Charge-fluctuation effect on the critical temperature of layered high-Tcsuperconductors

The value of the superconducting critical temperature (${\mathit{T}}_{\mathit{c}}$) of artificially layered superconductors made out of alternating Y-Ba-Cu-O and Pr-Ba-Cu-O layers is calculated as a function of both the number of layers of pure Y-Ba-Cu-O within a unit cell of the superlattice and the thickness of the insulating (Pr-Ba-Cu-O) layer. The calculation is performed within a model of electrostatically coupled two-dimensional (2D) arrays of ultrasmall Josephson junctions. The underlying mechanism is assumed to be the depression of the Beresinskii-Kosterlitz-Thouless transition temperature (${\mathit{T}}_{\mathrm{BKT}}$) by quantum phase fluctuations due to charging effects. The ${\mathit{T}}_{\mathit{c}}$ value of the entire structure can then be tuned by varying the charging energy that depends on the average neighborhood of a typical site in Cu-O planes of Y-Ba-Cu-O layers. Recent experiments on such structures are described very accurately by the model. Furthermore, the ratio (${\mathit{T}}_{\mathit{c}}^{\left(\mathit{n}\right)}$-${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(1\right)\mathrm{}}$)/(${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(2\right)\mathrm{}}$-${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(1\right)\mathrm{}}$), where ${\mathit{T}}_{\mathit{c}}^{\left(\mathit{n}\right)}$ is the critical temperature of a thin film made up of n Y-Ba-Cu-O unit cells, is found to be independent of the fitting parameters. This prediction is well confirmed by available experimental data. Furthermore, the model also applies for the series of Bi- and Tl-based cuprates of general formulas ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathit{n}}$ ${\mathrm{O}}_{\mathit{y}}$ and ${\mathrm{Tl}}_2$ (1)${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathit{n}}$ ${\mathrm{O}}_{\mathit{y}}$ containing n Cu-O planes per unit cell, for which the observed values of the ratio ρ=(${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(3\right)\mathrm{}}$-${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(1\right)\mathrm{}}$)/(${\mathit{T}}_{\mathit{c}}^{\mathrm{}\left(2\right)\mathrm{}}$-