Work on artificially structured superconducting superlattices up to 1984 was reviewed by Ruggiero and Beasley.[209] Results in the superconductivity of artificial superlattices are much broader in variety than those in the TMDC and their intercalation compounds, encompassing such species as superconductor/superconductor (S/S'), superconductor/normal metal (S/N), superconductor/insulator (S/I), and superconductor/magnetic (S/M) compounds. A greater variety of materials combinations is possible with high-vacuum vapor-phase deposition techniques because the sample grower is no longer limited to phases which represent a global free-energy minimum. These new synthesis methods are just beginning to play a role in some areas of materials research, but they have already made possible real advances in the field of superconductivity.
Some parameters from a few of the many recent superlattice experiments are gathered in Table 2.3. It is not possible to make a neat summary of the superconductivity of the artificially structured superlattices the way it is possible for the TMDC's. The reason clearly is that for any two materials that might be chosen for use in a superlattice, a potentially unlimited range of thickness ratios can be used. This situation corresponds to having stages 1 through infinity in an intercalation compound. With modern preparation techniques, even the "stage 1" limit of alternate monolayers of two different materials may have been achieved in the Mo/Ta system.[160]
The category of S/I superlattices was the first to be investigated. Pioneering work was done on the Al/Ge system by Haywood and Ast.[105] The dimensionality crossover model of Klemm, Luther and Beasley[131] was developed specifically for the S/I case, where the interlayer coupling occurs through tunnelling of Cooper pairs through the insulating layers. The excellent agreement of the KLB model with Hc2(T) data for an S/I superlattice (Nb/Ge) is shown in Figure 2.4. The dimensional crossover here is more impressive than it was in the case of the TMDCIC's, where there were fewer data points on the 2D side of the curve.
Figure 2.4: Evidence for dimensionality
crossover in a Nb/Ge superlattice.[208] Solid lines are fits to the
KLB theory.[131] The
direction marked ``||'' means _|_ ^c in the vernacular of
GIC's and the direction marked ``_|_'' is || ^c in GIC terms.
The Hc2 data marked _|_ is almost unaffected by
the dimensionality crossover. The Hc2 data marked
|| covers the range from the fully 3D regime (45 Å/ 7
Å specimen) to the fully 2D regime (45 Å/ 50
Å specimen). The intermediate 65 Å/35 Å
specimen shows a crossover from 3D to 2D character as the
temperature is lowered.
More recent studies have concentrated on S/S' and S/N
multilayers with niobium as one element. The
Josephson-tunnelling theory does not apply quantitatively to
these other types of superlattices, because they are coupled
through the superconducting proximity effect. The S/N and
S/S' multilayers are described by new proximity-effect
theories.[22,235] Although these new models
differ in detail from the KLB model, the basic physics of the
progressive decoupling of superconducting layers at low
temperatures remains the same. The root cause of the
low-temperature decoupling of superconducting layers is the
decrease of the coherence length in each case. A
dimensionality crossover has been observed in the critical
field behavior in several different systems, including the
S/N systems Nb/Cu,[42], and
V/Ag,[126] and the S/S'
system Nb/Ta.[30] In
these materials, as in the TMDCIC's and S/I multilayers, the
crossover is manifested by a discontinuity in the temperature
dependence of the critical field. The identification of the
kink in Hc2(T) with an effective dimensionality
change is confirmed by the good agreement obtained by several
groups[42,30] with the different
approximate temperature dependences expected in the two
regimes, namely the (1-t)1/2 dependence in the 2D
temperature region and the linear dependence near
Tc. The linear-to-square-root change in the
temperature dependence in the Nb/Ta multilayers is shown in
Figure 2.5.
Figure 2.5: Hc2(t) data on Nb/Ta
superlattices showing two low-temperature critical field
discontinuities. From Ref. [30]. The discontinuity in slope
at t 0.8-0.9 is the 3D-2D coupling change. The identity of
the lower transition at t = 0.49 has not been definitely
determined.
Figure 2.5 also demonstrates that the S/S' and S/N systems display additional phenomena besides the coupling-dimensionality change. The Nb/Ta multilayers show a second low-temperature critical field discontinuity after they have already become 2D-coupled. The origin of this second discontinuity is currently uncertain. It may be due to a shift of the flux-line-lattice from one set of layers to the other.[236,28] There is obviously a lot of interesting work left to be done on the S/N and S/S' multilayers.
In addition to the strong experimental confirmation of a dimensionality crossover from the Hc2(T) measurements, there is also positive corroboration from Hc2(theta) data. The Nb/Cu and Nb/Ta superconductors not only are fairly well-fit by Eqn. 4.3 in the temperature range where their behavior is three-dimensional, but they also are well-fit by Tinkham's formula (Eqn. 4.9) in their 2D-coupled range.[42,30] The agreement of the two different Hc2(theta) formulae with Nb/Ta data in the two different temperature regions is displayed in Figure 2.6. The observation of a change in the coupling dimensionality in both the Hc2(T) and Hc2(theta) measurements is strong evidence that the KLB model contains the right physics.
Figure 2.6: Hc2(theta)
data on Nb/Ta superlattices from Ref. [29]. The data is for three
samples at a reduced temperature t = 0.9. Lambda is
the bilayer period, which corresponds to Ic in the
GIC case. Data in the trace marked 3D are fit with Eqn. 4.3
while data in the traces marked 2D are fit with Eqn.
4.6.
Interpretation of the angular dependence of the superconducting superlattices is not as clear-cut as the temperature dependence, where more universal behavior is seen. As shown in Figure 2.6 in the crossover region neither the 3D nor 2D formulae fits well. Chun et al. found a continuous variation between the 2D-type and 3D-type Hc2(theta) behavior. Ruggiero et al. observed better agreement with Tinkham's formula in both the 2D and 3D regions of temperature.[208] While the agreement of theory and Hc2(theta) experiments for some of the S/I and S/N systems at most temperatures is gratifying, it is clear that the behavior of Hc2(theta) in anisotropic superconductors is not completely understood.[30,208] The agreement between the Hc2(theta) data and the two available formulae is usually at the semiquantitative level in the artificially structured superlattices, while the agreement in Hc2(T) is usually quite good quantitatively.[208] Quite possibly a calculation of the angular dependence of Hc2 near the dimensionality crossover in terms of the KLB and the proximity models would solve all these discrepancies. Such calculations have not been performed up to this point.
Another somewhat puzzling aspect of the superconducting superlattice experiments is the positive curvature often observed in Hc2, || ^c. Such positive curvature has been seen in both the Nb/Cu and Nb/Ta systems.[42,30] The coupling-dimensionality change should have no effect on Hc2 when the field is applied perpendicular to the layer planes since this critical field is determined solely by the in-plane transport properties. Broussard and Geballe[30] have attributed this positive curvature to the Fermi surface anisotropy of the Nb layers since it is similar to the positive curvature of Nb thin films. Biagi, Kogan, and Clem, on the other hand, say that the positive curvature seen in Hc2, || ^c is due to the proximity effect.[22]
Many interesting experiments have been performed on the superconducting multilayers besides the critical field experiments, as Table 2.3 suggests. The most relevant of these for the GIC work is the measurement of Tc for different layer thicknesses. An example is shown in Figure 2.7, where Tc is plotted versus layer thickness for the Nb/Cu multilayers. For large layer thicknesses, the increase of Tc with increasing thickness of the superconducting component is in accord with the predictions of standard proximity-effect theories.[49,54] The standard proximity-effect prediction is indicated by the solid line. For small layer thicknesses, the proximity theory needs some modifications to explain the data. The dashed line is also a proximity-effect calculation, but it incorporates a thickness-dependent Tc for the individual Nb layers.[14]
Note that the proximity effect is a feature of all interfaces formed by superconductors. It should not be confused with proximity coupling, which is a manifestation of the proximity effect that occurs only in the S/N and S/S' superlattices. Proximity coupling is the interlayer interaction in S/N superlattices which is mediated by the diffusion of Cooper pairs across the N layer. S/I interfaces can also exhibit the proximity effect, but proximity-effect depression of Tc is quite small there. The size of the proximity-effect depression of Tc goes as the factor eta, which is the ratio of the normal-state conductivities of the normal and superconducting layers (eta = sigmaN / sigmaS).[208,54] Thus proximity effects are almost negligible at S/I interfaces. Because the proximity effect is too weak to couple the layers in S/I superlattices, the layers are coupled instead by Josephson tunnelling.[209] The good agreement of the artificially structured superlattices with proximity-effect theories is in contrast with the mixed results for TDMCIC's (and GIC's).
Figure 2.7: Tc vs layer
thickness in Nb/Cu superlattices. From Ref. [14]. The decrease of
Tc with decreasing thickness of the
superconducting component is predicted by proximity-effect
theories.[49,54] The predictions of the
standard proximity-effect theories is indicated by the solid
line. The proximity effect calculation modified to allow a
thickness-dependent Tc for the Nb layers is
indicated by the dashed line.
The study of metallic multilayers has been a growth area in physics and materials science.[15] Already there have been some significant results from superconducting multilayers. The most impressive of these is the unambiguous observation of a coupling-dimensionality crossover in both Hc2(T) and Hc2(theta).[208,42,126,30] The real promise of the synthetic superlattices lies in the studies of new effects not easily observable in GIC's or TMDCIC's, such as the competition between superconductivity and magnetism in Mo/Ni superlattices,[256] or the two low-temperature transitions observed in the Nb/Ta superlattices.[30] The superconducting multilayer work has been somewhat eclipsed by the excitement over high-temperature superconductors, but hopefully it will continue to be pursued, both because of its intrinsic interest and its relevance to the high- Tc field.