Figure 1

Comparison between local and nonlocal magnetic penetration profiles for the same ${\lambda }_{\mathrm{L}}$ (parameters from Al for $T\to 0$, ${\lambda }_{\mathrm{L}}=18\mathrm{n}\mathrm{m}$, and ${\xi }_0=1600\mathrm{n}\mathrm{m}$). The dash-dotted line shows the typical exponential field profile predicted from the London theory. The solid line shows the nonlocal field profile from BCS theory. Specific features are (i) the penetration profile is nonexponential, (ii) the initial slope is less steep than in the local approximation, (iii) there is a field reversal before $B(z)$ decays towards zero, and (iv) the inset shows that $\log [B(z)]$ vs $z$ exhibits a clear curvature.Reuse & Permissions

Figure 2

Measured magnetic penetration profile $B(z)$ of Pb in the Meissner state for $T=3.05\mathrm{K}$ [$T_{\mathrm{c}}=7.21(2)\mathrm{K}$] in an external field of $8.82(6)\mathrm{m}\mathrm{T}$, applied parallel to the surface of the film. Implantation energies $E$ of the muons: 5.2 keV (open circles) and 14.8 keV (closed circles). The mean values are plotted as closed squares with implantation energies (2.5, 4.0, 5.4, 7.5, 10.0, 12.4, 15.0, 18.0, 22.5, 26.0, 30.0) keV from left to right. The solid curve is a fit according to Eq. (4) with the BCS parameters ${\lambda }_{\mathrm{L}}=57(2)\mathrm{n}\mathrm{m}$, ${\xi }_0=90(5)\mathrm{n}\mathrm{m}$, and $\ell =100\mathrm{n}\mathrm{m}$ (fixed). The dashed curve shows the exponential dependence assuming the values from the full BCS fit. The inset displays results of Meissner state measurements of optimally doped ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ at $T=20\mathrm{K}$ ($T_{\mathrm{c}}=87.5\mathrm{K}$). This curve is purely exponential, as expected.Reuse & Permissions

Figure 3

Magnetic penetration profile $B(z)$ of Pb in the Meissner state for $T=6.66\mathrm{K}$ [$T_{\mathrm{c}}=7.21(2)\mathrm{K}$] in an external field of 8.82(6) mT, applied parallel to the surface of the film. Implantation energies of the muons: 14.8 keV (open circles) and 30.0 keV (closed circles). The mean values are shown as closed squares with implantation energies (2.5, 5.4, 7.5, 10.0, 15.0, 18.0, 22.5, 26.0, 30.0) keV. The solid curve is a fit according to BCS theory, whereas the dashed curve shows an exponential with the same ${\lambda }_{\mathrm{L}}$.Reuse & Permissions