Insensitivity of Tc to the residual resistivity in high-Tc cuprates and the tale of two domes

Abstract

One of the few undisputed facts about hole-doped high-Tc cuprates is that their superconducting gap Δ has d-wave symmetry. According to ‘dirty’ d-wave BCS theory, even structural (non-magnetic) disorder can suppress Δ, the transition temperature Tc and the superfluid density ρs. The degree to which the latter is affected by disorder depends on the nature of the scattering. By contrast, Tc is only sensitive to the total elastic scattering rate (as estimated from the residual resistivity ρ0) and should follow the Abrikosov-Gor’kov pair-breaking formula. Here, we report a remarkable robustness of Tc in a set of Bi2201 single crystals to large variations in ρ0. We also survey an extended body of data, both recent and historical, on the LSCO family which challenge key predictions from dirty d-wave theory. We discuss the possible causes of these discrepancies, and argue that either we do not understand the nature of disorder in cuprates, or that the dirty d-wave scenario is not an appropriate framework. Finally, we present an alternative (non-BCS) scenario that may account for the fact that the superconducting dome in Tl2201 extends beyond that seen in Bi2201 and LSCO and suggest ways to test the validity of such a scenario.