Universal Correlations between Tc and nsm* (Carrier Density over Effective Mass) in High-Tc Cuprate Superconductors

The muon-spin-relaxation rate σ has been measured in sixteen specimens of high-Tc cuprate superconductors (the 2:1:4, 1:2:3, 2:2:1:2, and 2:2:2:3 series). This has allowed us to study the magnetic field penetration depth λ and thus the superconducting carrier density ns divided by the effective mass m*(σ∝1λ2∝nsm*). A universal linear relation between Tc and σ(T→0)∝nsm* has been found with increasing carrier doping. In heavily doped samples, however, Tc shows saturation and suppression with increasing nsm*. This saturation starts at different values of nsm* for materials with different multiplicities of CuO planes.