Pair weakening and tunnel channels at cuprate interfaces

Abstract

The very high superconducting transition temperatures ${\mathit{T}}_{\mathit{c}}$ of cuprates are not yet substantiated in applications which seem intimately related to the layered nature of the cuprous oxides. Based on a highly directional p-d hybridization and correlation, the layering causes a correlated quasi-two-dimensional conduction in the ${\mathrm{CuO}}_{2}$ planes. The basis for the superconductivity seems to be the low carrier density (${\mathit{n}}_{\mathit{s}}$\ensuremath{\ge}${10}^{21}$/${\mathrm{cm}}^{3}$ eV) close to the metal-insulator transition (MIT) in two dimensions. Thus, any perturbation degrading hybridization and correlation renders the cuprate insulating, which then by disorder contains localized states (${\mathit{n}}_{\mathit{L}}$\ensuremath{\le}${10}^{21}$/${\mathrm{cm}}^{3}$). In this layered material the correlated conduction is only weakly hindered by point defects. More prominent perturbations for the conduction are external or internal surfaces with reduced hybridization by a reduced dimensionality and by disorder in energy, distance, or bond angle which occurs intrinsically by relaxation of dangling bonds. This intrinsic, insulating seam with its localized states weakens superconductivity and supports tunneling in various channels. The weakening by on-site Coulomb repulsion close to the MIT smears out and roughens the metal-insulator interface and, e.g., causes reduced and locally varying energy gaps and leakage current ${\mathit{j}}_{\mathit{b}\mathit{l}}$.The different tunnel channels---direct and resonant or intermediate via localized states ${\mathit{n}}_{\mathit{L}}$---have different distance d, temperature T, and voltage U dependencies. This explains not only the observed I(d,T,U) dependencies in scanning-tunneling microscopy, break, or broad area junctions, but also the background conduction and the degradation of Josephson currents ${\mathit{j}}_{\mathit{c}}$(T,H) across weak links is explained together with the ${\mathit{j}}_{\mathit{c}}$${\mathit{R}}_{\mathit{b}\mathit{n}}$\ensuremath{\propto}1/${\mathit{R}}_{\mathit{b}\mathit{n}}^{\mathit{m}}$ (1\ensuremath{\le}m\ensuremath{\le}1.5) dependence on grain boundary resistance ${\mathit{R}}_{\mathit{b}\mathit{n}}$; the leakage current ${\mathit{j}}_{\mathit{b}\mathit{l}}$\ensuremath{\propto}1/${\mathit{R}}_{\mathit{b}\mathit{n}}$ and their noise \ensuremath{\propto}${\mathit{j}}_{\mathit{b}\mathit{l}}$; and the rf residual losses ${\mathit{R}}_{\mathrm{res}}$\ensuremath{\propto}${\mathit{R}}_{\mathit{b}\mathit{n}}^{2}$. The proposed intermediate-state tunnel model fits all a-b plane weak links and serves as a microscopic base for mean-field (proximity effect) descriptions for the intrinsic degradation of superconductivity at interfaces. The intermediate-state tunneling is correlated yielding the Coulomb barrier by localization; Cooper pair tunneling, e.g., by negative U centers; and other many particle effects.