Berry phase, conductance oscillations and phase breaking in mesoscopic transport

A novel class of interference phenomena originating from the geometric phase is discussed. Spin-orbit interaction results in the geometric phase and leads to the destructive interference and a phase shift of the Aharonov-Bohm conductance oscillations in ballistic and diffusive rings. In-plane magnetoresistance of rings exhibits abrupt "topological" transitions from destructive to constructive interference. The origin of the phase breaking due to the spin-orbit interaction in the weak localization conductance and in the universal conductance fluctuations is clarified.