Weak localization in inhomogeneous magnetic fields

A theoretical analysis of weak localization in inhomogeneous magnetic fields is presented. The weak-localization correction to the classical conductivity is the result of interference effects characteristic of quantum-mechanical motion in a disordered conductor. The phase-coherence length, set by inelastic collisions, describes the spatial limit to single-particle quantum-mechanical interference. When this length exceeds the length scale over which the magnetic field is uniform the standard theory of the weak-localization magnetoresistance in a uniform magnetic field is no longer applicable. The coherent quantum-mechanical motion probes the inhomogeneity of the magnetic field, and the conductivity thus exhibits its nonlocal dependence on the magnetic field. The inhomogeneity of the magnetic field is shown to lead to observable changes in macroscopic quantities; one possible experimental method of testing the effects of weak localization in inhomogeneous magnetic fields is presented.