Concerning the nature of high-${\mathit{T}}_{\mathit{c}}$ superconductivity: Survey of experimental properties and implications for interlayer coupling

An increasing body of data suggests the existence of a unique set of criteria characterizing ‘‘ideal’’ high-${\mathit{T}}_{\mathit{c}}$ superconductivity. Common to those materials exhibiting these high-${\mathit{T}}_{\mathit{c}}$ characteristics, i.e., the layered cuprates and certain layered organic superconductors, is the reduced dimensionality of the superfluid density. In cases where the carriers are confined to two dimensions, the parameters specifying the superconducting state would include the two-dimensional carrier density ${\mathit{n}}_{2\mathrm{D}}$, the interlayer spacing d, the two-dimensional effective mass ${\mathit{m}}_{\mathit{a}\mathit{b}}^{\mathrm{*}}$, the two-dimensional Fermi energy ${\mathit{E}}_{\mathit{F}}^{2\mathrm{D}}$, and the average dielectric constant ε. To determine these parameters, we tabulate the relevant known properties on a variety of two- and three-dimensional superconductors. While partially limited by the quality of existing data, we nevertheless find that the data representative of the phase-pure high-${\mathit{T}}_{\mathit{c}}$-like layered compounds of simple geometry, with stoichiometry optimized for minimum disorder effects and highest ${\mathit{T}}_{\mathit{c}}$, exhibit clean-limit correlations of the form ${\mathit{n}}_{2\mathrm{D}}$${\mathit{d}}^2$=1, ${\mathit{m}}_{\mathit{a}\mathit{b}}^{\mathrm{*}}$∝ε/d, ${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$∝1/εd∝${\mathit{E}}_{\mathit{F}}^{2\mathrm{D}}$, and ${\mathit{H}}_{1/2}$∝${\mathit{H}}_0$. Here, ${\mathit{H}}_0$ is a characteristic field related to the upper critical field and ${\mathit{H}}_{1/2}$ is the characteristic field at which the specific-heat jump at ${\mathit{T}}_{\mathit{c}}$ is reduced to half its zero-field value. The observed correlations may be understood in terms of a simple interlayer Coulomb-coupling hypothesis.