Gauge-invariant theory for semiclassical magnetotransport through ballistic microstructures

Within the semiclassical theory of magnetotransport through ballistic cavities, fluctuations in the transmission amplitude and in the conductance originate from the Aharonov-Bohm phase of directed areas. We formulate the semiclassical transmission amplitude in gauge-invariant form. The gauge invariant phases can be visualized in terms of areas enclosed by classical paths, which consist of the real path connecting the entrance point to the exit point and a virtual path leading back to the entrance point. We implement this method on different levels of a semiclassical description of magnetotransport with applications to magnetoconductance fluctuations and correlations. The validity of the semiclassical theories is analyzed. {copyright} {ital 1999} {ital The American Physical Society}