Four-Terminal Phase-Coherent Conductance

A conductance formula for a sample of arbitrary shape with four terminals is derived to describe transport in the limit where carriers can traverse the sample without suffering phase-destroying events. The Onsager-Casimir symmetry relations are deduced. Experiments measure an off-diagonal Onsager coefficient and the magnetoconductance of such a sample is asymmetric even in the presence of an Aharonov-Bohm flux only. Symmetry relations between conductance measurements which exchange the role of current and voltage leads are predicted.