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Correlations between normal state properties and superconductivity

Phys. Rev. B
**55**, 9007 (1997).

Despite many years of intense theoretical effort it is still not
possible to predict whether a material will be superconducting or not
at low temperatures by measurement of its physical properties at higher
temperatures. Nor is it possible in general to estimate the magnitude
of the superconducting critical temperature $T_c$ from measurements
of normal state properties. Here we address these questions from a statistical
point of view. The metallic elements in the first six rows of the periodic
table are assumed to be a ``representative sample'' drawn from a
larger set of materials, and various statistical measures of
correlations between the magnitude of $T_c$ and a normal state
property, as well as between a normal state property and the fact
whether the material is or is not a superconductor, are considered.
Thirteen normal state physical properties are studied, some of which
are believed to be important to determine superconducting properties
within conventional BCS theory and others not. It is found that
properties assumed to be important within BCS theory rank lowest in
predictive power regarding whether a material is or is not a
superconductor. Instead, properties with highest predictive power
in this respect are found to be bulk modulus, work function and
Hall coefficient. With respect to the magnitude of
$T_c$, it is found to be positively correlated with electronic heat
capacity, magnetic susceptibility
and atomic volume, and negatively correlated with electrical
and thermal conductivity and Debye temperature. No significant correlations
with ionic mass and ionization potential are found.
Consequences of these findings for the
theoretical understanding of superconductivity are discussed.

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