Surface impedance and optimum surface resistance of a superconductor with an imperfect surface

Abstract

We calculate a low-frequency surface impedance of a dirty, s-wave superconductor with an imperfect surface incorporating either a thin layer with a reduced pairing constant or a thin, proximitycoupled normal layer. Such structures model realistic surfaces of superconducting materials which can contain oxide layers, absorbed impurities or nonstoichiometric composition. We solved the Usadel equations self-consistently and obtained spatial distributions of the order parameter and the quasiparticle density of states which then were used to calculate a low-frequency surface resistance Rs(T ) and the magnetic penetration depth λ(T ) as functions of temperature in the limit of local London electrodynamics. It is shown that the imperfect surface in a single-band s-wave superconductor results in a non-exponential temperature dependence of Z(T ) at T ≪ Tc which can mimic the behavior of multiband or d-wave superconductors. The imperfect surface and the broadening of the gap peaks in the quasiparticle density of states N (ǫ) in the bulk give rise to a weakly temperaturedependent residual surface resistance. We show that the surface resistance can be optimized and even reduced below its value for an ideal surface by engineering N (ǫ) at the surface using pairbreaking mechanisms, particularly, by incorporating a small density of magnetic impurities or by tuning the thickness and conductivity of the normal layer and its contact resistance. The results of this work address the limit of Rs in superconductors at T ≪ Tc, and the ways of engineering the optimal density of states by surface nano-structuring and impurities to reduce losses in superconducting micro-resonators, thin film strip lines, and radio frequency cavities for particle accelerators.

Weak-field dissipative conductivity of a dirty superconductor with Dynes subgap states under a dc bias current up to the depairing current density

“…The interplay of the broadening of the DOS peaks, which decreases σ 1 , and the reduction of the spectrum gap, which increases σ 1 , determines the optimum Γ. Then, tuning the quasiparticle spectrum via engineering Γ can reduce electromagnetic dissipation in superconducting devices [2,22]. While the physics and materials mechanisms behind Γ are not yell understood, comparison of tunneling spectroscopy and various materials treatments can give useful information on how to engineer Γ.…”

“…When Γ > ω γ , the denominator in the logarithmic factor is replaced with Γ and the divergence at ω γ → 0 disappears. As Γ increases, σ 1 logarithmically decreases [2,19,22].…”

“…Pair-breaking effects due to realistic materials features including magnetic impurities, Dynes Γ parameters, and a proximity-coupled normal layer at the surface can also reduce R s via the broadening of the DOS peaks [22]. For instance, sparse magnetic impurities can reduce R s by ∼ 50% for the weak rf field.…”

“…In this paper, we consider a superconductor with Dynes subgap states. The Dynes Γ has not been derived from a microscopic theory, yet we can incorporate a finite Γ into the quasiclassical theory of the BCS model [2,22,23]. We study the effect of a combination of Γ and the dc bias for all Γ and all currents up to the deparing current density j d .…”

Surface density of states in superconductors with inhomogeneous pairing constant: Analytical results

“…A theoretical description of those effects is complicated and definitely nonuniversal. To model suppression of superconductivity near the surface, one can assume surface suppression of the BCS pairing constant λ(r) [15][16][17][18]. Microscopically, this effect can be due to changes in lattice properties (i.e., phonons) or in electron-phonon interaction in the vicinity of an imperfect surface.…”