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 against experimental data of vortex surface resistance at high microwave amplitude measured by means of bulk niobium superconducting-radio frequency cavities operating at 1.3 GHz. The good qualitative agreement of simulations and experiments suggests that the non-linear dependence of the trapped flux surface resistance with the microwave field amplitude is generated by progressive microwave depinning and vortex jumps.
Abrikosov vortex melting in high-temperature superconductors of ErBa2Cu3O7-δ system is investigated using mechanical contactless method of energy dissipation.
We use a model of vortex dynamics and collective weak pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency NbCu, doped-Nb and Nb$_3$Sn cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a f…
The dissipation process in two dimensional BCS superconductor due to the quasiparticles in the core of moving vortex is studied from a quantum mechanical point of view, especially paying attention to the spectral flow of the bound state energies in the vortex core. In order to clarify the nature of the spectral flow, we performed a numerical study of a finite system and, by extending the analysis to include the effect of impurities, we discuss the quantum mechanical origin of the dissipation in the vortex core.
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.
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 study parametric level statistics of the discretized excitation spectra inside a moving vortex core in layered superconductors with impurities. The universal conductivity is evaluated numerically for the various values of rescaled vortex velocities $κ$ from the clean case to the dirty limit case. The random matrix theoretical prediction is verified numerically in the large $κ$ regime. On the contrary in the low velocity regime, we observe $σ_{xx} \propto κ^{2/3}$ which is consistent with the theoretical result for the super-clean case, where the energy dissipation is due to the Landau-Zener…
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…
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…
Current-voltage $I-V$ curves have been carefully measured for YBa$_2$Cu$_3$O$_{7-δ}$ thin films by following different thermal or field annealing procedures. Although all data can be described quite well by the vortex-glass theory, it is found that the dissipation in a small region just above the vortex-glass transition is history dependent: the dissipation in the warming up or field-increasing process is larger than that in the cooling down or field-decreasing process. We attribute this history dependent dissipation to possible existence of a slush vortex phase.
We have studied mixed-state dissipation in epitaxial MgB$_2$ thin films by measurements of resistive transition, current-voltage characteristics, Hall effect, and point-contact tunnelling spectrum. We found that unlike single gap superconductors with negligible vortex quantum fluctuations in which vortices are frozen at T=0 K, finite zero-temperature dissipation due to vortex motion exists in MgB$_2$ over a wide magnetic field range. This dissipation was found to be associated with proliferation of quasiparticles from the $π$-band of MgB$_2$. The result shows that the vortex fluctuations are e…
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 …
Transport properties of the vortex lattice in high temperature superconductors are studied using numerical simulations in the case in which the non-local interactions between vortex lines are dismissed. The results obtained for the longitudinal and transverse resistivities in the presence of quenched disorder are compared with the results of experimental measurements and other numerical simulations where the full interaction is considered. This work shows that the dependence on temperature of the resistivities is well described by the model without interactions, thus indicating that many of th…
A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length XI; and of width w much narrower than the Pearl length LAMBDA >> w >> XI. At high bias currents, I* < I < Ic, the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt f…
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 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 obt…
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…
The dissipative currents due to normal excitations are included in the London description. The resulting time dependent London equations are solved for a moving vortex and a moving vortex lattice. It is shown that the field distribution of a moving vortex looses it cylindrical symmetry, it experiences contraction which is stronger in the direction of the motion, than in the direction normal to the velocity $\bm v$. The London contribution of normal currents to dissipation is small relative to the Bardeen-Stephen core dissipation at small velocities, but approaches the latter at high velocities…
In strongly anisotropic layered superconductors in tilted magnetic fields the Josephson vortex lattice coexists with the lattice of pancake vortices. Due to the interaction between them, the dissipation of the Josephson-vortex lattice occurs to be very sensitive to the presence of the pancake vortices. If the c-axis magnetic field is smaller then the corresponding lower critical field, the pancake stacks are not formed but the individual pancakes may exist in the fluctuational regime either near surface in large-size samples or in the central region for small-size mesas. We calculate the contr…
The presence of magnetic fields and/or transport currents can cause penetration of vortices in superconductors. Their motion leads to dissipation and resistive state arises, which in turn strongly affects the performance of superconducting devices such as single-photon and single-electron detectors. Therefore, an understanding of the dissipation mechanisms in mesoscopic superconductors is not only of fundamental value but also very important for further technological advances. In the present work, we analyzed the contributions and interplay of the dissipative mechanisms due to the locally indu…
Superconducting 2H-NbSe2 single crystals show intrinsic low pinning values. Therefore, they are ideal materials with which to explore fundamental properties of vortices. (V, I) characteristics are the experimental data we have used to investigate the dissipation mechanisms in a rectangular shape 2H-NbSe2 single crystal. Particularly, we have studied dissipation behavior with magnetic fields applied in the plane of the crystal and parallel to the injected currents, i.e. in the force-free state where the vortex helical instability governs the vortex dynamics. In this regime, the data follow the …
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…
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…
Observation of individual vortex penetration in a coplanar superconducting resonator
The University of Tokyo（东京大学）；University of Connecticut（康涅狄格大学）；University of Arizona（亚利桑那大学）；Institute of Science Tokyo（东京科学大学）；National Institute for Materials Science（物质材料研究机构）
The notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time $τ$ is comparable with the quantum Heisenberg time $t_H=\hbar/ΔE$, where $ΔE$ is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of th…
Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order -- such as the XY model -- can be realize…
A method, using a Corbino disk sample geometry, is described and applied to study of resistive tails of sintered $YBCO$. When the transport current passes radially from the rim of the disk sample to its center, the two component potential drop signal is detected below $T_c$, which is due to (i) quasiparticles $W_q$ and (ii) vortex-core-motion related contribution $W_{ϕ}$. When the contact pairs for $W$ are placed radially, $W_q(r)$ and $W_{ϕ}(r)$ are found to follow the markedly distinctive functional dependences, providing a unique possibility to deconvolute the relative strengths of both con…
IIt is shown that in a bilayer excitonic superconductor dissipative losses emerge under transmission of the current from the source to the load. These losses are proportional to the square of the interlayer tunneling amplitude and independent on the value of the input current. The case of quantum Hall bilayer is considered. The bilayer may work as a transmission line if the input current exceeds certain critical value. The input current higher than critical one induces Josephson vortices in the bilayer. The difference of electrochemical potentials is required to feed the load and it forces Jos…
A junction with two superconductors coupled by a normal metal hosts Andreev bound states whose energy spectrum is phase-dependent and exhibits a minigap, resulting in a periodic supercurrent. Phase-dependent dissipation also appears at finite frequency due to relaxation of Andreev bound states. While dissipation and supercurrent versus phase have previously been measured near thermal equilibrium, their behavior in nonequilibrium is still elusive. By measuring the ac susceptibility of a graphene-superconductor junction under microwave irradiation, we find supercurrent response deviates from adi…
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…
We present measurements of the vortex-state surface impedance, Z_s = R_s + i X_s, of a high quality, ortho-II-ordered single crystal of the cuprate high temperature superconductor YBa2Cu3O6.52 (T_c = 59K). Measurements have been made at four microwave frequencies (ω/2π= 2.64, 4.51, 9.12 and 13.97 GHz), for magnetic fields ranging from 0 to 7 T. From these data we obtain the field, frequency and temperature dependence of the vortex viscosity, pinning constant, depinning frequency and flux-flow resistivity. The vortex viscosity, η(ω,T), has a surprisingly strong frequency dependence and bears a …
Vortex dynamics in a bilayer thin film superconductor are studied through a Josephson-coupled double layer XY model. A renormalization group analysis shows that there are three possible states associated with the relative phase of the layers: a free vortex phase, a logarithmically confined vortex-antivortex pair phase, and a linearly confined phase. The phases may be distinguished by measuring the resistance to counterflow current. For a geometry in which current is injected and removed from the two layers at the same edge by an ideal (dissipationless) lead, we argue that the three phases yiel…
An enhancement of vortex-motion damping in thin Pb/In superconducting films is obtained through coupling to an adjacent two-dimensional electron gas formed in a modulation-doped GaAs/AlGaAs heterostructure. This effect is observed by monitoring the power dissipation at the superconductor in the vortex state while increasing the density of the electron gas using a gate voltage. Quantitative agreement is found with calculations based on a viscous model of vortex damping which considers generation of eddy currents in the electron gas by moving flux lines. In the regime of filamentary and channel …
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…
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 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 …
Strongly disordered pseudogapped superconductors are expected to display arbitrary high values of kinetic inductance close to superconductor-insulator transition (SIT) that makes them attractive for the implementation of dissipationless superinductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become relevant source of dissipation and noise in the far vicinity of SIT.
We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the absence of an applied magnetic field. The resulting zero-temperature resistance derives from two equally possible mechanisms: 1) quantum tunneling of vortices from the edges of the sample; and 2) homogeneous quantum nucleation of vortex-antivortex pairs in the bulk of the sample, arising from the instability of the Magnus field's ``vacuum''. We study both situations in the case where quantum dissipation dominates over the inertia of the vortices. We find that the vortex tunneling and nucleation rates…
We show that the vortex dynamics in Fermi superfluids at ultra-low temperatures is governed by the local heating of the vortex cores creating the heat flux carried by non-equilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of $^3$He-B the temperature of vortex cores is estimated to be of the order $0.2 T_c$. The dispersion of Kelvin waves is derived and the heat flow generated by Kelvin cascade is shown to have the value clo…
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 …
LiFeAs is one of the iron-based superconductors having multiple gaps with the possible sign reversal. To clarify how those novel natures affect the energy dissipation of magnetic vortices, we investigated the microwave surface impedance of LiFeAs single crystals under finite magnetic fields. The flux-flow resistivity enhanced rapidly at low magnetic fields, which is similar to the case of MgB$_{2}$. This is probably the consequence of the multiple-gap nature and the gap anisotropy. This suggest that the sign-reversal is not important for the flux-flow even for multiple-gap superconductors. As …
The vortex contribution to the dc field (H) dependent microwave surface impedance Z_s = R_s+iX_s of YBa_2Cu_3O_{7-x} thin films was measured using suspended patterned resonators. Z_s(H) is shown to be a direct measure of the flux density B(H) enabling a very precise test of models of flux penetration. Three regimes of field-dependent behavior were observed: (1) Initial flux penetration occurs on very low field scales H_i(4.2K) 100Oe, (2) At moderate fields the flux penetration into the virgin state is in excellent agreement with calculations based upon the field-induced Bean critical state for…
We consider a vortex line in the B phase of superfluid $^3$He under uniformly precessing magnetization. The magnetization exerts torque on the vortex, causing its order parameter to oscillate. These oscillations generate spin waves, which is analogous to an oscillating charge generating electromagnetic radiation. The spin waves carry energy, causing dissipation in the system. Solving the equations of spin dynamics, we calculate the energy dissipation caused by spin wave radiation for arbitrary tipping angles of the magnetization and directions of the magnetic field, and for both vortex types o…
We report numerical simulations of a trapped elastic vortex driven by a strong ac magnetic field $H(t)=H\sinωt$ parallel to the surface of a superconducting film. The surface resistance and the power dissipated by an oscillating vortex perpendicular to the film surface were calculated as functions of $H$ and $ω$ for different spatial distributions, densities, and strengths of pinning centers, including bulk pinning, surface pinning, and cluster pinning. Our simulations were performed for both the Bardeen-Stephen viscous vortex drag and the Larkin-Ovchinnikov (LO) drag coefficient $η(v)$ decrea…
By using thermal and Lorentz force, the vortex motion is successfully manipulated in the mixed state of underdoped La$_{2 - x}$Sr$_{x}$CuO$_{4}$ single crystals and optimally doped YBa$_{2}$Cu$_{3}$O$_{7 - δ}$ thin films. A conclusion is drawn that the strong Nernst signal above $T_{c}$ is induced by vortex motion. In the normal state, in order to reduce the dissipative contribution from the quasiparticle scattering and enhance the signal due to the possible vortex motion, a new measurement configuration is proposed. It is found that the in-plane Nernst signal ($H$ $| | $ $c$) can be measurabl…
We report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $H(t)=H\sinωt$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $η(v)$. We show that the LO decrease of $η(v)$ with the vortex velocity $v$ can radically change the field dependence of the surface resistance $R_i(H)$ caused by trapped vortices. At low fre…
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…
Using the high-sensitive mechanical method of measuring the dissipation processes in superconductors, the 3D-2D phase transition in magnetic field was investigated in the vortex lattice of strongly anisotropic high-temperature superconductors of Bi(2223) system. It was shown that with the increase of external magnetic field the dissipation connected with a motion of vortexes relative to the crystal lattice of a sample, first increases, reaching the maximum and then with a further increase of the magnetic field sharply reduces as a result of pinning enhancement in connection with the transition…
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…
Universal bound on microwave dissipation in superconducting circuits
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，内耳研究所）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）；Google Quantum AI（谷歌量子人工智能）；Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；CENN Nanocenter（CENN纳米中心）
