Weak-localization effects and conductance fluctuations: Implications of inhomogeneous magnetic fields

Low-temperature transport in disordered conductors exhibits a variety of fascinating quantum-mechanical interference effects associated with the phenomenon of weak localization. Such effects are typically isolated and probed by virtue of their sensitivity to applied homogeneous magnetic fields, which introduce Aharonov-Bohm phase factors into quantum-mechanical amplitudes. Analogous interference effects have been proposed in the context of the quantum transport of (possibly electrically neutral) particles with spin in the presence of inhomogeneous magnetic fields, which have the effect of introducing Berry phases. Thus, the possibility is raised of isolating and probing quantum interference effects through their sensitivity to the inhomogeneity of applied magnetic fields. In this paper we develop an approach to the study of quantum transport in disordered conductors in the presence of almost arbitrarily inhomogeneous magnetic fields, which is based on diagrammatic and semiclassical path-integral techniques and a subsequent adiabatic approximation. We illustrate these ideas with applications to three examples: anomalous weak-field magnetoconductance, conductance oscillations in mesoscopic multiply connected structures, and sample-dependent mesoscopic conductance fluctuations. Among other things, we find that while in the context of the disorder-averaged conductance it is accurate to regard systems as being composed of two independent subsystems (having spins aligned or antialigned with the local external magnetic field) a more interesting and refined structure emerges in the context of conductance fluctuations.