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

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 $Δ γ (T_{c}) / γ_{n} \approx 0.6$ for $T_{c} = 14$ - $25$ 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 $T_{c} (p)$ cannot be driven predominantly by increasing disorder and is instead consistent with a smoothly decreasing pairing strength.

Robust thermodynamics constrain disorder and pairing in far-overdoped Tl $_{2}$ Ba $_{2}$ CuO $_{6}$

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Robust thermodynamics constrain disorder and pairing in far-overdoped Tl $_{2}$ Ba $_{2}$ CuO $_{6}$

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Robust thermodynamics constrain disorder and pairing in far-overdoped Tl22​Ba22​CuO66​

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Robust thermodynamics constrain disorder and pairing in far-overdoped Tl22​Ba22​CuO66​

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Robust thermodynamics constrain disorder and pairing in far-overdoped Tl $_{2}$ Ba $_{2}$ CuO $_{6}$

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Robust thermodynamics constrain disorder and pairing in far-overdoped Tl $_{2}$ Ba $_{2}$ CuO $_{6}$

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