The Landauer conductance G between two appropriate contacts of a one-dimensional (1D, single-channel) ring with elastic scatterers is considered as function of an enclosed Aharonov-Bohm flux φ through the ring’s opening. It is demonstrated analytically and numerically that upon averaging over an ensemble of different microscopic systems prepared under the same macroscopic conditions, the basic period of G(φ) changes from ${\phi }_0$=hc/e to ${\phi }_0$/2. This agrees with existing experiments. It is also shown that self-averaging out of the ${\phi }_0$-periodic component is obtained at temperatures higher than a suitable energy-correlation range which is discussed in several regimes. Special effects due to the broad distribution of resistances are found numerically and understood theoretically. These may lead to a non-Ohmic size dependence of the conductance even at finite temperatures when a classical addition of many rings is valid.

• Received 5 December 1985

DOI:https://doi.org/10.1103/PhysRevB.34.659