Inverse Faraday effect (IFE) in superconductors is proposed, where a static magnetization is generated under the influence of a circularly polarized microwave field. Classical modeling of the IFE explicitly provides superconducting gyration coefficient in terms of its complex conductivity. IFE is then considered as a source of nonlinearity and gyrotropy even at a low-power microwave regime giving rise to a spectrum of phenomena and applications. Microwave-induced gyroelectric conductivity, Hall effect, microwave birefringence, flux quantization and vortex state are predicted and quantitatively analyzed. Peculiar microwave birefringence in gyrotropic superconductors due to radical response of superelectrons has been highlighted.
A sensitive polarization modulation technique uses photoelastic modulation and hetrodyne detection to simultaneously measure the Faraday rotation and induced ellipticity in light transmitted by semiconducting and metallic samples. The frequencies measured are in the mid-infrared and correspond to the spectral lines of a CO2 laser. The measured temperature range is continuous and extends from 35 to 330K. Measured samples include GaAs and Si substrates, gold and copper films, and YBCO and BSCCO high temperature superconductors.
We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc-depairing the density of states acquires, for microwaves with frequency $ω_0$, steps at multiples of the photon energy $Δ\pm n\hbarω_0$ and shows an exponential-like tail in the subgap regime. We show that this ac-depairing explains the measured frequency shift of a superconducting resonator with microwave power at low temperatures.
Microwave-field distribution, dissipation, and surface impedance are theoretically investigated for superconductors with laminar grain boundaries (GBs). In the present theory we adopt the two-fluid model for intragrain transport current in the grains, and the Josephson-junction model for intergrain tunneling current across GBs. Results show that the surface resistance $R_s$ nonmonotonically depends on the critical current density $J_{cj}$ at GB junctions, and $R_s$ for superconductors with GBs can be smaller than the surface resistance $R_{s0}$ for ideal homogeneous superconductors without GBs…
Using a real-space renormalization group (RSRG) technique, we compute the microwave conductivity of a d-wave superconductor disordered by extended impurities. To do this, we invoke a semiclassical approximation which naturally accesses the Andreev bound states localized near each impurity. Tunneling corrections (which are captured using the RSRG) lead to a delocalization of these quasiparticles and an associated contribution to the microwave conductivity.
This paper discusses some of the major experimental features of microwave nonlinearity in high temperature superconductors, both intrinsic and extrinsic. The case is made for solving the problem of extrinsic nonlinearity through the use of localized measurements of microwave surface impedance and electromagnetic fields. Along these lines, a brief introduction is given to our work on scanning near-field microwave microscopy
We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticle relaxation time. This contribution also determines the supercurrent dependence of the conductivity. It may significantly exceed the conventional contribution because in typical superconductors the inelastic relaxation time is several orders of magnitude longer than the elastic one. We show that the aforementioned contribution to the conductivity …
Relaxation of the microwave second order response of YBa2Cu3O7 and Ba0.6K0.4BiO3 crystals in the critical state is studied. The samples are exposed to static and pulsed microwave magnetic fields. The second harmonic signals decay during the time in which the microwave pulse endures. The decay times depend on the supercon-ductor investigated and on the way the value of the static field has been reached.
We discuss the applied magnetic field dependence of the absorption of microwaves by a 3-dimensional array up to 30x30x30 Josephson junctions with random parameters including the resistivity, capacity and inductance of each junction. The numerical simulation results for the networks show characteristic microwave absorption anomalies observed in the ceramic samples of high temperature superconductor YBa2Cu3O(7-x). We also provide a discussion of the absorption in simple analytical terms of Josephson loop instabilities.
Enhanced microwave absorption, larger than that in the normal state, is observed in fine grains of type-II superconductors (MgB$_2$ and K$_3$C$_{60}$) for magnetic fields as small as a few $\%$ of the upper critical field. The effect is predicted by the theory of vortex motion in type-II superconductors, however its direct observation has been elusive due to skin-depth limitations; conventional microwave absorption studies employ larger samples where the microwave magnetic field exclusion significantly lowers the absorption. We show that the enhancement is observable in grains smaller than the…
Within the framework of the time-dependent Ginzburg-Landau theory we show that circularly polarized THz or far-infrared radiation induces a dc supercurrent that influences the dynamics of vortex-antivortex pair formation in a mesoscopic superconductor undergoing rapid thermal quenching. The Lorentz force arising from the supercurrents promotes vortex-antivortex separation and allows survival of the vortex polarity defined by the helicity of light. Based on this idea, we propose a two-stage irradiation scheme that provides a powerful method for controlled all-optical generation of Abrikosov vor…
Broadband microwave spectroscopy can probe material properties in wide spectral and temperature ranges, including superconductors at cryogenic temperatures. The quality of such measurements crucially depends on the calibration, which also removes from the obtained spectra signatures of standing waves. Here we consider low-temperature reflection measurements in Corbino geometry, and we show that the non-linear response of superconducting samples close to the critical temperature can lead to strong signatures of standing waves even in a well-calibrated Corbino spectrometer. We demonstrate our fi…
We discuss the microwave energy losses in superconductors in the critical state. The field-induced variations of the surface resistance are determined, in the framework of the Coffey and Clem model, by taking into account the distribution of the vortex magnetic field inside the sample. It is shown that the effects of the critical state cannot generally be disregarded to account for the experimental data. Results obtained in bulk niobium at low temperatures are quantitatively justified.
There has long been a discrepancy between microwave conductivity measurements in high temperature superconductors and the conductivity spectrum expected in the simplest models for impurity scattering in a d-wave superconductor. Here we present a new type of broadband measurement of microwave surface resistance that finally shows some of the spectral features expected for a d_{x^2-y^2} pairing state. Cusp-shaped conductivity spectra, consistent with weak impurity scattering of nodal quasiparticles, were obtained in the 0.6-21 GHz frequency range in highly ordered crystals of YBa_2Cu_3O_{6.50} a…
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.
Recent microwave conductivity measurements of detwinned, high-purity, slightly overdoped YBa$_{2}$Cu$_{3}$O$_{6.993}$ crystals reveal a linear temperature dependence and a near-Drude lineshape for temperatures between 1 and 20 K and frequencies ranging from 1 to 75 GHz. Prior theoretical work has shown that simple models of scattering by point defects (impurities) in d-wave superconductors are inconsistent with these results. It has therefore been suggested that scattering by extended defects such as twin boundary remnants, left over from the detwinning process, may also be important. We calcu…
We report a set of experimental data on local third-harmonic generation at microwave frequencies (0.5 GHz) in $YBa_2Cu_3O_7$ and Nb films. For local investigations of the nonlinear response a probe with inductive coupling was elaborated. The map of the nonlinear microwave response of a $YBa_2Cu_3O_7$ thin film is plotted below $T_c$ with high resolution. The third-harmonic power is measured as a function of temperature, input power and dc magnetic field at some areas of the film. The correlation between the depinning current density ${J_p}$ and the nonlinear microwave response is also demonstr…
Microwave spectroscopy is a powerful experimental tool to reveal information on the intrinsic properties of superconductors. Superconducting stripline resonators, where the material under study constitutes one of the ground planes, offer a high sensitivity to investigate superconducting bulk samples. In order to improve this measurement technique, we have studied stripline resonators made of niobium, and we compare the results to lead stripline resonators. With this technique we are able to determine the temperature dependence of the complex conductivity of niobium and the energy gap $Δ(0)=2.1…
We address, using concepts of the microscopic theory of superconductivity, parametric amplifiers and kinetic inductance detectors focusing on the interaction of microwave radiation with the superconducting condensate. This interaction was identified recently as the source of the apparent dissipation in microwave superconducting micro-resonators at low temperatures. Since the evaluation of the performance of practical devices based only on the microwave-response is not sufficiently informative about the underlying physical processes, we propose an experimental system to measure the microscopica…
We discuss the temperature, frequency, and power-dependent surface resistance of the boride superconductor MgB2 in relation to possible applications for passive microwave devices. The data available in the literature are compared with results for polycrystalline Nb3Sn and epitaxial YBa2Cu3O7-x, which are representative of the classical and cuprate superconductors. MgB2 displays all specific features that make superconductors attractive for high-performance devices, even though the fabrication technology is not yet mature. We attempt to identify promising areas of applications, as well as mater…
The cusp-like behavior of the microwave conductivity observed in clean ortho-II YB$_{2}$Cu$_{3}$O$_{6.50}$ at low temperature and low frequency is shown to be related directly to a linear in frequency dependence of the impurity scattering rate with a negligibly small value at zero frequency. In the weak scattering limit, the conductivity decreases linearly with the frequency. In the vortex state, assuming a random (Gaussian) distribution of vortices, we show that the magnetic field profoundly alters the impurity scattering rate, which now acquires a finite zero frequency value. As a consequenc…
We have investigated both the temperature and the power dependence of microwave losses for various dielectrics commonly used as substrates for the growth of High critical Temperature Superconductor thin films. We present measurement of niobium superconducting $λ/2$ coplanar waveguide resonators, fabricated on $La_{0.3}Sr_{0.7}Al_{0.65}Ta_{0.35}O_3$ (LSAT), $MgO$ (MgO) and $LaAlO_3$ (LAO), at the millikelvin temperature range and at low input power. By comparing our results with the Two-Level System (TLS) model, we have discriminated among different dominant loss mechanisms. LSAT has shown the …
In-plane microwave penetration depth $λ_{ab}$ and quaiparticle conductivity at 28 GHz are measured in underdoped single crystals of the Fe-based superconductor PrFeAsO$_{1-y}$ ($T_c\approx 35$ K) by using a sensitive superconducting cavity resonator. $λ_{ab}(T)$ shows flat dependence at low temperatures, which is incompatible with the presence of nodes in the superconducting gap $Δ({\bf k})$. The temperature dependence of the superfluid density demonstrates that the gap is non-zero ($Δ/k_BT_c\gtrsim 1.6$) all over the Fermi surface. The microwave conductivity below $T_c$ exhibits an enhancemen…
We review recent progress in the theory of electromagnetic response of dirty superconductors subject to microwave radiation. The theory originally developed by Eliashberg in 1970 and soon after that elaborated in a number of publications addressed the effect of superconductivity enhancement in the vicinity of the transition temperature. This effect originates from nonequilibrium redistribution of quasiparticles and requires a minimal microwave frequency depending on the inelastic relaxation rate and temperature. In a recent series of papers we generalized the Eliashberg theory to arbitrary tem…
A theory of dissipative nonlinear conductivity, $σ_1(ω,H)$, of s-wave superconductors under strong electromagnetic fields at low temperatures is proposed. Closed-form expressions for $σ_1(H)$ and the surface resistance $R_s(ω,H)$ are obtained in the nonequilibrium dirty limit for which $σ_1(H)$ has a significant minimum as a function of a low-frequency $(\hbarω\ll k_BT)$ magnetic field $H$. The calculated microwave suppression of $R_s(H)$ is in good agreement with recent experiments on alloyed Nb resonator cavities. It is shown that superimposed dc and ac fields, $H=H_0+H_a\cosωt$, can be used…
The self-consistent t-matrix approximation for impurity scattering in unconventional superconductors is used to interpret recent measurements of the temperature and frequency dependence of the microwave conductivity of YBCO crystals below 20K. In this theory, the conductivity is expressed in terms of a fequency dependent single particle self-energy, determined by the impurity scattering phase shift which is small for weak (Born) scattering and approaches $π/ 2$ for unitary scattering. Inverting this process, microwave conductivity data are used to extract an effective single-particle self-ener…
We report on transient effects in the microwave second-order response of two ceramic MgB2 samples. The time evolution of the second-harmonic signal is investigated for about 500 s after the sample has been exposed to a variation of the dc magnetic field. We suggest that during the first seconds the response is determined by diffusive motion of fluxons, while in the time scale of minutes it is ruled by magnetic relaxation over the surface barrier.
A phenomenological model is proposed which describes the effect of both dc and rf magnetic fields, $H$, on the microwave surface impedance, Z_s=R_s+jX_s, of a superconductor containing weak link. Two cases are considered; a weak link between two grains, shunted by another grain, and a non-shunted weak link. In both cases the dependences of R_s and X_s on applied field H were found to be anomalous. Under certain conditions, the values of Z_s(H) can fall below the zero-field values. Comparison with experiment is performed, and very good qualitative and (in some cases) quantitative agreement is f…
We report experimental results of the field-induced variations of the microwave surface resistance in samples of MgB2, produced by different methods. By sweeping the DC magnetic field at increasing and decreasing values, we have detected a magnetic hysteresis that can be ascribed to the different magnetic induction, due to the critical state of the fluxon lattice. The hysteresis observed in the bulk samples has an unusual shape, which cannot be justified in the framework of the critical-state models.
The temperature dependence of the microwave surface impedance and conductivity are used to study the pairing symmetry and properties of cuprate superconductors. However, the superconducting properties can be hidden by the effects of paramagnetism and antiferromagnetic long-range order in the cuprates. To address this issue we have investigated the microwave electrodynamics of GdBa_2Cu_3O_{7-δ}, a rare-earth cuprate superconductor which shows long-range ordered antiferromagnetism below T_N=2.2 K, the Neel temperature of the Gd ion subsystem. We measured the temperature dependence of the surface…
We investigate the influence of extended scatterers on the finite temperature and finite frequency microwave conductivity of d-wave superconductors. For this purpose we generalize a previous treatment by Durst and Lee, which is based on a nodal approximation of the quasiparticle excitations and scattering processes, and apply it to the analysis of experimental spectra of YBCO-123 and BSCCO-2212. For YBCO, we find that accounting for a slight spatial extension of the strong scattering in-plane defects improves the fit of the low temperature microwave conductivity to experiment. With respect to …
Almost any use of a superconductor implies a nonequilibrium state. Remarkably, the non-equilibrium states induced by a microwave stimulus and the dynamics of magnetic flux quanta (Abrikosov vortices) can give rise to strikingly contrary effects: A sufficiently high-power electromagnetic field of GHz frequency can stimulate superconductivity, whereas fast vortex motion can trigger an instability abruptly quenching the superconducting state. Here, we advance or delay such dynamical quenching of the vortex state in Nb thin films by tuning the power and frequency of the microwave ac stimulus added…
We report on transient effects in the microwave second-order response of different type of superconductors in the mixed state. The samples have contemporarily been exposed to a dc magnetic field, varying with a constant rate of 60 Oe/s, and a pulsed microwave magnetic field. The time evolution of the signal radiated at the second-harmonic frequency of the driving field has been measured for about 500 s from the instant in which the dc-field sweep has been stopped, with sampling time of about 0.3 s. We show that the second-harmonic signal exhibits two relaxation regimes; an initial exponential …
We report on the microwave properties of a resonant cylindrical cavity made of bulk MgB2 superconductor, produced by the reactive liquid Mg infiltration process. The frequency response of the cavity has been measured in the range 5-13GHz. Among the various modes, the TE011, resonating at 9.79GHz, exhibits the highest quality factor. For this mode, we have determined the temperature dependence of the quality factor, obtaining values of the order of 10^5 in the temperature range 4.2-30K. The values of the surface resistance deduced from the measurements of the quality factor agree quite well wit…
We probe the effects of strong disorder (2.4 < kFl < 8.6) on superconductivity in thin films of niobium titanium nitride and titanium nitride by measuring the microwave electrodynamics in coplanar waveguide resonators. We find a gradual evolution of the electromagnetic response with disorder, deviating from Mattis-Bardeen theory, for both materials. This result can be understood as due to changes in the quasiparticle density of states, induced by the short elastic scattering length. The observations are consistent with a model using an effective pair breaker, dependent on the level of disorder…
The field-induced variations of the microwave surface resistance are investigated in two different samples of powdered MgB2. The experimental results can be justified in the framework of the Coffey and Clem model with fluxons moving in the flux-flow regime, provided that the anisotropy of the upper critical field is taken into due account. Assuming the angular dependence of the upper critical field expected from the anisotropic Ginzburg-Landau theory, we determine the anisotropy factor by fitting the experimental data of the field dependence of the microwave surface resistance. We show that th…
We briefly review some non-accelerator high-frequency applications of superconductors. These include the use of high-Tc superconductors in front-end band-pass filters in cellular telephone base stations, the High Temperature Superconductor Space Experiment, and high-speed digital electronics. We also present an overview of our work on a novel form of near-field scanning microscopy at microwave frequencies. This form of microscopy can be used to investigate the microwave properties of metals and dielectrics on length scales as small as 1 mm. With this microscope we have demonstrated quantitativ…
We consider the implications of the small Fermi surface for the ab-plane microwave absorption. The small Fermi surface results in two superconducting condensates. Linear combinations of these condensates correspond to the d- and g-wave pairings. Microwave electric field applied in the ab-plane induces Josephson transitions between the condensates. Dependence of the absorption upon direction, amplitude and frequency of the external microwave field is calculated. Results of the calculation are compared with the observed recently novel non-linear phenomena in microwave absorption of $YBaCu_2O_{7-…
We consider the far-infrared and the microwave conductivities of a two-band superconductor with non-magnetic impurities. The strong coupling expressions for the frequency and temperature dependent conductivity of a two-band superconductor are developed assuming isotropic bands and interactions. Our numerical results obtained using realistic interaction parameters for MgB$_{2}$ are compared with experiments on this compound. We find that the available experimental results for the far-infrared conductivity of MgB$_{2}$ are consistent with multi-band superconductivity in the presence of a suffici…
It is now well known that the properties of the disordered s wave superconductors can deviate significantly from the prediction of standard Bardeen-Cooper-Schrieffer (BCS) theory. By measuring the temperature dependence of the resonance frequency, $f_0$, of microwave resonators made from disordered NbTiN and TiN thin films, at low temperatures, below half of the superconducting critical temperature, $T_c$, Driessen et al. \cite{driessen2012PRL} demonstrated that $f_0$ vanishes faster than predicted from the BCS theory. Here, we report on the temperature dependence of $f_0$ of microwave resonat…
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 …
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.
In the approximation of validity of the Drude expression for quasiparticle conductivity and the assumption that all electrons at T = 0 transform into a superfluide condensate, the expression for the quasiparticle scattering rate tau -1 in terms of the real and imaginary parts of the microwave surface impedance has been obtained. The resulting expression is a generalization of the well-known expression for tau^-1, valid for omega x tau is much less 1, to an arbitrary value of omega x tau, where omega is the frequency of the microwave field. From experimental Ka-band impedance measurements, temp…
The linear and nonlinear response to a microwave electromagnetic field of two c-axis oriented polycrystalline samples of the newly discovered superconductor CaC6 (Tc = 11.5 K) is studied in the superconducting state down to 2 K. The surface resistance Rs and the third order intermodulation distortion, arising from a two-tone excitation, have been measured as a function of temperature and microwave circulating power. Experiments are carried out using a dielectrically loaded copper cavity operating at 7 GHz in a "hot finger" configuration. The results confirm recent experimental findings that Ca…
Here we give a results of experimental study of enhancement of superconductivity by microwave irradiation in superconducting films. An influence of the power, frequency of microwave irradiation, as well as temperature and width of superconducting films on behavior of experimental dependencies of enhanced critical current and the current at which a vortex structure of the resistive state vanishes and the phase-slip first line appears is analyzed. The experimental studies of films with different width reveal that the effect of superconductivity enhancement by microwave field is common and occurs…
The proximity coupled topological insulator / superconductor (TI/SC) bilayer system is a representative system to realize topological superconductivity. In order to better understand this unique state and design devices from the TI/SC bilayer, a comprehensive understanding of the microscopic properties of the bilayer is required. In this work, a microwave Meissner screening study, which exploits a high-precision microwave resonator technique, is conducted on the SmB6/YB6 thin film bilayers as an example TI/SC system. The study reveals spatially dependent electrodynamic screening response of th…
We investigate the coupling between ferromagnet and superconducting phase dynamics in superconductor-ferromagnet-superconductor Josephson junction. The current-voltage characteristics of the junction demonstrate a pattern of subharmonic current steps which forms a devil's staircase structure. We show that a width of the steps becomes maximal at ferromagnetic resonance. Moreover, we demonstrate that the structure of the steps and their widths can be tuned by changing the frequency of the external magnetic field, ratio of Josephson to magnetic energy, Gilbert damping and the junction size.
We performed resonant microwave measurements on superconducting titanium (Ti) down to temperatures of 40~mK, well below its critical temperature $T_\mathrm{c} \approx 0.5$~K. Our wide frequency range 3.3-40~GHz contains the zero-temperature energy gap $2Δ_0$ and allows us to probe the full electrodynamics of the superconducting state, including excitations across the gap and the low-frequency responses of superfluid condensate and thermal quasiparticles. The observed behavior follows the predictions of the BCS-based Mattis-Bardeen formalism, which implies that superconducting Ti is in the dirt…
We study the variation of the differential conductance $G=dj/dV$ of a normal metal wire in a Superconductor/Normal metal heterostructure with a cross geometry under external microwave radiation applied to the superconducting parts. Our theoretical treatment is based on the quasiclassical Green's functions technique in the diffusive limit. Two limiting cases are considered: first, the limit of a weak proximity effect and low microwave frequency, second, the limit of a short dimension (short normal wire) and small irradiation amplitude.
