Gauge-invariant theory for semiclassical magnetotransport through ballistic microstructures

Within the semiclassical theory of magnetotransport through ballistic cavit ies, fluctuations in the transmission amplitude and in the conductance orig inate from the Aharonov-Bohm phase of directed areas. We formulate the semi classical transmission amplitude in gauge-invariant form. The gauge invaria nt 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 po int and a virtual path leading back to the entrance point. We implement thi s method on different levels of a semiclassical description of magnetotrans port with applications to magnetoconductance fluctuations and correlations. The validity of the semiclassical theories is analyzed. [S0163-1829(99)109 03-2].