Non-abelian aharonov–casher phase factor in mesoscopic systems

The matrix-valued Aharonov–Casher phase factor F_AC (related to the c-number Aharonov–Casher phase λ_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 Schrödinger equation, we relate F_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 find that the dependence of the conductance on the set of spin–orbit couplings is encoded only in the traceful part of F_AC (i.e., the Aharonov–Casher phase λ_AC). Moreover, we derive the closed expressions of the conductance and show them to be simple universal rational functions of the Aharonov–Casher phase. 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_AC. This analysis then suggests a direct way for an experimental access to this elusive quantity.