18 February 2002
Physics Letters A 294 (2002) 117–121
www.elsevier.com/locate/pla
Universal scaling of plateau width in the quantum Hall effect
F.Y. Huang
Advanced Semiconductor Technology Center (ASTC) and T.J. Watson Research Center, IBM, 1580 Route 52,
Hopewell Junction, NY 12533, USA
Received 1 May 2000; accepted 15 October 2001
Communicated by A.R. Bishop
Abstract
The plateau width in the quantum Hall effect follows a general scaling rule with ∆B/B
2
0
being a constant for all the filling
factors of integer intervals. This scaling rule can be derived based on the energy spectrum of two-dimensional electrons forming
a crystal lattice in the presence of a strong magnetic field.
2002 Published by Elsevier Science B.V.
PACS: 73.40.Hm; 72.20.My
Keywords: Two-dimensional electrons; Magnetic-field-induced localization; Magnetization; Quantum Hall effect
The quantum Hall effect (QHE) is characterized by
the precise quantization of the Hall resistance, ρ
xy
,
of two-dimensional (2D) electrons forming the so-
called Hall plateaus at certain applied magnetic field
such that the Landau-level filling factor ν
H
is either
an integer, as referred to as the integer QHE (IQHE),
or a rational fraction, as referred to as the fractional
QHE (FQHE) [1,2]. Accompanying the Hall plateau,
the longitudinal resistance ρ
xy
decreases and eventu-
ally vanishes as the temperature becomes sufficiently
low. Current understanding of the QHE includes the
formation of an impurity-induced mobility gap based
on a gauge invariance argument for the IQHE, and an
incompressible liquid with the elementary excitation
of a fractional charge for the odd-denominator FQHE
[3,4]. It was pointed out about ten years ago that there
exists a general scaling rule for the plateau width for
E-mail address: huangf@us.ibm.com (F.Y. Huang).
different filling factors, and a possible explanation has
been provided [5].
The previously derived scaling rule indicated that
the normalized plateau width ∆B/B
2
0
is a constant for
all the Landau-level filling factors of integer intervals.
And experimental data from different groups strongly
supported its validity when applied to the even-integer
QHE. The previous model was based on an analogy
between the QHE and the proximity-coupled super-
conducting Josephson-junction arrays. It was assumed
in Ref. [5] that the vanishing longitudinal resistance in
the QHE corresponds to the superconducting state in
the Josephson-junction arrays. And by further assum-
ing that the energy spectrum for the QHE is periodic
in the inverse of the flux quanta, the above scaling rule
can be derived.
However, the ground-stateenergyof the Josephson-
junction arrays in the presence of a magnetic field is
periodic in the magnetic field f with a period one
flux quantum per lattice cell [6,7], in contradiction
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