A Novel Model for the Fractional Quantum Hall Effect
A Novel Model for the Fractional Quantum Hall Effect
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Date
2015-12-13
Authors
Arbab, Arbab I.
Journal Title
Journal ISSN
Volume Title
Publisher
UOFK
Abstract
A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional
quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained.
The two sequences are found to express a quantity and its complex conjugated partner. The oscillator
is found to have two degenerates states, ψn, with angular momenta ± n ~ , where h = 2π~ is the Planck’s constant,
and n is the principal quantum number of the oscillator. The filling factor, i, that Klitzing has found for
the integer quantum Hall effect (IQHE) is i = n + 1. Analytical expressions for longitudinal resistance and
Hall’s voltage are obtained. The width of the plateau between two states is found to be B = 1
n(n+1)
nsh
e , where
ns is the electron number density.
Description
Keywords
novel model,
fractional quantum,
Hall effect