Robust thermodynamics constrain disorder and pairing in far-overdoped Tl$_2$Ba$_2$CuO$_6$

Abstract

The physical origin of the suppression of superconductivity with hole doping in overdoped cuprates remains unclear. We measure the electronic specific heat of microgram-scale Tl$_2$Ba$_2$CuO$_6$ crystals and find sharp superconducting anomalies persisting far into the overdoped regime, with $Δγ(T_{\rm c})/γ_n\approx0.6$ for $T_{\rm c}=14$-$25$K. A weak-coupling BCS-like framework incorporating the known Fermi surface and cation disorder quantitatively reproduces the observed anomaly and its weak doping dependence. We conclude that the observed $T_{\rm c}(p)$ cannot be driven predominantly by increasing disorder and is instead consistent with a smoothly decreasing pairing strength.