Superconducting transition temperatures of the elements related to elastic constants

Abstract

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian H in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M , (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, Ω. Since the thermodynamic quantities can be determined from H, we conclude that Tc, the superconducting transition temperature, when it is non-zero, may be formally expressed asOne piece of evidence in support is that, in an atomic number vs atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) Tc is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C11, C12, and C44, the atomic weight and the atomic volume, and (b) Tc for five bcc transition metals is linear in the Cauchy deviation C * = (C12 − C44)/(C12 + C44). Finally, via elastic constants, mass density and atomic volume, a correlation between C * and the Debye temperature is established for the five bcc transition elements.PACS. 74.62.-c Transition temperature variations -74.70.Ad Metals; alloys and binary compounds

Velocity of sound and the BCS interaction parameter in five body-centred-cubic crystals

“…A measure of this coupling is the average velocity of sound, vs . Then, incorporating the finding of Angilella et al [6] that the superconducting transition temperature, T c , varies linearly with the Cauchy discrepancy, c * , for the five bcc transition metals, it follows that for this proposal to be valid, there must exist a relationship between vs and c * .…”

“…This may be contrasted with the value ρ v2 s ∼ 75 GPa in the extreme case of Nb which has the highest T c . In this context, we note that combining equation (3) with the linear relation in [6] between T c and the Cauchy discrepancy, c * , one has a relatively simple empirical relation between the superconducting critical temperature, the sound velocity and the Cauchy discrepancy. Of course, while the exponential form (3) provides a truly excellent fit of the data shown in figure 1, other (probably more complex) fitting forms are doubtless possible: we must therefore regard equation (3) as empirical as at present we have no fundamental insight into its final, first-principles, justification.…”

“…It is clear that a central pair potential description is not appropriate for any of these metals. Recently, Angilella et al [6] showed that there exists a relationship between the superconducting transition temperature, T c , and the Cauchy discrepancy, c * , for the five bcc metals. This led us to enquire whether the possible factors influencing c * for this group of superconducting bcc transition metals in table 1 are in any way qualitatively different from those for the non-superconducting fcc transition metals.…”

Scaling of the superconducting transition temperature in underdoped high-Tccuprates with a pseudogap energy: Does this support the anyon model of their superfluidity?

“…In recent work [1,2,3,4,5], we have been concerned with the connection between superconducting transition temperature T c and other physical properties in (a) heavy Fermion materials [1,2,5] and (b) five body-centred cubic (bcc) transition metals [4]. For case (a), k B T c was shown to correlate strongly with a 'kinetic energy of localization' h 2 /m * ξ 2 , where m * is the effective mass of the charge carriers, while ξ is the coherence length.…”

Is MgB2a BCS-like charged superfluid?

“…In a recent study [1], we have related the superconducting transition temperature T c of five body-centred cubic (bcc) transition metals to elastic constants and especially to the so-called Cauchy deviation (see figure 1). Here, we want to relate such results for these BCS-like transition metals to recent work on MgB 2 , with a relatively high transition temperature T c ¼ 39 K [2].…”