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

Superconductivity in the Tl-based cuprates encompasses a notably broad range of measured optimal transition temperatures T_C0, ranging from lowest in the charge-depleted Tl-1201 compounds (Tl_1–x(Ba/Sr)_1+yLa_1–yCuO_5–δ), such as Tl_0.7LaSrCuO₅ (37 K) and TlBa_1.2La_0.8CuO₅ (45.4 K), to highest in the Tl-1223 compound TlBa₂Ca₂Cu₃O_9±δ (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 T_C0∝(ση/A)^1/2ζ⁻¹ is determined by the superconducting interaction charge fraction σ, the number η of CuO₂ layers, and the basal-plane area A, each per formula unit, and the transverse distance ζ between interacting layers. Herein it is demonstrated that σ 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 σ and T_C0 values in the Tl-based compounds relative to their Bi-based cuprate homologs. A derivation of σ is introduced for the optimal Tl₂Ba₂Ca_η–1Cu_ηO_2η+4 (for η=1, 2, 3) compounds, which exhibit a Tl oxidation state at or near +3, obtaining the fundamental value σ₀=0.228 previously established for YBa₂Cu₃O_6.92. Also reported is the marked enhancement in σ associated with Tl⁺¹ and analogous inner-layer cations relative to higher-valence cations. For a model proposition of σ=σ₀, the fractional Tl⁺¹ content of the mixed-valence compound, TlBa₂Ca₂Cu₃O_9±δ, is predicted to be 1/3 at optimization, in agreement with existing data. Charge depletion is illustrated for the two Tl-1201 compounds, where σ<σ₀ values are determined according to substitution of Ba⁺² or Sr⁺² by La⁺³, and/or Tl depletion. Additionally, statistical analysis of calculated and experimental transition temperatures of 48 optimal superconductors shows an absence of bias in determining σ, A, and ζ.