Conductance fluctuations in diffusive rings: Berry phase effects and criteria for adiabaticity

We study Berry phase effects on conductance properties of diffusive mesoscopic conductors, which are caused by an electron spin moving through an orientationally inhomogeneous magnetic field. Extending previous work, we start with an exact, i.e., not assuming adiabaticity, calculation of the universal conductance fluctuations in a diffusive ring within the weak localization regime, based on a differential equation that we derive for the diffuson in the presence of Zeeman coupling to a magnetic field texture. We calculate the field strength required for adiabaticity and show that this strength is reduced by the diffusive motion. We demonstrate that not only the phases but also the amplitudes of the $h/2e$ Aharonov-Bohm oscillations are strongly affected by the Berry phase. In particular, we show that these amplitudes are completely suppressed at certain magic tilt angles of the external fields and thereby provide a useful criterion for experimental searches. We also discuss Berry phase–like effects resulting from spin-orbit interaction in diffusive conductors and derive exact formulas for both magnetoconductance and conductance fluctuations. We discuss the power spectra of the magnetoconductance and the conductance fluctuations for inhomogeneous magnetic fields and for spin-orbit interaction.