On extrinsic effects in the surface impedance of cuprate superconductors by weak links

Abstract

The reported rf surface impedance of superconducting cuprates continues to drop with 2 years of improving material quality. As leading indicator for quality the weak-link critical current jcJ(T≊ 0, B ≊ 0) has grown from 102 to 106 A/cm2 and thus the Josephson penetration depth λJ ∝ 1/√jcJ and the excess normal (leakage) tunnel current jbl are shrinking. This jcJ growth has now saturated, whereas the rf residual surface impedance Zres is still shrinking with material improvements. This shows clearly that Zres is an extrinsic property. Evidence that Zres is due to the large leakage current jbl and the small jcJ of weak links, where the latter destroys the intrinsic shielding from a λI thin-seam λJ deep into the bulk, is presented. This causes rf residual losses Rres ≊ (ωμ0)2λJ3σbl/2. Rres stays finite at T ≂ 0 by σbl(T → 0) ≊ σbl (∝jbl) being amplified by (λJ/λI)3 ≳ 103 as a weighting factor. With slow crystal growth weak links are improved and their density is reduced so that Rres values better than RNb(4.2 K) are now obtainable. The jcJ(T,B) values explain λres and Rres quantitatively and in temperature proportional to (a + Tm); m ≊ 1, T < Tc/2, and proportional to (b + Hn), n ≊ 1; H ≳ Hc1J in field dependence. Here Hc1J is the field where flux enters into weak links as Josephson fluxons having negligible viscous losses, but act by enhancing the penetration depth.