Hierarchical Wentzel-Kramers-Brillouin quantization of nonseparable variables: Magnetic-flux effects in a varying width geometry

M. Ya Azbel, O. Entin-Wohlman

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The energy spectrum of a problem described by nonseparable variables is derived by an approximation procedure based upon the existence of small geometrical parameters. The method is exemplified for the states of an electron confined to a doubly connected, varying-width geometry in the presence of a magnetic field. It is shown that the spectrum includes extended states as well as states that are exponentially decaying over macroscopic parts of the sample, the latter yielding exponential quenching of the Aharonov-Bohm effect. The modifications introduced by a homogeneous magnetic field are analyzed; the Aharonov-Bohm periodicities of the states extending between the sample boundaries and the magnetic edge states are derived. The relevance to mesoscopic systems of varying dimensions is discussed.

Original languageEnglish
Pages (from-to)395-401
Number of pages7
JournalPhysical Review B
Volume41
Issue number1
DOIs
StatePublished - 1 Jan 1990
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics

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