Superconducting interaction charge in thallium-based high-Tc cuprates: Roles of cation oxidation state and electronegativity

TL;DR

This paper investigates how the oxidation state and electronegativity of cations influence the superconducting transition temperature in thallium-based cuprates, proposing a model linking electronic interactions to structural and compositional factors.

Contribution

It introduces a new model relating cation oxidation state and electronegativity to superconducting charge transfer, explaining Tc variations in Tl-based cuprates.

Findings

Higher Tc in Tl-based cuprates linked to lower electronegativity of Tl.

Derived a formula for superconducting interaction charge {\sigma} based on cation properties.

Predicted optimal fractional Tl$^{+1}$ content at 1/3 for maximum Tc.

Abstract

Superconductivity in the Tl-based cuprates encompasses a notably broad range of measured optimal transition temperatures Tc0, ranging from lowest in the charge-depleted Tl-1201 compounds (Tl$_{1-x}$(Ba/Sr)$_{1+y}$La$_{1-y}$CuO$_{5-{\delta}}$), such as Tl$_{0.7}$LaSrCuO$_5$ (37 K) and TlBa$_{1.2}$La$_{0.8}$CuO$_5$ (45.4 K), to highest in the Tl-1223 compound TlBa$_2$Ca$_2$Cu$_3$O$_{9{\pm}{\delta}}$ (133.5 K). Seven Tl-based cuprates are considered and compared using the model of superconductive pairing via electronic interactions between two physically separated charge reservoirs, where Tc0 $\propto$ ({\sigma}{\eta}/A)$^{1/2}${\zeta}$^{-1}$ is determined by the superconducting interaction charge fraction {\sigma} the number {\eta} of CuO$_2$ layers, and the basal-plane area A, each per formula unit, and the transverse distance {\zeta} between interacting layers. Herein it is demonstrated that {\sigma} follows from the elemental electronegativity and the oxidation state of Tl, and other structurally analogous cations. The comparatively lower elemental electronegativity of Tl, in conjunction with its oxidation state, explains the higher {\sigma} and Tc0 values in the Tl-based compounds relative to their Bi-based cuprate homologues. A derivation of {\sigma} is introduced for the optimal Tl$_2$Ba$_2$Ca$_{{\eta}-1}$Cu$_{\eta}$O$_{2{\eta}+4}$ (for {\eta} = 1, 2, 3) compounds, which exhibit a Tl oxidation state at or near +3, obtaining the fundamental value {\sigma}$_0$ = 0.228 previously established for YBa$_2$Cu$_3$O$_{6.92}$. Also reported is the marked enhancement in {\sigma} associated with Tl$^{+1}$ and analogous inner-layer cations relative to higher-valence cations. For a model proposition of {\sigma} = {\sigma}$_0$, the fractional Tl$^{+1}$ content of the mixed-valence compound, TlBa$_2$Ca$_2$Cu$_3$O$_{9{\pm}{\delta}}$, is predicted to be 1/3 at optimization, in agreement ...