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.

Department(s)

Electrical and Computer Engineering

Sponsor(s)

Max-Planck Institute for Solid State Research

Comments

C.H.W. acknowledges financial support from Max-Planck Institute for Solid State Research at Stuttgart, Federal Republic of Germany.

International Standard Serial Number (ISSN)

0163-1829; 1098-0121

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 1991 American Physical Society (APS), All rights reserved.

Publication Date

01 Feb 1991

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