Systematic variation of magnetic-field penetration depth in high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors studied by muon-spin relaxation

Abstract

The muon-spin relaxation rate $\ensuremath{\sigma}$ has been measured in the high-${T}_{c}$ superconductors $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ for $x=6.66, 6.95, 7.0$, and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_{4}$ in transverse external magnetic fields \ensuremath{\sim}1-4 kG. We find a simple relation which connects the transition temperature ${T}_{c}$, the magnetic-field penetration depth ${\ensuremath{\lambda}}_{L}$, the carrier concentration ${n}_{s}$, and the effective mass ${m}^{*}$ as ${T}_{c}\ensuremath{\propto}\ensuremath{\sigma}\ensuremath{\propto}\frac{1}{{\ensuremath{\lambda}}_{L}^{2}}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$. The linear dependence ${T}_{c}\ensuremath{\propto}\frac{{n}_{s}}{{m}^{*}}$ suggests a high-energy scale for the coupling between superconducting carriers.