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.
C. Wu and G. Mahler, "Quantum Network Theory of Transport with Application to the Generalized Aharonov-Bohm Effect in Metals and Semiconductors," Physical Review B (Condensed Matter), vol. 43, no. 6, pp. 5012-5023, American Physical Society (APS), Feb 1991.
The definitive version is available at https://doi.org/10.1103/PhysRevB.43.5012
Electrical and Computer Engineering
Max-Planck Institute for Solid State Research
International Standard Serial Number (ISSN)
Article - Journal
© 1991 American Physical Society (APS), All rights reserved.