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The standard interpretation of superconductivity (S) is based on the London theory (LT) with minor modifications adopted in the GL and BCS. In all theories the sample bulk is totally inert and microscopic parameters of the S state can be obtained exclusively from the surface properties, i.e., the penetration depth $\lambda$ and the induction profile B vs depth z. Herewith, $B(z)$ is or close to exponential and does not depend on the applied field $H_0$ in the LT and BCS, while in the GL it does. According to the standard interpretation of vortices $\lambda^2$~$H_0$. An attempt to verify $\lambda(H_0)$ was made by Pippard in 1950 using a microwave resonator; in 1976 he noted that the problem is still unsolved.
LE-and bulk muSR experiments were performed on different instruments in PSI and ISIS on high-purity In and Nb films and single crystal In, Sn and Nb samples. The entire $B(z)$ [from $H_0$ to $0$] was measured for the first time. In all cases B(z) is close to linear and does not depend on the field. As measured on LEM and Dolly (PSI), the muon depolarization rate $\sigma$ in the bulk of the S phase where B=0, strongly depends on the field intensity H within the samples, being directly proportional to H. However, in the data obtained on MUSR (ISIS) $\sigma$ does not depend on the field. In addition, in an independent study performed on GPD (PSI) [Karl et al., 2019], no H-dependence of $\sigma$ was noticed. Possible reasons of these discrepancies will be discussed.
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