Surface impedance of superconductors with magnetic impurities

Abstract

Motivated by the problem of the residual surface resistance of the superconducting radio-frequency (SRF) cavities, we develop a microscopic theory of the surface impedance of s-wave superconductors with magnetic impurities. We analytically calculate the current response function and surface impedance for a sample with spatially uniform distribution of impurities, treating magnetic impurities in the framework of the Shiba theory. The obtained general expressions hold in a wide range of parameter values, such as temperature, frequency, mean free path, and exchange coupling strength. This generality, on the one hand, allows for direct numerical implementation of our results to describe experimental systems (SRF cavities, superconducting qubits) under various practically relevant conditions. On the other hand, explicit analytical expressions can be obtained in a number of limiting cases, which makes possible further theoretical investigation of certain regimes. As a feature of key relevance to SRF cavities, we show that in the regime of "gapless superconductivity" the surface resistance exhibits saturation at zero temperature. Our theory thus explicitly demonstrates that magnetic impurities, presumably contained in the oxide surface layer of the SRF cavities, provide a microscopic mechanism for the residual resistance.

Field-dependent nonlinear surface resistance and its optimization by surface nanostructuring in superconductors

“…The pairbreaking parameter s = DQ 2 /2 + Γ p contains two contribution: the first term comes from the effect of pairbreaking currents and the second term accounts for spin-flip scattering on magnetic impurities. Here Q = ∇θ + 2πA/φ 0 is the gauge invariant phase gradient, A is the vector potential, φ 0 is the flux quantum, and Γ p is the spin-flip parameter due to magnetic impurities [31][32][33] . For the planar geometry shown in Fig.…”

“…Sparse magnetic impurities in Nb are among realistic materials features 28,29 which broaden the DOS peaks 24,[30][31][32][33] and can reduce the low-field R s by ∼ 50% despite a small reduction of T c 27 . The DOS broadening and the appearance of subgap states at quasiparticle energies |ǫ| < ∆ have been revealed by numerous tunneling experiments 17,34 .…”

Elucidating the local atomic and electronic structure of amorphous oxidized superconducting niobium films

“…Previous works suggest magnetic impurities contribute to impedance-based losses in superconducting qubits. 11,13 In particular, d-type magnetic impurities on Nb atoms were found to be more detrimental than p-type impurities on O atoms in Nb oxides. 13 To investigate if our XAS measurements can identify a low density of magnetic impurities, we compare our calculated XAS spectra with those measured.…”

“…Non-TLS noise intrinsic in QIS materials includes the presence of nonequilibrium quasiparticles (QP) 9,10 and of magnetic impurities. [11][12][13] While careful shielding can mitigate some of these effects, the decay and control of QPs is materials dependent, and can be crucially influenced by nanofabrication and materials' control. 9,14,15 Another key non-TLS loss mechanism is Cooper pair breaking induced by the presence of magnetic impurities, 11 which can occur due to materials' defects, interfaces, and surfaces, and cause impedance losses in the superconductor.…”

“…[11][12][13] While careful shielding can mitigate some of these effects, the decay and control of QPs is materials dependent, and can be crucially influenced by nanofabrication and materials' control. 9,14,15 Another key non-TLS loss mechanism is Cooper pair breaking induced by the presence of magnetic impurities, 11 which can occur due to materials' defects, interfaces, and surfaces, and cause impedance losses in the superconductor. [11][12][13] Therefore, to understand the structure-coherence relationships associated with the materials' properties in superconducting qubits, knowledge of the local structural and chemical environment is needed, regardless of the origin (TLS, non-TLS) of the noise.…”