Superconducting transition temperatures of the elements related to elastic constants

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian 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, Omega. 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 as Tc = Tc^(M) (Z, Omega). One 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 C_{11}, C_{12}, and C_{44}, the atomic weight and the atomic volume, and (b) Tc for five bcc transition metals is linear in the Cauchy deviation C* = (C_{12} - C_{44})/(C_{12} + C_{44}). 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.Comment: EPJB, accepte

Linear response theory around a localized impurity in the pseudogap regime of an anisotropic superconductor: precursor pairing vs the d-density-wave scenario

We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave-vector Q=(pi,pi), albeit imperfect, due to a nonzero value of the hopping ratio t'/t in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the (q,omega) dependence of the retarded polarizability.Comment: accepted in Phys. Rev.

Multiband superconductors close to a 3D-2D electronic topological transition

Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the superconducting critical temperature by tuning the chemical potential.Comment: J. Supercond., to appea

Extended d_{x^2 - y^2}-wave superconductivity

Remarkable anisotropic structures have been recently observed in the order parameter Delta_k of the underdoped superconductor Bi-2212. Such findings are strongly suggestive of deviations from a simple d_{x^2 - y^2}-wave picture of high-Tc superconductivity, i.e. Delta_k ~ cos (k_x) - cos (k_y). In particular, flatter nodes in Delta_k are observed along the k_x = (+/-) k_y directions in k-space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the k-dependence of Delta_k near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping dependence of the flatness of the gap near the nodes is also attributable to Fermi surface effects, in addition to possible screening effects modifying the in-plane pairing kernel, as recently proposed.Comment: 7 pages, 4 embedded PostScript figures. Uses svjour, epsfig, amsmath, amssymb, xspace. To be published in Eur. Phys. J.

Symmetry breaking and restoring under high pressure: the amazing behaviour of the "simple" alkali metals

We argue that an ionic lattice surrounded by a Fermi liquid changes phase several times under pressure, oscillating between the symmetric phase and a low-symmetry dimerized structure, as a consequence of Friedel oscillations in the pair potential. Phase oscillations explain the tendency towards dimerization which has been recently reported for the light alkali metals under high pressure. Moreover, a restoring of the symmetric phase is predicted for such elements at an even higher density.Comment: accepted in Eur. Phys. J.

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

In earlier work, we have been concerned with the scaling properties of some classes of superconductors, specifically with heavy Fermion materials and with five bcc transition metals of BCS character. Both of these classes of superconductors were three-dimensional but here we are concerned solely with quasi-two-dimensional high-Tc cuprates in the underdoped region of their phase diagram. A characteristic feature of this part of the phase diagram is the existence of a pseudogap (pg). We therefore build our approach around the assumption that kB Tc / E_pg is the basic dimensionless ratio on which to focus, where the energy E_pg introduced above is a measure of the pseudogap. Since anyon fractional statistics apply to two-dimensional assemblies, we expect the fractional statistics parameter allowing `interpolation' between Fermi-Dirac and Bose-Einstein statistical distribution functions as limiting cases to play a significant role in determining kB Tc / E_pg and experimental data are analyzed with this in mind.Comment: Phys. Chem. Liquids, to be publishe