In recent years, ``high-Tc'' superconductors have generated a frenzy of experimental and theoretical endeavours, motivated by the likelihood of spawning revolutionary technologies. Their mere existence challenges our present-day understanding of many facets of condensed matter physics. The particular features which distinguish this class of materials from conventional BCS superconductors have been well documented. Besides the extraordinarily high transition temperatures in excess of 120K, some of the more noteable differences include: anomalous normal-state properties, strong anisotropy, a very small coherence length and unconventional behaviour in the superconducting state.
Early experiments intended to answer some of the broader questions concerning the nature of the mechanism forming the basis for superconductivity in the high-Tc materials, yielded conflicting and questionable results. More recently, the experiments have become more reliable, mainly because of vast improvements in sample quality. Researchers now recognize that the inherent differences between high-Tc powders, thin films and single crystals, are significant enough that they must be accounted for when interpreting and comparing results. Furthermore, it is now understood that impurities play a major role in the outcome of many of these experiments, so that often only experiments done with the same sample are comparable.
Theories regarding the high-Tc compounds are divided into two major categories: ``Fermi liquid'' and ``non-Fermi liquid'' theories. The normal state of a conventional BCS superconductor is well described by a Fermi liquid. However, the anomalous normal-state properties of the high-Tc compounds hint at the possible absence of a Fermi surface in this class of materials. The interpretation of experimental measurements is dependent upon which class of theories one assumes. For now at least, there is an unwillingness to stray too far from conventional thinking and the successes of BCS theory, so that experimental results are usually interpreted in the context of Fermi liquid theories.
With the general assumption that the electronic ground state of the high-Tcsuperconductors is composed of paired charge carriers, determining the symmetry of the paring state has been the subject of much controversy. Despite many of the earlier reports, it is now generally agreed that conventional s-wave pairing of carriers is unlikely. The pairing state is almost certainly anisotropic, but beyond this, little is known for certain. A leading candidate in the high-Tc materials is the d-wave form of pairing called dx2-y2 [1,2]. For dx2-y2 symmetry, the wave-vector dependence of the energy gap which develops at the Fermi surface in the superconducting state is such that line nodes appear in the gap.
Measurements of the temperature dependence of the magnetic penetration
depth
are one way to probe the nature of the low-energy
excitations and the symmetry of the pairing state.
For an isotropic s-wave superconductor, the magnetic penetration
depth
varies exponentially at low
temperatures. Even if
the superconducting gap is anisotropic, as long as it does not vanish
anywhere on the Fermi surface, the penetration depth
will
still exhibit exponential behaviour at temperatures such that kB Tis less than the minimum value of the energy gap for excitations [3].
However, if the symmetry of the superconducting state is
dx2-y2,
with the associated line nodes running along the
cylindrical Fermi surface, Cooper
pairs can be broken more easily and
is expected to
change linearly with temperature at low temperatures
[4,5]. Recent microwave cavity perturbation
measurements of
(i.e.
)
on
high quality
single crystals show a strong
linear term below 30K [6]. Studies of
Tl2CaBa2Cu2O
single crystals also show a linear
dependence on T for
at low temperatures [7].
However, previous experiments in Bi2Sr2CaCu2O8 and
thin films showed a T2 dependence on
[8]. It has been pointed out that impurity scattering
in a
dx2-y2-wave superconductor can change the low-temperature
behaviour from
to
[5,6,7].
Muon spin rotation is the most direct way
to measure
(the penetration
depth in the ab-plane) in the bulk of the sample.
Unlike other techniques, which are performed in zero-static magnetic
field,
SR directly measures the magnetic field distribution
associated with the vortex lattice of a type II superconductor.
The penetration depth
is the length scale
over which magnetic flux leaks into the superconducting regions
around the vortex cores. The
SR technique provides a means
by which one can investigate not only the temperature dependence
of
,
but also its field dependence.
The difficulty in the
SR technique lies in the extraction of
from the measured data. Here, one relies heavily on a
phenomenological model of the magnetic field distribution and the
ability of the fitting program to extract the relevant parameters.
Previous SR studies on sintered powders and crystals of
,
which were of lower quality than the
ones used in this study, provide evidence in support of an
isotropic s-wave pairing state [9]. However,
impurities or other crystalline
imperfections could lead to
a T2 dependence. Furthermore,
conclusions regarding the pairing mechanism were based on the overall
behaviour of
rather than that in the low-temperature
regime. It has been argued that the temperature dependence of
at higher temperatures can be drastically altered by strong-coupling
corrections, impurity scattering,
the precise shape of the Fermi surface and gap
anisotropy [4].
A universal equation for
at all T < Tc,
based on the d-wave formalism, has yet to be determined.
One must rely solely on the low-temperature deviations from s-wave
theory, anticipated from purely qualitative arguments. Consequently,
conclusions with regard to the pairing mechanism in
requires precise low temperature data.
Previous
SR measurements of
either lacked good low-temperature data or were done on sintered powders.
Low-temperature measurements of
should also be able
to reconcile the nature of the nodes in the gap, if they do indeed
exist. That is to say, point nodes on the Fermi surface should be
distinguishable from the line nodes associated with
dx2-y2pairing [4].
This present study is
concerned with recent SR measurements of
in
single crystals of
.
Some words of caution must be provided
to the reader. Recent discovery of a significant
-
anisotropy in the magnetic penetration depth [10] may have a
dramatic influence on the interpretation of measurements of
.
Although the existence of
-
anisotropy is acknowledged in this study, it is not included in the
final analysis, as the matter is presently under investigation.
Also, during the final stages of this thesis there have been recent
suggestions that
is controlled by critical fluctuations
down to very low temperatures [11]. In this case, the
measured
has little to do with the pairing mechanism,
but is determined by the 3D XY and 2D XY universality
classes. This possibility is not discussed any further in this thesis.