We discuss and propose a complete data treatment, in close contact to typical microwave experimental data, in order to derive vortex parameters, such as pinning constant and viscous drag coefficient (also referred to as ``vortex viscosity''), in a way as model-independent as possible. We show that many of the accepted models for the complex resistivity can be described by a single, very general analytical expression. Using typical measurements of real and imaginary resistivity as a function of the applied field, we show that, even for single-frequency measurements, it is always possible to obtain (a) estimates of viscous drag coefficient and pinning constant with well-defined upper and lower bounds and (b) quantitative information about thermal creep. It turns out that neglecting thermal creep, in particular and counterintuitively at low temperatures, might result in a severe overestimation of the viscous drag coefficient. We also discuss the impact of thermal creep on the determination of the pinning constant. The present results might lead to a reconsideration of several estimates of the vortex parameters.
The vortex liquid-to-glass transition has been studied in Ba0.72K0.28Fe2As2, Ba0.9Co0.1Fe2As2, and Ba(Fe0.45Ni0.05)2As2 single crystal with superconducting transition temperature, Tc = 31.7, 17.3, and 18 K, respectively, by magnetoresistance measurements. For temperatures below Tc, the resistivity curves were measured in magnetic fields within the range of 0 \leq B \leq 13 T, and the pinning potential was scaled according to a modified model for vortex liquid resistivity. Good scaling of the resistivity ρ(B, T) and the effective pinning energy U0(B,T) was obtained with the critical exponents s…
Measurements of the high-frequency complex resistivity in superconductors are a tool often used to obtain the vortex parameters, such as the vortex viscosity, the pinning constant and the depinning frequency. In anisotropic superconductors, the extraction of these quantities from the measurements faces new difficulties due to the tensor nature of the electromagnetic problem. The problem is specifically intricate when the magnetic field is tilted with respect to the crystallographic axes. Partial solutions exist in the free-flux-flow (no pinning) and Campbell (pinning dominated) regimes. In thi…
The conductivity of vortex lattices in multiband superconductors with high concentration of impurities is calculated based on microscopic kinetic theory. Both the limits of high and low fields are considered, when the magnetic induction is close to or much smaller than the critical field strength $H_{c2}$, respectively. It is shown that in contrast to single-band superconductors the resistive properties are not universal but depend on the pairing constants and ratios of diffusivities in different bands. The low-field magneto-resistance can strongly exceed Bardeen-Stephen estimation in a quanti…
We report on study of the vortex liquid in Pb-doped Bi-2223 single crystal using the in-plane resistivity measurements as a function of temperature and magnetic field up to 6T applied perpendicular to CuO planes. Below Tc at the upper part of superconducting transition we found Arrhenius-like resistivity behavior. With further temperature decrease close to resistivity onset resistivity shows power law dependence on temperature signaling approaching vortex-glass transition. The critical exponents nu(z-1)=4.6 plus-minus 0.5 are found to be field independent within experimental errors. We also pr…
Longitudinal and Hall voltages are measured in a clean twinned YBCO single crystal in the liquid and solid vortex phases. For magnetic fields tilted away from the c-axis more than about 2 deg, a scaling law |rho_xy|=A (rho_xx)^beta with beta approx.=1.4 is observed, which is unaffected by the vortex-lattice melting transition. The vortex-solid Hall conductivity is non-linear and diverges to negative values at low temperature. When the magnetic field is aligned to the c-axis, the twin-boundary correlated disorder modifies the scaling law, and beta approx.=2. The scaling law is unaffected by the…
We discuss the excess conductivity above Tc due to renormalized order-parameter fluctuations in YBCO at microwave frequencies. We calculate the effects of the uniaxial anisotropy on the renormalized fluctuations in the Hartree approximation, extending the isotropic theory developed by Dorsey [Phys. Rev. B 43, 7575 (1991)]. Measurements of the real part of the microwave resistivity at 24 and 48 GHz and of the dc resistivity are performed on different YBCO films. The onset of the superconducting transition and the deviation from the linear temperature behavior above Tc can be fully accounted for…
The flux flow regime of high-T$_{\rm c}$ samples of different normal state resistivities is studied in the temperature range where the sign of the Hall effect is reversed. The scaling of the vortex viscosity with normal state resistivity is consistent with the Bardeen-Stephen theory. Estimates of the influence of possible mechanisms suggested for the sign reversal of the Hall effect are also given.
We report measurements of the complex resistivity in $YBCO$ and $MgB_2$ thin films over a continuous frequency spectrum in the microwave range, making use of a Corbino disk geometry. The paper mainly focuses on the extraction of the resistivity from raw data, displaying data analisys procedure and its limits of validity. We obtain and show resistivity curves as a function of frequency and temperature denoting a frequency dependent widening of the superconductive transition.
The influence of dendritic magnetic-flux penetration on the microwave response of superconducting MgB2 films is investigated by a coplanar resonator technique. The peculiar feature consists of jumps in the resonance curve, induced by vortex avalanches freezing flux inside the resonator. Due to a shaking effect, microwave currents maintain the vortex system close to a nonequilibrium state, resulting in dendrite branching. Avalanche-size distributions before and after flux-pinning tailoring by heavy-ion irradiation are fully consistent with molecular dynamics simulations reported in literature.
The vortex dynamics of uniaxial anisotropic superconductors with arbitrary angles between the magnetic field, the applied current and the anisotropy axis is theoretically studied, by focusing on the models for electrical transport experiments in the linear regime. The vortex parameters, such as the viscous drag, the vortex mobility and the pinning constant (in the weak point pinning regime), together with the vortex motion resistivity, are derived in tensor form by considering the very different free flux flow and pinned Campbell regimes. The results are extended to high frequency regimes wher…
We report measurements of the complex resistivity in YBCO and MgB$_2$ thin films over a continuous frequency spectrum in the microwave range, making use of a Corbino disk geometry. The paper mainly focuses on the extraction of the resistivity from raw data, displaying data analysis procedure and its limits of validity. We obtain and show resistivity curves as a function of frequency and temperature denoting a frequency dependent widening of the superconducting transition.
We use the three-dimensional Josephson junction array system as a model for studying the temperature dependence of the c-axis resistivity of high temperature superconductors, in the presence of an external magnetic field H applied in the c-direction. We show that the temperature at which the dissipation becomes different from zero corresponds to a percolation transition of the vortex lattice. In addition, the qualitative features of the resistivity vs. temperature curves close to the transition are obtained starting from the geometrical configurations of the vortices. The results apply to the …
We investigate the physics of the microwave response in YBa$_{2}$Cu$_{3}$O$_{7-δ}$, SmBa$_{2}$Cu$_{3}$O$_{7-δ}$ and MgB$_{2}$ in the vortex state. We first recall the theoretical basics of vortex-state microwave response in the London limit. We then present a wide set of measurements of the field, temperature, and frequency dependences of the vortex state microwave complex resistivity in superconducting thin films, measured by a resonant cavity and by swept-frequency Corbino disk. The combination of these techniques allows for a comprehensive description of the microwave response in the vortex…
We make comments on the paper presented by Kim \textit{et al.} [Phys. Rev. B \textbf{61}, 11317 (2000)]. The authors analyzed activation energies of HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ thin films with a scaling relation, and defined four vortex regions for thin films. We find that the definitions of four vortex regions and the scaling relation are questionable when studying their definition of the resistivity range for thermally activated flux flow. Using the empirical activation energy form suggested by Zhang \textit{et al.} [Phys. Rev. B \textbf{71}, 052502 (2005)] for lower resistivity data, we f…
We present measurements of the field induced changes in the 47 GHz complex resistivity, $Δ\tilde ρ(H,T)$, in Tl$_{2}$Ba$_{2}$CaCu$_{2}$O$_{8+x}$ (TBCCO) thin films with $T_{c}\simeq$ 105 K, prepared on CeO$_{2}$ buffered sapphire substrates. At low fields ($μ_{0}H<$10 mT) a very small irreversible feature is present, suggesting a little role of intergranular phenomena. Above that level $Δ\tilde ρ(H,T)$ exhibits a superlinear dependence with the field, as opposed to the expected (at high frequencies) quasilinear behaviour. We observe a crossover between predominantly imaginary to predominantly …
We present surface impedance measurement of the vortex linear response in a large untwinned YBCO crystal. The depinning spectra obtained over a broad frequency range (100 Hz- 30 MHz) are those of a surface pinned vortex lattice with a free flux flow resistivity (two modes response). The critical current in the "Campbell" like regime and the flux flow resistivity in the dissipative regime are extracted. Those two parameters are affected by the first order transition, showing that this transition may be related to the electronic state of vortices.
While the electrodynamic treatment of a superconducting thin film by Yeh et al. [Phys. Rev. B 48, 9861 (1993)] ostensibly has application for the "thin-film limit," their work is shown to employ bulk-like instead of thin-film electrodynamics, and as such obtains an ostensible violation of the first law of thermodynamics and a surface resistance independent of the resistivity. Other theoretical and experimental difficulties are briefly noted.
We experimentally investigate the vortex induced energy losses in niobium coplanar waveguide resonators with and without quasihexagonal arrays of nanoholes (antidots), where large-area antidot patterns have been fabricated using self-assembling microsphere lithography. We perform transmission spectroscopy experiments around 6.25 and 12.5 GHz in magnetic field cooling and zero field cooling procedures with perpendicular magnetic fields up to B=27 mT at a temperature T=4.2 K. We find that the introduction of antidot arrays into resonators reduces vortex induced losses by more than one order of m…
We report peculiar vortex motion in clean Bi$_2$Sr$_2$CaCu$_2$O$_8$ single crystals, which reveals nearly linear-$T$ resistivity tails extending to low temperatures. The resistivity was found to satisfy the classical Bardeen-Stephen model for free flux flow, which is otherwise hard to observe under normal experimental conditions in high-$T_c$ cuprates. Moreover, in the superclean regime, a universal temperature-independent value for the flux flow resistivity was observed, $ρ_f = 1.4(B-B^*)$. We interpret this carrier-relaxation {\it independent} behavior as being related to the dissipation cau…
In this paper, we describe the vortex dynamics under high-amplitude microwave drive and its effect on the surface resistance of superconductors. The vortex surface resistance is calculated with a Montecarlo approach, where the vortex motion equation is solved for a collection of vortex flux lines each oscillating within a random pinning landscape. This approach is capable of providing a detailed description of the microscopic vortex dynamics and in turn important insights into the microwave field amplitude dependence of the vortex surface resistance. The numerical simulations are compared agai…
In order to clarify electronic states and energy dissipations due to a motion of a vortex core in pure FeSe, which is a candidate superconductor possessing a super-clean core, we measured the microwave surface impedance of pure FeSe single crystals under finite magnetic fields. From the magnetic-field dependence of the flux-flow resistivity, we found that a barometer of electronic states inside the vortex core $ω_{0}τ_{\rm core}$ is $1\pm0.5$, suggesting that the vortex core of pure FeSe is in the moderately clean regime contrary to the expectation of the super-clean core. We also found that t…
In the superclean case the spectrum of vortex core excitations in the presence of disorder is not random but consists of two series of equally-spaced levels. The I-V characteristics of such superconductors displays many interesting phenomena. A series of resonances is predicted at frequencies commensurate with the spacing of the vortex excitations. These resonances reveal an even-odd anomaly. In the presence of one weak impurity the excitation levels can approach each other and almost cross. Absorption at very low frequencies is identified with the resonances arising in this case. The results …
We have investigated the Josephson plasma excitations in magnetic fields parallel to the $ab$-plane in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals in a wide microwave frequency region (9.8 -- 75 GHz). It was found that there are two kind of phase-collective modes: one increases with magnetic fields in higher fields, approaching linear asymptotic dependence with $ck$, which lies well above the inherent plasma frequency $ω_p$, while the other does not show considerable field dependence. The higher linear mode is attributed to the Josephson plasma mode propagating along the reciprocal lattice v…
Simultaneous transport and magnetization studies in Bi2Sr2CaCu2O8 crystals at elevated currents reveal large discrepancies, including finite resistivity at temperatures of 40K below the magnetic irreversibility line. This resistivity, measured at the top surface, is non-monotonic in temperature and extremely non-linear. The vortex velocity derived from magnetization is six orders of magnitude lower than the velocity derived from simultaneous transport measurements. The new findings are ascribed to a shear-induced decoupling, in which the pancake vortices flow only in the top few CuO2 planes, a…
The microwave complex surface impedance Z_s of Y(Ni_{1-x}Pt_x)_2B_2C was measured at 0.5 K under magnetic fields H up to 7T. In nominally pure YNi_2B_2C, which is a strongly anisotropic s-wave superconductor, the flux flow resistivity ρ_f calculated from Z_s was twice as large as that expected from the conventional normal-state vortex core model. In Pt-doped samples where the gap anisotropy is smeared out, the enhancement of ρ_f is reduced and ρ_f approaches to the conventional behavior. These results indicate that energy dissipation in the vortex core is strongly affected by the anisotropy of…
We have determined HC2(T) for FeSe1-xTex (x=0.52) single crystals using resistivity measurements at high static and pulsed magnetic field, as well as specific heat measurements up to 9T. We find that the significant anisotropy of the initial slope of HC2(T) determined from resistivity measurements, is not present when HC2 is determined from the specific heat results. This suggests that the thermodynamic upper critical field is almost isotropic, and that anisotropic vortex dynamics play a role. Further evidence of anisotropic vortex dynamics is found in the behaviour in pulsed field. We also fi…
We report measurements of the microwave complex resistivity at 48 GHz in SmBaCuO thin films. Measurements are performed with a moderate magnetic field, $μ_{0}H<$ 0.8T, applied along the c-axis. We find that the complex resistivity presents clear sublinear field dependences, and that the imaginary part is remarkably sensitive to the moderate magnetic field. Interpretation considering an unusually strong pinning leads to very anomalous field dependences of the single-vortex viscosity and of the pinning constant. By contrast, allowing for a significant effect of the magnetic field on the depletio…
We present a compared experimental investigation of the (a,b) plane vortex-state complex resistivity at 48 GHz in YBaCuO, SmBaCuO and BiSrCaCuO (2212). In YBaCuO and SmBaCuO the field dependence of the response can be consistently described by a combination of flux flow and strong pair breaking due to the presence of lines of nodes in the gap. In BiSrCaCuO (2212), by contrast, the data might be described by the pair breaking alone.
We have measured the microwave dissipation at 10 GHz in a Bi2Sr2CaCu2O8 single crystal, between 75 and 50 K, as a function of the static magnetic field applied parallel to the c axis. We observe a clear-cut onset in the dissipation precisely at the melting field Hm(T), that we identify in the same sample by a step in the static magnetization. We show that this onset can be assigned to the c-axis resistivity becoming finite in our whole temperature range, whereas the in-plane resistivity displays a thermally activated behavior. This suggests that pinning is efficient even at 10 GHz. The normal …
We report measurements of the magnetic-field induced microwave complex resistivity in REBa$_{2}$Cu$_{3}$O$_{7-δ}$ thin films, with RE = Y, Sm. Measurements are performed at 48 GHz by means of a resonant cavity in the end-wall-replacement configuration. The magnetic field dependence is investigated by applying a moderate (0.8 T) magnetic field along the c-axis. The measured vortex state complex resistivity in YBa$_{2}$Cu$_{3}$O$_{7-δ}$ and SmBa$_{2}$Cu$_{3}$O$_{7-δ}$ is analyzed within the well-known models for vortex dynamics. It is shown that attributing the observed response to vortex motion…
We report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal o…
We present measurements of the effective surface impedance changes due to a static magnetic field, $ΔZ(H,T)=ΔR(H,T)+\rmi ΔX(H,T)$, in a Tl-2212 thin film with $T_c>$ 103 K, grown on a CeO$_2$ buffered sapphire substrate. Measurements were performed through a dielectric resonator operating at 47.7 GHz, for temperatures 60 K$\leq T<T_c$ and magnetic fields $\leq0.8$ T. We observe exceptionally large field induced variations and pronounced super-linear field dependencies in both $ΔR(H)$ and $ΔX(H)$ with $ΔX(H)>ΔR(H)$ in almost the whole $(H,T)$ range explored. A careful analysis of the data allow…
In the mixed state of type II superconductors penetrated by an external magnetic field in the form of a lattice of Abrikosov vortices the dc resistance is known to increase with increasing velocity of the vortex lattice. Accordingly, vortex pinning sites impeding the vortex motion are widely used to preserve the low-dissipative response of the system. Here, while subjecting superconducting Nb films with nanogrooves to a combination of dc and ac current stimuli and tuning the number of mobile and pinned vortices by varying the magnetic field around the so-called matching values, we observe a co…
The longitudinal resistivity (rho_{xx}) and transverse resistivity (rho_{xy}) of MgB2 thin films in the mixed state were studied in detail. We found that the temperature dependencies of rho_{xx} and ρ_{xy} at a fixed magnetic field (H) satisfy the scaling law of $ρ_{xy}=Aρ_{xx}^β$, where the exponent beta varies around 2.0 for different fields. In the low field region (below 1T), beta maintains a constant value of 2.0 due to the weak pinning strength of the vortices, mainly from the superfluid of the pi band. When H>1T, beta drops abruptly to its lowest value at about 2T because of the prolife…
We present a study of the frequency dependence of the vortex dynamics in a conventional superconductor. We have employed a swept-frequency, Corbino-disk technique to investigate the temperature (3.6K-Tc) and high-field (from Hc2/2 to Hc2) microwave complex resistivity in Nb thin (20-40 nm) films as a function of the frequency (1-20 GHz). We have found several previously unnoticed features: (i) a field-dependent depinning frequency in the GHz range; (ii) deviations from the accepted frequency dependence, that can be ascribed to some kind of vortex creep; (iii) the presence of switching phenomen…
Demanding microwave applications in a magnetic field require the material optimization not only in zero-field but, more important, in the in-field flux motion dominated regime. However, the effect of artificial pinning centers (APC) remains unclear at high frequency. Moreover, in coated conductors the evaluation of the high frequency material properties is difficult due to the complicated electromagnetic problem of a thin superconducting film on a buffered metal substrate. In this paper we present an experimental study at 48 GHz of 150-200 nm YBa$_2$Cu$_3$O$_{7-x}$ coated conductors, with and …
We report the free flux flow (FFF) resistivity associated with a purely viscous motion of the vortices in moderately clean d-wave superconductor Bi:2201 in the strongly overdoped regime (T_c=16K) for a wide range of the magnetic field in the vortex state. The FFF resistivity is obtained by measuring the microwave surface impedance at different microwave frequencies. It is found that the FFF resistivity is remarkably different from that of conventional s-wave superconductors. At low fields (H<0.2H_c2) the FFF resistivity increases linearly with H with a coefficient which is far larger than that…
We have grown superconducting TiN films by atomic layer deposition with thicknesses ranging from 6 to 89 nm. This deposition method allows us to tune the resistivity and critical temperature by controlling the film thickness. The microwave properties are measured, using a coplanar-waveguide resonator, and we find internal quality factors above a million, high sheet inductances (5.2-620 pH), and pulse response times up to 100 μs. The high normal state resistivity of the films (> 100 μΩcm) affects the superconducting state and thereby the electrodynamic response. The microwave response is modele…
We present wideband microwave measurements (1-22 GHz) taken on Superconductor/Ferromagnet heterostructures with the Corbino disk technique. We apply the technique to Nb/PdNi/Nb trilayers in the vortex state and we compare the results to data taken with the same technique on a Nb thin film. We show that it is possible to directly extract the genuine flux-flow resistivity from our frequency-dependent measurements without overcoming the (depinning) critical current. The characteristic frequency for vortex relaxation can also be estimated, without resorting to a specific model. We find that the F …
We investigated the nature of the quasi-particle state in the vortex core by means of the flux-flow Hall effect measurements at 15.8 GHz. We measured the flux-flow Hall effect in cuprate superconductors, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{y}$ and YBa$_{2}$Cu$_{3}$O$_{y}$ single crystals, whose equilibrium $B$-$T$ phase diagrams were different. As a result, we found that the Hall angle is independent of the magnetic field, and reaches an order of unity at low temperatures in BSCCO. However, in YBCO, the angle increases with increasing magnetic field even at low temperatures. We understood that this …
There is a renewed interest in superconductors for high-frequency applications, leading to a reconsideration of already known low-$T_c$ and high-$T_c$ materials. In this view, we present an experimental investigation of the millimeter-wave response in moderate magnetic fields of Tl$_2$Ba$_2$CaCu$_2$O$_{8+x}$ superconducting films with the aim of identifying the mechanisms of the vortex-motion-induced response. We measure the dc magnetic-field-dependent change of the surface impedance, $ΔZ_s(H) = ΔR_s(H) + iΔX_s(H)$ at 48 GHz by means of the dielectric resonator method. We find that the overall…
The $\rm Fe_{1+y}Te_{1-x}Se_x$\ single crystals with the various Se/Te ratios were studied by the microwave absorption and direct current resistivity measurements. The comparison of the microwave absorption data and the resistivity versus temperature made it possible to separate the contributions of two types of spin fluctuations. One of them is due to the anisotropic magnetic (nematic) fluctuations. It is observed over the wide temperature range from 30K to 150 or 200K. In FeSe it has the maximum close to the structural transition temperature. Another MWA anomaly is located in the narrow temp…
We present measurements of the magnetic field-induced microwave complex resistivity changes at 47 GHz in Tl$_2$Ba$_2$CaCu$_2$O$_{8+δ}$ (TBCCO) thin films, in the ranges 58 K$<T<T_{c}$ and 0$<μ_{0}H<$0.8 T. The large imaginary part $Δρ_{2}(H)$ points to strong elastic response, but the data are not easily reconciled with a rigid vortex model. We find that, over a wide range of temperatures, all the pairs of curves $Δρ_{1}(H)$ and $Δρ_{2}(H)$ can be collapsed on a pair of scaling curves $Δρ_{1}[H/H^{*}(T)]$, $Δρ_{2}[H/H^{*}(T)]$, with the same scaling field $H^{*}(T)$. We argue that $H^{*}(T)$ i…
The vortex phase diagrams of NdFeAsO0.85F0.15 and NdFeAsO0.85 superconductors are determined from the analysis of resistivity and current-voltage (I-V) measurements in magnetic fields up to 9 T. A clear vortex glass to liquid transition is identified only in the oxygen deficient NdFeAsO0.85, in which I-V curves can be well scaled onto liquid and glass branches consistent with the vortex glass theory. With increasing magnetic field, the activation energy U0, deduced from the Arrhenius plots of resistivity based on the thermally activated flux-flow model (TAFF), decays more quickly for NdFeAsO0.…
The two tone intermodulation distortion arising in MgB2 thin films synthesized by hybrid physical-chemical vapour deposition is studied in order to probe the influence of the two bands on the nonlinear response of this superconductor. The measurements are carried out by using a dielectrically loaded copper cavity operating at 7 GHz. Microwave data on samples having critical temperatures above 41 K, very low resistivity values, and residual resistivity ratio larger than 10, are shown. The dependence of the nonlinear surface losses and of the third order intermodulation products on the power fee…
We investigate the effect of the anisotropy and of the directional pinning in YBa$_2$Cu$_3$O$_{7-x}$ films grown by pulsed laser ablation from targets containing BaZrO$_3$ at 5% mol. BaZrO$_3$ inclusions self-assemble to give nanorods oriented along the c-axis, thus giving a preferential direction for vortex pinning. The directionality of vortex response is studied at high ac frequency with the complex microwave response at 48 GHz, as a function of the applied field and of the angle $θ$ between the field and the c-axis. The complex microwave response does not exhibit any angular scaling, sugge…
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum electrodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to a reduction of the device performance due to energy dissipating Abrikosov vortices. We experimentally investigate the vortex induced energy losses in such Nb resonators with different spatial distributions of micropatterned pinning sites (antidots) by transmission spectroscopy measurements at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex induced losses and th…
Vortices in superconductors driven at microwave frequencies exhibit a response related to the interplay between the vortex viscosity, pinning strength, and flux creep effects. At the same time, the trapping of vortices in superconducting microwave resonant circuits contributes excess loss and can result in substantial reductions in the quality factor. Thus, understanding the microwave vortex response in superconducting thin films is important for the design of such circuits, including superconducting qubits and photon detectors, which are typically operated in small, but non-zero, magnetic fie…
