On intrinsic and extrinsic effects in the surface impedance of cuprate superconductors

Abstract

Surface impedance measurements in the normal and superconducting state are an excellent method to study conduction electron dynamics and extended defects. Electron dynamics show up most clearly in the relaxation range, i.e., for distances traveled in one rf periods=νF/ω (νF Fermi velocity) being smaller or of the order of the penetration depthλ and mean free pathl. For materials withνF≤107 cm/sec the relaxation range is easily accessible forf≥0.1 THz. Then, in the normal state, relaxation defines the surface impedance with an intrinsic penetration depthλI approaching the London penetration depthλL andRI≈μ0λL/ 2τ as surface resistance, allowing measurement ofλL and relaxation timeτ(T, ω). In the superconducting state the photon interaction scales withξL/λL=1/γ(ξF dimension of Cooper pairs forl→∞) and causes at low frequencies an absorption rate growing withγ, which is decreasing withξF/l. The rate increase proportional toγ turns to a decrease above 0.1 THz, which is accompanied by a decrease ofλA with frequency which is stronger for largeγ and smallξF/l. These characteristic dependences allow measurement of material parameters, anisotropy, and dynamics of electrons, especially the relaxation rateτ. But presently, the rf surface impedanceZ is still shrinking with material improvements, which shows, clearly, that theZ=ZI+Zres is still dominated by extrinsic properties summarized inZres. We present evidence thatZres is due to the large leakage currentjbl and the smalljcJ of weak links where the latter destroys the intrinsic shielding from aλI-thin seamλJ deep into the bulk. This causes rf residual lossesRres≈(ωμ0)2λ J 3 σbl/2.Rres stays finite atT-0 due toσbl(T→0)≈σbl(∝jbl) being amplified by (λJ/λI)3>103 as a weighting factor. The appropriate measure of weak links are the grain-boundary resistanceRbn(∝ρ(0)) enhancingλJ∝Rbn andRres∝R bn 2 . Thus,Zres is minimal for minimal extrapolated resistivityρ(T→0).