Microwave Properties of Superconductors

Hein, Matthias

doi:10.1007/978-94-010-0450-3_2

Cited by 6 publications

(16 citation statements)

References 71 publications

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“…The broadening of DOS at the surface can become much more pronounced if a thin proximity-coupled normal layer is present (see Figs. [4][5][6]. Thus, fitting the tunneling data with Eq.…”

Section: Discussionmentioning

confidence: 99%

“…where ∆ ≡ ∆(∞) denotes an equilibrium order parameter in S region far away from the surface, as opposed to the varying pair potential ∆(x) in Eq. (4). For the case shown in Fig.…”

Section: Usadel Equations and Boundary Conditionsmentioning

confidence: 99%

“…At temperatures T well below the critical temperature T c and hω ≪ ∆, s-wave superconductors have very small R s giving rise to extremely high quality factors instrumental for micro-resonators for quantum computing 2 or radio-frequency superconducting (SRF) cavities for particle accelerators 3 . The surface resistance in the Meissner state has the following generic temperature dependence observed in many experiments 4 :…”

Section: Introductionmentioning

confidence: 98%

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

2017

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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.

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“…The broadening of DOS at the surface can become much more pronounced if a thin proximity-coupled normal layer is present (see Figs. [4][5][6]. Thus, fitting the tunneling data with Eq.…”

Section: Discussionmentioning

confidence: 99%

“…where ∆ ≡ ∆(∞) denotes an equilibrium order parameter in S region far away from the surface, as opposed to the varying pair potential ∆(x) in Eq. (4). For the case shown in Fig.…”

Section: Usadel Equations and Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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

2017

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“…The physics of electromagnetic response of superconductors, and the fundamental limits dissipation in the Meissner state at low temperatures and frequencies has recently attracted much interest. The issue of ultra-lowdissipation is particularly important for microresonators for quantum computing or radio-frequency (rf) superconducting cavities for particle accelerators [1][2][3][4][5] . At temperatures T well below the critical temperature T c and frequencies ω smaller than the gap frequency 2∆/h, swave superconductors have very small surface resistance R s ∝ exp(−∆/T ) 6 .…”

Section: Introductionmentioning

confidence: 99%

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

Kubo

Gurevich

2019

Phys. Rev. B

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We propose a theory of nonlinear surface resistance of a dirty superconductor in a strong radiofrequency (RF) field, taking into account magnetic and nonmagnetic impurities, finite quasiparticle lifetimes, and a thin proximity-coupled normal layer characteristic of the oxide surface of many materials. The Usadel equations were solved to obtain the quasiparticle density of states (DOS) and the low-frequency surface resistance Rs as functions of the RF field amplitude H0. It is shown that the interplay of the broadening of the DOS peaks and a decrease of a quasiparticle gap caused by the RF currents produces a minimum in Rs(H0) and an extended rise of the quality factor Q(H0) with the RF field. Paramagnetic impurities shift the minimum in Rs(H0) to lower fields and can reduce Rs(H0) in a wide range of H0. Subgap states in the DOS can give rise to a residual surface resistance while reducing Rs at higher temperatures. A proximity-coupled normal layer at the surface can shift the minimum in Rs(H0) to either low and high fields and can reduce Rs below that of an ideal surface. The theory shows that the behavior of Rs(H0) changes as the temperature and the RF frequency are increased, and the field dependence of Q(H0) can be very sensitive to the materials processing. Our results suggest that the nonlinear RF losses can be minimized by tuning pairbreaking effects at the surface using impurity management or surface nanostructuring.

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“…For s-wave superconductors, the BCS and Eliashberg theories [10][11][12] predict an exponentially small R s (T ) in the Meissner state at low rf frequencies ω ≪ k B T c / and temperatures T ≪ T c much lower than the critical temperature T c . However, R s (T ) observed on many s-wave superconducting materials is usually described by [13][14][15]…”

Section: Introductionmentioning

confidence: 99%

Effect of vortex hotspots on the radio-frequency surface resistance of superconductors

2013

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We present detailed experimental and theoretical investigations of hotspots produced by trapped vortex bundles and their effect on the radio-frequency (rf) surface resistance Rs of superconductors at low temperatures. Our measurements of Rs combined with the temperature mapping and laser scanning of a 2.36 mm thick Nb plate incorporated into a 3.3 GHz Nb resonator cavity cooled by the superfluid He at 2 K, revealed spatial scales and temperature distributions of hotspots and showed that they can be moved or split by thermal gradients produced by the scanning laser beam. These results, along with the observed hysteretic field dependence of Rs which can be tuned by the scanning laser beam, show that the hotspots in our Nb sample are due to trapped vortex bundles which contain ∼ 10 6 vortices spread over regions ∼ 0.1 − 1 cm. We calculated the frequency dependence of the rf power dissipated by oscillating vortex segments trapped between nanoscale pinning centers, taking into account all bending modes and the nonlocal line tension of the vortex driven by rf Meissner currents. We also calculated the temperature distributions caused by trapped vortex hotspots, and suggested a method of reconstructing the spatial distribution of vortex dissipation sources from the observed temperature maps. Vortex hotspots can dominate the residual surface resistance at low temperatures and give rise to a significant dependence of Rs on the rf field amplitude Hp, which can have important implications for the rf resonating cavities used in particle accelerators and for thin film structures used in quantum computing and photon detectors.

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Microwave Properties of Superconductors

Cited by 6 publications

References 71 publications

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

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

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

Effect of vortex hotspots on the radio-frequency surface resistance of superconductors

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