Microwave Surface Impedance Measurements Research Articles

Electronic States and Energy Dissipations of Vortex Core in Pure FeSe Single Crystals Investigated by Microwave Surface Impedance Measurements

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 $\omega_{0}\tau_{\rm core}$ 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 the mean-free path inside the vortex core is suppressed at the distance of the order of the core radius. Based on observed results and previous reports, we discussed possible origins of rather small $\omega_{0}\tau_{\rm core}$ value in terms of the multiple-bands nature of FeSe and additional mechanisms producing extra energy dissipations specific to the vortex core in motion.

Physics of vortex motion by means of microwave surface impedance measurements (Review article)

In this paper we present a short overview on the results that can be obtained through the study of vortex motion at high frequencies. The phenomenological force balance for isolated-like vortices shaken by microwave currents and subjected to viscous drag, pinning forces and thermal creep is recalled and physically presented. The derived vortex motion resistivity, together with the main vortex parameters (viscosity η and flux flow resistivity ρff, pinning constant kp, creep factor χ), is then commented. Sample measurements are reported to illustrate the main aspects of the involved physical models.

Extraction of the Complex Resistivity and Pinning Parameters from Microwave Surface Impedance Measurements of Coated Conductors

The search for continuous improvement of the magnetic properties of coated conductors requires in-depth knowledge of vortex pinning. Microwave measurements of the superconductor complex resistivity are a very effective tool in obtaining complementary information on vortex pinning, in addition to conventional critical current density $J_c$ measurements. The microwave characterization suffers, however, from geometrical effects when the superconducting films are not thick with respect to the penetration depth, as the high-frequency field leaks through the superconductor and also probes the underlying substrate structure. Whilst the resulting electromagnetic problem has largely been addressed in the case of insulating or semiconducting substrates, metal substrates in coated conductors require further consideration. In this paper, we address the issue of obtaining the microwave resistivity of thin superconducting films grown on metal substrates, with particular emphasis on the correct determination of the vortex parameters. We finally illustrate the extraction procedure on a real sample measurements performed on a YBCO film deposited on metal tape.

Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature

Results of X-band microwave surface impedance measurements of FeSe1−xTex very thin film are reported. The effective surface resistance shows appearance of peak at T ≤ Tc when plotted as a function of temperature. The authors suggests that the most well-reasoned explanation can be based on the idea of the changing orientation of the microwave magnetic field at a S–N phase transition near the surface of a very thin film. The magnetic penetration depth exhibits a power-law behavior of δλL(T) ∝ CTn, with an exponent n ≈ 2.4 at low temperatures, which is noticeably higher than in the published results on FeSe1−xTex single crystal. However the temperature dependence of the superfluid conductivity remains very different from the behavior described by the BCS theory. Experimental results are fitted very well by a two-gap model with Δ1/kTc = 0.43 and Δ2/kTc = 1.22, thus supporting s±-wave symmetry. The rapid increase of the quasiparticle scattering time is obtained from the microwave impedance measurements.

Investigation of DC current injection effect on the microwave characteristics of HTS YBCO microstrip resonators

The DC current injection effect from a ferromagnetic (FM) La0.7Sr0.3MnO3 (LSMO) to a high temperature superconducting (HTS) Y1Ba2Cu3O7−x (YBCO) thin film was investigated by the microwave surface impedance measurements in a FM/HTS structure, formed as a microstrip resonator for improving the sensitivity of the experiments. The quality factor and the resonance frequency of this structure were found to strongly depend on the current strength, injected from the LSMO electrode into the HTS microstrip electrode. The magnetic penetration depth and the quasiparticle conductivity of the HTS component were determined to increase under DC current injection process, which in all probability stimulated breaking of Cooper pairs and led to a decrease of the superfluid concentration and an increase of the normal fluid concentration without significantly affecting the relaxation time of the quasiparticles.

Microwave surface impedance measurements on reduced graphene oxide

Here we report a non-contact method for microwave surface impedance measurements of reduced graphene oxide samples using a high Q dielectric resonator perturbation technique, with the aim of studying the water content of graphene oxide flakes. Measurements are made before, during and after heating and cooling cycles. We have modelled plane wave propagation of microwaves perpendicular to the surface of graphene on quartz substrates, capacitively coupled to a dielectric resonator. Analytical solutions are derived for both changes in resonant frequency and microwave loss for a range of water layer thicknesses. In this way we have measured the presence of adsorbed water layers in reduced graphene oxide films. The water can be removed by low temperature annealing on both single and multilayer samples. The results indicate that water is intercalated between the layers in a multilayer sample, rather than only being adsorbed on the outer surfaces, and it can be released by applying a mild heating.

Microwave surface impedance measurements of LiFeAs, LiFe(As,P) and FeSe1−xTex single crystals

We study microwave surface impedance measurements of LiFeAs, LiFe(As,P) and FeSe1−xTex single crystals. The in-plane penetration depths of LiFeAs and LiFe(As,P) depend on temperature exponentially at low temperatures, which is a strong indication that these two materials have the nodeless superconducting gap. The temperature dependence of the superfluid density indicates that LiFeAs and LiFe(As,P) are multi-gap superconductors with at least two isotropic gaps. In FeSe1−xTex, on the other hand, the quadratic temperature dependence of the in-plane penetration depth appears, which indicates the existence of some sort of quasiparticle excitations. In addtion, the real part of the microwave conductivity exhibits a large enhancement below Tc in all three materials, which results from the increase of the quasiparticle relaxation time, τ, below Tc.

Microwave Surface Impedance Measurements of LiFeAs Single Crystals

We report results of microwave surface impedance measurements of LiFeAs single crystals. The in-plane penetration depth depends on temperature exponentially at low temperatures, which strongly suggests that this material has the nodeless superconducting gap. The temperature dependence of the superfluid density indicates that LiFeAs is a multi-gap superconductor with at least two isotropic gaps. In addtion, the real part of the microwave conductivity exhibits a large enhancement below $T_\mathrm{c}$, indicating that the quasi-particle relaxation time, $\tau$, increases rapidly below $T_\mathrm{c}$. We believe that this enhancement is rather common to all superconductors where an inelastic scattering is dominant above $T_\mathrm{c}$, irrespective of the strength of the electron correlation.

Microwave surface impedance measurements ofTlxPb1−xTe: A proposed negative-Uinduced superconductor

Microwave surface impedance measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Tl</mml:mtext></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mtext>Pb</mml:mtext></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mtext>Te</mml:mtext></mml:mrow></mml:math>: A proposed negative-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>induced superconductor

Microwave surface impedance measurements ofSr2RuO4: The effect of impurities

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Penetration depth, lower critical fields, and quasiparticle conductivity in Fe-arsenide superconductors

In this article, we review our recent studies of microwave penetration depth, lower critical fields, and quasiparticle conductivity in the superconducting state of Fe-arsenide superconductors. High-sensitivity microwave surface impedance measurements of the in-plane penetration depth λ ab in single crystals of electron-doped PrFeAsO 1 - y ( y ∼ 0.1 ) and hole-doped Ba 1 - x K x Fe 2 As 2 ( x ≈ 0.55 ) are presented. In clean crystals of Ba 1 - x K x Fe 2 As 2 , as well as in PrFeAsO 1 - y crystals, the penetration depth shows flat temperature dependence at low temperatures, indicating that the superconducting gap opens all over the Fermi surface. The temperature dependence of superfluid density λ ab 2 ( 0 ) / λ ab 2 ( T ) in both systems is most consistent with the existence of two different gaps. In Ba 1 - x K x Fe 2 As 2 , we find that the superfluid density is sensitive to degrees of disorder inherent in the crystals, implying unconventional impurity effect. We also determine the lower critical field H c 1 in PrFeAsO 1 - y by using an array of micro-Hall probes. The temperature dependence of H c 1 saturates at low temperatures, fully consistent with the superfluid density determined by microwave measurements. The anisotropy of H c 1 has a weak temperature dependence with smaller values than the anisotropy of upper critical fields at low temperatures, which further supports the multi-gap superconductivity in Fe-arsenide systems. The quasiparticle conductivity shows an enhancement in the superconducting state, which suggests the reduction of quasiparticle scattering rate due to the gap formation below T c . From these results, we discuss the structure of the superconducting gap in these Fe-arsenides, in comparison with the high- T c cuprate superconductors.

Electrical transport measurements in the superconducting state ofBi2Sr2CaCu2O8+xandTl2Ba2CuO6+δ

Precise measurements of the in-plane microwave surface impedance of high-quality single crystals of Bi2212 and Tl2201 are used to probe the relaxation time of nodal quasiparticles in the d-wave superconducting state through a two-fluid analysis of the microwave conductivity. While this analysis requires us to posit a form for the frequency-dependent quasiparticle conductivity, we clearly demonstrate that the extraction of the relaxation rate is quite insensitive to the assumed shape of the quasiparticle spectrum. The robustness of the analysis is rooted in the oscillator-strength sum rule and the fact that we simultaneously measure the real and imaginary parts of the conductivity. In both Bi2212 and Tl2201 we infer a linear temperature dependence of the transport relaxation rate 1/tau and a small but finite zero-temperature intercept. The linear temperature dependence of 1/tau is in accord with expectations for weak elastic scattering in an unconventional superconductor with line nodes and a small residual density of states. The same analysis reveals an onset of inelastic scattering at higher temperatures similar to that seen in the YBCO superconductors. Finally we extrapolate the two-fluid model over a range of frequencies up to five times the measurement frequency, where the extrapolation predicts behaviour that is qualitatively similar to terahertz conductivity data on Bi2212 thin films. While relaxation rates in Bi2212 and Tl2201 are substantially higher than in YBCO there are qualitative similarities between all three materials, and the differences can likely be attributed to varying levels of static disorder. We therefore conclude that a universal picture of quasiparticle scattering in the cuprates is emerging.

Dependence of magnetic penetration depth on the thickness of superconducting Nb thin films

In this paper we present the results of a systematic study on the magnetic field penetration depth of superconducting niobium thin films. The films of thicknesses ranging from $8\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ were deposited on a Si substrate by dc magnetron sputtering. The values of the penetration depth $\ensuremath{\lambda}(0)$ were obtained from the measurements of the effective microwave surface impedance by employing a sapphire resonator technique. Additionally, for the films of thickness smaller than $20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the absolute values of $\ensuremath{\lambda}(0)$ were determined by a microwave transmission method. We found that the reduction of the film thickness below $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ leads to a significant increase of the magnetic field penetration depth from about $80\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for $300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick film up to $230\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for a $8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick film. The dependence of the penetration depth on film thickness is described well by taking into account the experimental dependences of the critical temperature and residual resistivity on the thickness of the niobium films. Structural disordering of the films and suppression of superconductivity due to the proximity effect are considered as mechanisms responsible for the increase of the penetration depth in ultrathin films.

Accurate measurements of the intrinsic surface impedance of thin YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// films using a modified two-tone resonator method

We propose a modified two-tone method that could be used for sensitive measurements of the intrinsic microwave surface impedance (Z/sub S/) of thin superconductor films and the tan/spl delta/ of a low-loss dielectric. An open-gap resonator scheme is used to measure the penetration depth (/spl lambda/) of thin superconductor films and extract the intrinsic Z/sub S/ of the superconductor films from its measured R/sub S//sup eff/ and /spl lambda/. We use a very small gap of 10 /spl mu/m between the top plate and the rest parts of the resonator. The tan/spl delta/ of rutile in the low 10/sup -7/ range and the dielectric constant as high as /spl sim/110 are observed at temperatures below 10 K at /spl sim/15.2 GHz, which enable to measure the R/sub S/ of the 10 mm-in-diameter YBCO films as low as /spl sim/100 /spl mu//spl Omega/ at the same frequency (f). The discrepancy between the R/sub S//sup eff/ at /spl sim/15.2 GHz and that at /spl sim/8.5 GHz scaled to /spl sim/15.2 GHz appears less than 2% when the relations of R/sub S/ /spl prop/ f/sup 2/ and tan/spl delta/ /spl prop/ f are used. We describe usefulness of our measurement method for measuring the intrinsic microwave properties of various superconductor samples.

Observation of the coherence peak in MgB 2 thin films

The coherence peak is observed in the temperature dependence of the real part of the microwave conductivity ( σ 1) of c-axis oriented MgB 2 thin film, which is extracted from microwave surface impedance ( Z s) measurements using a sapphire resonator at 17.9 GHz. The peak appears at a temperature around 0.6 times the critical temperature ( T c), which is greatly shifted downwards in temperature compared with conventional superconductors for which the peak occurs around 0.9 T c. Calculations based on the two-band model suggest that this peak corresponds to the smaller of the two energy gaps.

The superconducting gap of in situ MgB2 thin films by microwave surface impedance measurements

Precision measurements of the microwave surface resistance Rs of in situ MgB2 films directly reveal an exponential behavior of Rs at low temperature indicating a fully-gapped order parameter. The entire temperature dependence of Rs is well described by a Mattis–Bardeen formalism, but with a small gap ratio of Δ(0)/kTc=0.72, corresponding to Δ(0)=1.9 meV.

Microwave spectroscopy of novel superconductors

A hollow dielectric resonator technique has been developed for accurate measurements of the complex microwave surface impedance of novel superconductors from 2 to 20 GHz down to 100 mK. Illustrative measurements of the antiferromagnetic ordering and spin-dynamics of Gd ions in GdBa 2Cu 3O 7 and of microwave penetration and losses in MgB 2 wires and high quality single crystals of Sr 2RuO 4 are presented. Measurements on Sr 2RuO 4 imply an unchanged electron relaxation time τ on entering the superconducting state, a power law temperature dependence of the normal state fraction implying nodes in the superconducting order parameter, and residual low temperature losses on increasing frequency.

Microwave conductivity and penetration depth in the heavy fermion superconductor CeCoIn5.

The electrodynamic properties of the quasi-two-dimensional heavy fermion superconductor CeCoIn5 have been investigated by microwave surface impedance measurements over a wide range of microwave frequencies and temperatures. We derive a value penetration depth lambda(0) approximately 190 nm, with a strong linear term in the temperature dependence of lambda(T) below T(c)/3, consistent with a superconducting gap with line nodes. The real part of the conductivity displays a broad peak at low temperatures consistent with a decreased scattering rate of almost 2 orders of magnitude below T(c). CeCoIn5 has remarkably similar properties to those of the high-T(c) cuprates.

Superconducting gap anisotropy ofLuNi2B2Cthin films from microwave surface impedance measurements

Surface impedance measurements of LuNi2B2C superconducting thin films as a function of temperature have been performed down to 1.5 K and at 20 GHz using a dielectric resonator technique. The magnetic penetration depth closely reproduces the standard B.C.S. result, but with a reduced value of the energy gap at low temperature. These data provide evidence for an anisotropic s-wave character of the order parameter symmetry in LuNi2B2C. From the evaluation of the real part of complex conductivity, we have observed constructive (type II) coherence effects in the electromagnetic absorption below Tc.

Determination of magnetic penetration depth from the reversible magnetization inBi2Sr2CaCu2O8+δ:Dependence on weak disorder and interlayer coupling

The reversible magnetization in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ is analyzed within existing theoretical models. The field-induced suppression of the empirical ``superfluid density'' $dM/d(\mathrm{ln}H)$ are compared for the fluctuation mechanism and for the suppression of the order parameter in the vortex core. The thermal fluctuation term is found to be essentially reduced compared to the theoretical prediction for decoupled pancake vortices. We suggest that the energy of Josephson and magnetic coupling between two-dimensional (2D) layers is at the origin of observed decrease in the entropy term. The interlayer coupling is best maintained in samples with reduced disorder. In the samples of the best quality, the fluctuation contribution to the reversible magnetization drops down to less than ${k}_{B}T/10s{\ensuremath{\Phi}}_{0}$ $(s\ensuremath{\approx}15.4\mathrm{\AA{}}\mathrm{}).$ Taking into account this reduction we obtain the curve ${\ensuremath{\lambda}}^{2}(0)/{\ensuremath{\lambda}}^{2}(T)$ versus T from the reversible magnetization similar to the one obtained from measurements of microwave surface impedance, which is also consistent with ${H}_{c1}$ derived from micro-Hall ac technique. The accuracy of determination of ${H}_{c1}$ from the scaled M vs T curves is found to be even better than that for ${\ensuremath{\lambda}}^{2}(0)/{\ensuremath{\lambda}}^{2}(T).$