Universal Correlations between $T_{c}$ and $\frac{n_{s}}{m^{*}}$ (Carrier Density over Effective Mass) in High- $T_{c}$ Cuprate Superconductors

The muon-spin-relaxation rate

σ

has been measured in sixteen specimens of high-

T_{c}

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

n_{s}

divided by the effective mass

m^{*} (σ \propto \frac{1}{λ^{2}} \propto \frac{n_{s}}{m^{*}})

. A universal linear relation between

T_{c}

and

σ (T \to 0) \propto \frac{n_{s}}{m^{*}}

has been found with increasing carrier doping. In heavily doped samples, however,

T_{c}

shows saturation and suppression with increasing

\frac{n_{s}}{m^{*}}

. This saturation starts at different values of

\frac{n_{s}}{m^{*}}

for materials with different multiplicities of CuO planes.

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