**7. Conclusions**

a *new* state. One of the reasons for this could well be the fact that the BCS equation for Δ is quadratic in Δ and is therefore unaffected when Δ ! �Δ. On the other hand, GBCSE for W1 is linear in this variable and has been derived by assuming that W1 undergoes a change in signature upon crossing the Fermi surface. This is also a feature of GBCSEs for W2, etc. Since s�-wave is an inbuilt feature of GBCSEs, one does not have to invent a new state for any SC, as has been suggested in [32].

The following relation between Tc and the average mass of ions M in an

While in the BCS theory α = 0.5, values significantly different from it have also been found for some elements such as Mo, Os, and Ru, for which α = 0.33, 0.2, and 0, respectively. Therefore, while Eq. (30) does not have the status of a *law*, it nonetheless helped in the formulation of BCS theory because it sheds light on the role of the ion lattice in the scenario of 1PEM, which has been shown to be the

We now draw attention to the fact that when Bi and Sr. in Bi2Sr2CaCu2O8 are replaced by Tl and Ba, respectively, the Tc of the SC increases from 95 to 110 K. Consequent upon these substitutions, the only property that can be unequivocally determined is the mass of the SC. Because the operative mechanism for pairing in composite SCs is not 1PEM, it becomes interesting to ask if Eq. (30) can be generalized to address the scenarios of 2PEM and 3PEM. A generalization of Eq. (30) that

*Tc* <sup>¼</sup> *p M*ð Þ <sup>1</sup>*M*<sup>2</sup> �*<sup>α</sup>*

where p is the constant of proportionality and M1 and M2 are the masses of ion species that cause pairing. Assuming that the value of Tc = 95 K for Bi2Sr2CaCu2O8 is due to 2PEM as in [25], an explanation for the increase in the Tc of Bi2Sr2CaCu2O8 when Tl2Ba2CaCu2O8 is obtained from it via substitutions was given in [33]. Noting that Bi and Tl belong to the same period and Sr. and Ba to the same group of the periodic table, several suggestions were made in [33] to further increase the Tc of the Bi-based SC. An example, following from our study, it was shown that Tc (Bi2

The Tcs and Δs of most of the hetero-structured, multi-gapped SCs which were studied above via the GBCSE-based approach have also been studied via the morewidely followed multiband approach (MBA) which originated with the work of Suhl et al. [34]. Because the former approach sheds light on additional features of these SCs, such as j0, s, ns, etc., as also because of its distinctly different conceptual basis, it complements the latter approach. Since the conceptual bases of both the approaches have been dealt with in detail in a recent paper [35], we confine our-

i. Employing the concept of a superpropagator, the GBCSE-based approach invariably invokes a λ for each of the ion species in an SC that may cause

*Tc*∞*M*�*<sup>α</sup>:* (30)

*,* (31)

**5.4 Isotope-like effect for composite SCs**

*On the Properties of Novel Superconductors*

operative mechanism for elemental SCs.

Mg2 CaCu2O8) should be 171 K.

selves here to the following remarks:

**6. Discussion**

**70**

suggests itself naturally for the 2PEM scenario is

elemental SC is well-known as the isotope effect:


generalized to deal with the situation when the SC is in heat bath in an external magnetic field, i.e., when T 6¼ H 6¼ 0, a procedure for which has been given in [38]. The import of this remark is that not only will such an undertaking enable theory to address the j0 values of an SC which are generally reported for such values of T and H but also that it may shed new light on the Volovik effect for the Fe-based SCs, as discussed in, e.g., [32].

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