Quantum network theory of transport with application to the generalized Aharonov-Bohm effect in metals and semiconductors

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Abstract
Quantum transport for resistor networks is developed with a general form factor, where each node point of the network is associated with a potential. The phase factor of the wave function in between two adjacent nodes is related to the reflection coefficient along that path. The exact transmission probability for a generalized Aharonov-Bohm ring is derived for a clean and cold crystal ring of arbitrary two-lead connections. The even- and odd-numbered rings have distinctly different transmission behaviors. The periodicity of the odd-numbered ring with respect to the threaded magnetic flux is shown to be double to that of an even-numbered one. The origin of this double periodicity is universal and is shown to be due to the standing wave produced by the two wave paths differing by odd-numbered lattice spacings at the Fermi energy. We also show that the double periodicity survives temperature averaging. Thus a mere one-atomic-spacing difference in electron paths of the ring will manifest itself in the difference of flux periodicity from the mesoscopic scale to the molecular scale.