Factor in Mesoscopic Systems

The matrix-valued Aharonov-Casher phase factor $F_{\text{AC}}$ (related to the c-number Aharonov-Casher phase $\lambda_{\text{AC}}$) plays an important role in the physics of mesoscopic systems in which spin-orbit coupling is relevant. Yet, its relation to experimental observables is rather elusive. Based on the SU(2)-gauge-invariant formulation of the Schroedinger equation, we relate $F_{\text{AC}}$ to measurable quantities in electronic interferometers subject to electric fields that generate Rashba or Dresselhaus spin-orbit coupling. Specifically, we consider electron transmission through (i) a single-channel ring interferometer and (ii) a two-channel square interferometer. In both examples, we derive the closed expressions of the conductance and show them to be simple rational functions of the traceful part of $F_{\text{AC}}$. In the second case, we also derive a closed expression for the electron spin polarization vector and find it to be a simple function of both the traceful and traceless parts of $F_{\text{AC}}$. This analysis then suggests a direct way for an experimental access to this elusive quantity.