Magnetoresistance in Granular Metals
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MAGNETORESISTANCE
IN GRANULAR METALS
W.L. MCLEAN Rutgers University, Serin Physics Laboratory, Piscataway,
P.O. Box 849,
NJ 08855
ABSTRACT
We review the origins of the magnetoresistance in
granular metals with
emphasis on the quantum coherence effects arising from the interference electrons
traveling by different
paths.
magnetoresistance expected from scaling arguments and observed in aluminum.
Two theories of the magnetoresistance
hopping regime,
of
We discuss the maximum in the
one based on the magnetic-field
in
granular
the variable range
induced shift
mobility edge and the other dealing with "directed" hopping,
of the
are compared
with experiments.
INTRODUCTION
Granular metals, a rich
variety
complexity. follows its contact,
as this week-long Symposium well demonstrates,
of properties This is
many of which themselves
exhibit
reveal great
certainly true of the magnetoresistance
when one
evolution from the metallic case where the grains are in close
then through the metal-insulation transition,
and finally on into
the hopping conduction regime where the grains are well separated. magnetoresistance in granular metals can be large and negative
(Ap/p
The - -1)
even though experience with impure simple metals might lead us to expect it to be small and positive.
The most obvious anticipated effect of a magnetic
field on an individual grain is
shrinkage of its
electron wavefunctions
which reduces overlap with neighboring grains and hence would also increase the resistance of the system. magnetoresistance,
particularly in
began with the work in
the late
However,
a proper understanding of the
the metallic regime of a granular system, 1970's
and early
localization in metals with increasing disorder localization in
(1].
1980's on the onset of The scaling theory of
particular [2] seemed of such wide generality that it
be directly applicable in
should
the case where the scale of the granularity was
smaller than the relevant length scales of the theory, scattering length or the "magnetic length",
LH,
where
such as the inelastic 2 LH = (tc/eH) [3]. As
Mat. Res. Soc. Symp. Proc. Vol. 195. 11990 Materials Research Society
118
the granular metal is grains,
made more disordered by reducing the concentration of
percolataion
After percolation
effects begin to affect the transport ceases,
electrical
electrons between disconnected concentrations
there is
the magnetoresistance
in
properties.
conduction occurs by hopping of
clusters
of grains.
At still
hopping from grain to grain.
smaller
Our understanding of
this case has been aided by theoretical attempts to
deal with the effects of a small magnetic field on variable range hopping in doped semiconductors.
One of the recent developments
the study of a directed-hopping
in
this area has been
effect on the magnetoresistance
discuss some experimental evidence
for the
analogue of this
and later we effect
in
a
granular metal.
It
is
not surprising that the magnetoresistance
in
spectrum of
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