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 enhancement larger than the coherence peak, reminiscent of high-$T_c$ cuprate superconductors.
We have studied the lower critical fields H_{c1} of superconducting iron oxipnictide PrFeAsO_{1-y} single crystals for H parallel and perpendicular to the ab-planes. Measurements of the local magnetic induction at positions straddling the sample edge by using a miniature Hall-sensor array clearly resolve the first flux penetration from the Meissner state. The temperature dependence of H_{c1} for H || c is well scaled by the in-plane penetration depth without showing any unusual behavior, in contrast to previous reports. The anisotropy of penetration lengths at low temperatures is estimated to …
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 in single crystals of electron-doped PrFeAsO1-y (y~0.1) and hole-doped Ba1-xKxFe2As2 (x~0.55) are presented. In clean crystals of Ba1-xKxFe2As2, as well as in PrFeAsO1-y crystals, the penetration depth shows flat temperature dependence at low temperatures, indicating that the superconducting gap opens all over the…
High resolution measurements of superfluid density and broadband quasiparticle conductivity have been used to probe the low energy excitation spectrum of nodal quasiparticles in underdoped YBCO. Penetration depth is measured to temperatures as low as 0.05 K. Microwave conductivity is measured from 0.1 to 20 GHz and is a direct probe of zero-energy quasiparticles. The data are compared with predictions for a number of theoretical scenarios that compete with or otherwise modify pure d-wave superconductivity, in particular commensurate and incommensurate spin and charge density waves; d + i s and…
The in-plane magnetic penetration depth, $λ(T)$, was measured down to 0.4 K in single crystals of electron-doped superconductors, Pr$_{1.85}$Ce$_{0.15}$CuO$_{4-δ}$ (PCCO) and Nd$_{1.85}$Ce$_{0.15}$CuO$_{4-δ}$ (NCCO). In PCCO, the superfluid density varies as $T^2$ from 0.025 up to roughly 0.3 $T/T_c$ suggestive of a d-wave state with impurities. In NCCO, $λ(T)$ shows a pronounced upturn for $T < 4$ K due to the paramagnetic contribution of Nd$^{3+}$ ions. Fits to an s-wave order parameter over the standard BCS range ($T/T_c$ = 0.32) limit any gap to less than $Δ_{min} (0)/T_c = 0.57$ in NCCO. …
A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this r…
Local magnetic measurements are used to quantitatively characterize heterogeneity and flux line pinning in PrFeAsO_1-y and NdFeAs(O,F) superconducting single crystals. In spite of spatial fluctuations of the critical current density on the macroscopic scale, it is shown that the major contribution comes from collective pinning of vortex lines by microscopic defects by the mean-free path fluctuation mechanism. The defect density extracted from experiment corresponds to the dopant atom density, which means that dopant atoms play an important role both in vortex pinning and in quasiparticle scatt…
The London penetration depth for the unconventional superconductor Sr$_2$RuO$_4$ is analyzed assuming an order parameter which breaks time reversal symmetry and parity simultaneously. Such a superconducting state possesses chiral quasiparticle states with subgap energies at the surface. We show that these subgap states can give a significant contribution to the low-temperature behavior of the London penetration depth yielding a $ T^2 $ power-law even though bulk quasiparticle spectrum is gapped. The presence of several electron bands gives rise to interband transition among the subgap surface …
Charge doping of iron-pnictide superconductors leads to collective pinning of flux vortices, whereas isovalent doping does not. Moreover, flux pinning in the charge-doped compounds is consistently described by the mean-free path fluctuations introduced by the dopant atoms, allowing for the extraction of the elastic quasiparticle scattering rate. The absence of scattering by dopant atoms in isovalently doped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ is consistent with the observation of a linear temperature dependence of the low-temperature penetration depth in this material.
Comparing ARPES measurements on Bi2212 with penetration depth data, we show that a description of the nodal excitations of the d-wave superconducting state in terms of non-interacting quasiparticles is inadequate, and we estimate the magnitude and doping dependence of the Landau interaction parameter which renormalizes the linear T contribution to the superfluid density. Furthermore, although consistent with d-wave symmetry, the gap with underdoping cannot be fit by the simple coskx-cosky form, which suggests an increasing importance of long range interactions as the insulator is approached.
The temperature ($T$) and magnetic field ($H$) dependence of the magnetic penetration depth, $λ(T,H)$, in Ca(Al$_{0.5}$Si$_{0.5}$)$_2$ exhibits significant deviation from that expected for conventional BCS superconductors. In particular, it is inferred from a field dependence of $λ(H)$ ($\propto H$) at 2.0 K that the quasiparticle excitation is strongly enhanced by the Doppler shift. This suggests that the superconducting order parameter in Ca(Al$_{0.5}$Si$_{0.5}$)$_2$ is characterized by a small energy scale $Δ_S/k_B\le 2$ K originating either from anisotropy or multi-gap structure.
The London penetration depth, $λ(T)$, has been measured in several single crystals of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$. Thermodynamic, electromagnetic, and structural characterization measurements confirm that these crystals are of excellent quality. The observed low temperature variation of $λ(T)$ follows a power-law, $Δλ(T) \sim T^n$ with $n=2.4 \pm 0.1$, indicating the existence of normal quasiparticles down to at least $0.02T_c$. This is in contrast to recent penetration depth measurements on single crystals of NdFeAsO$_{1-x}$F$_x$ and SmFeAsO$_{1-x}$F$_x$, which indicate an anisotropi…
We report on generic trends in the behavior of the interlayer penetration depth $λ_c$ of several different classes of quasi two-dimensional superconductors including high-T$_c$ cuprates, Sr$_2$RuO$_4$, transition metal dichalcogenides and organic materials of the $(BEDT-TTF)_2X$ - series. Analysis of these trends reveals two distinct patterns in the scaling between the values of $λ_c$ and the magnitude of the c-axis DC conductivity $σ_{DC}$: one realized in the systems with a ground state formed out of well defined quasiparticles and the other seen in systems in which the quasiparticles are no…
We report on a microscopic evaluation of electrodynamic response for the vortex lattice state of a model s-wave superconductor. Our calculation accounts self-consistently for both quasiparticle and order parameter response and establishes the collective nature of linear response in the clean limit. We discuss the effects of homogeneous and inhomogeneous pinning on the optical conductivity and the penetration depth, and comment on the relationship between macroscopic and local penetration depths. We find unexpected relationships between pinning arrangements and conductivity due to the strongly …
We formulate a model describing the doping ($x$) and temperature ($T$) dependence of the $ab$-plane and c-axis penetration depth of a cuprate superconductor. The model incorporates the suppression of the superfluid density with underdoping as the system approaches the Mott-Hubbard insulating state by augmenting a d-wave BCS model with a phenomenological charge renormalization factor that is vanishingly small for states away from the nodes of the d-wave pair potential but close to unity in the vicinity of the nodes. The c-axis penetration depth is captured within a model of incoherent electron …
This article develops a quantitative quasiparticle model of the low-temperature properties of d-wave superconductors which incorporates both Fermi-liquid effects and band-structure effects. The Fermi-liquid interaction effects are found to be classifiable into strong and negligible renormalizaton effects, for symmetric and antisymmetric combinations of the energies of $k\uparrow$ and $-k\downarrow$ quasiparticles, respectively. A particularly important conclusion is that the leading clean-limit temperature-dependent correction to the superfluid density is not renormalized by Fermi-liquid inter…
We argue based on theoretical considerations and analysis of experimental data that quasiparticle excitations near the nodes determine the low temperature properties in the superconducting state of cuprates. Quantum effects of phase fluctuations are shown to be quantitatively important, but thermal effects are small for $T \ll T_c$. An anisotropic superfluid Fermi liquid phenomenology is presented for the effect of quasiparticle interactions on the temperature and doping dependence of the low $T$ penetration depth.
Using mm-wave transmission we obtain information about both the real and imaginary part of the dielectric function of superconducting thin films. This is done by fitting the Fabry-Perot resonance spectrum for the film plus substrate over a broad frequency range (110-180 GHz) using the full Fresnel equations and a two-fluid description for the dielectric function. Depending on the thickness of the film, the transmission is mainly determined by the real or the imaginary part of the dielectric function. For NbN we find a behavior consistent with the BCS-formalism. For DyBa_2Cu_3O_7, results on fi…
The quasiparticle excitations in the mixed state of Cd2Re2O7 have been studied by means of muon spin rotation/relaxation. The temperature dependence of the magnetic penetration depth (lambda) is consistent with a nearly isotropic superconducting order parameter, although a slight discrepancy which is dependent on the details in the analysis may be present. This is also supported by the relatively weak field dependence of lambda.
We report the in-plane penetration depth $λ_{\parallel}$ of single crystals $κ$-(BEDT-TTF)$_2X$ ($X=$ Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br) by means of the reversible magnetization measurements under the control of cooling-rate. In $X$ = Cu(NCS)$_2$, $λ_{\parallel}(0)$ as an extrapolation toward $T$ = 0 K does not change by the cooling-rate within the experimental accuracy, while $T_{\textrm{c}}$ is slightly reduced. On the other hand, in $X$ = Cu[N(CN)$_2$]Br, $λ_{\parallel}(0)$ indicates a distinct increase by cooling faster. The different behavior of $λ_{\parallel}(0)$ on cooling-rate between th…
We have measured the temperature dependence of the microwave surface impedance Z_s = R_s + iΩμ_0 of a MgB2 film at a frequency Ω/2Πof 18 GHz employing a dielectric resonator technique. We found that the temperature dependence of the magnetic field penetration depth \Lamda can be fitted by \Lamda(T)= \Lamda(0) [1-(T/Tc)^2] ^(-1/2) with \Lamda(0)=(260 +/- 20)nm. The absolute value of \Lamda(0) was confirmed by direct measurements employing submillimeter wave transmission spectroscopy at 430 GHz. The analysis of the \Lamda(T) data below Tc/2 revealed significant deviations from the quadratic temp…
We report high-sensitivity microwave measurements of the in-plane penetration depth $λ_{ab}$ and quasiparticle scattering rate $1/τ$ in several single crystals of hole-doped Fe-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x\approx 0.55$). While power-law temperature dependence of $λ_{ab}$ with the power $\sim 2$ is found in crystals with large $1/τ$, we observe exponential temperature dependence of superfluid density consistent with the existence of fully opened two gaps in the cleanest crystal we studied. The difference may be a consequence of different level of disorder inherent in the…
We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth $λ$ based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard $U_p$ and interaction between the holes on next-nearest-neighbor oxygen ions $V_2$, allows one to achieve a much better agreement of the calculated temperature dependencies of the value $λ^{-2}$ with the experimental data in La$_{2-x}$Sr$…
The physical properties of low energy superconducting quasiparticles in high- $T_c$ superconductors are examined using magnetic penetration depth and specific heat experimental data. We find that the low energy density of states of quasiparticles of La$_{2-x}$Sr$_x$CuO$_4$ scales with $(x-x_c)/T_c$ to the leading order approximation, where $x_c $ is the critical doping concentration below which $T_c=0$. The linear temperature term of the superfluid density is renormalized by quasiparticle interactions and the renormalization factor times the Fermi velocity is found to be doping independent.
We present a theory of Andreev reflection in a ferromagnet/superconductor/ferromagnet double junction system. The spin polarized quasiparticles penetrate to the superconductor in the range of penetration depth from the interface by the Andreev reflection. When the thickness of the superconductor is comparable to or smaller than the penetration depth, the spin polarized quasiparticles pass through the superconductor and therefore the electric current depends on the relative orientation of magnetizations of the ferromagnets. The dependences of the magnetoresistance on the thickness of the superc…
The magnetic penetration depth $λ$ in the mixed state of MgB$_2$ has been determined microscopically from the field distribution around magnetic vortices probed by muon spin rotation. Both the temperature and magnetic field dependence of $λ$ strongly suggest the presence of delocalized quasiparticles around the vortex cores. In particular, the effect of Doppler shift has been clearly observed as a finite gradient of the field dependence of $λ$, strongly suggesting an anisotropic order parameter with the region of a vanishingly small energy gap.
We have revisited the magnetic penetration depth data on the electron-doped cuprates Pr(2-x)Ce(x)CuO(4-y) and La(2-x)Ce(x)CuO(4-y). It is proposed that the transition between the nodal-gap-like and nodeless-gap-like behaviors upon electron-doping [see, e.g., M. Kim et al., Phys. Rev. Lett. 91, 87001 (2003)] can be due to a scattering of the quasiparticles in the d-wave superconducting state by an incipient or weak antiferromagnetic spin-density-wave. This conjecture is supported by the inelastic neutron scattering and angle-resolved photoemission experiments on some closely related electron-do…
Transverse-field muon spin relaxation rates in single crystals of the heavy-fermion superconductor PrOs4Sb12 (Tc = 1.85 K) are nearly constant in the vortex state for temperatures below ~0.5Tc. This suggests that the superconducting penetration depth lambda(T) is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency measurements yield a stronger temperature dependence of lambda(T), indicative of point nodes in the gap. A similar discrepancy exists in superconducting Sr2RuO4 which, like PrOs4Sb12, breaks time-reversa…
In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ_a), the penetration depth anisotropy (γ=λ_c/λ_a) and the temperature dependence of 1/λ_i^2 (i=a,c) were studied in single crystals. A strong decrease of λ_a with pressure was observed, while γand λ_i^2(0)/λ_i^2(T) are pressure independent. A linear relationship between 1/λ_a^2(270 mK) and Tc was also found. The large decrease of λ_a with pressure is the signature of an increase of the…
The effective superconducting penetration depth measured in the vortex state of PrOs4Sb12 using transverse-field muon spin rotation (TF-muSR) exhibits an activated temperature dependence at low temperatures, consistent with a nonzero gap for quasiparticle excitations. In contrast, Meissner-state radiofrequency (rf) inductive measurements of the penetration depth yield a T^2 temperature dependence, suggestive of point nodes in the gap. A scenario based on the recent discovery of extreme two-band superconductivity in PrOs4Sb12 is proposed to resolve this difference. In this picture a large diffe…
High-precision measurements of magnetic penetration depth $λ$ in clean single crystals of LiFeAs and LiFeP superconductors reveal contrasting low-energy quasiparticle excitations. In LiFeAs the low-temperature $λ(T)$ shows a flat dependence indicative of a fully gapped state, which is consistent with previous studies. In contrast, LiFeP exhibits a $T$-linear dependence of superfluid density $\propto λ^{-2}$, indicating a nodal superconducting order parameter. A systematic comparison of quasiparticle excitations in the 1111, 122, and 111 families of iron-pnictide superconductors implies that th…
Microwave penetration depth $λ$ and surface resistance at 27 GHz are measured in high quality crystals of KOs$_2$O$_6$. Firm evidence for fully-gapped superconductivity is provided from $λ(T)$. Below the second transition at $T_{\rm p}\sim 8$ K, the superfluid density shows a step-like change with a suppression of effective critical temperature $T_{\rm c}$. Concurrently, the extracted quasiparticle scattering time shows a steep enhancement, indicating a strong coupling between the anomalous rattling motion of K ions and quasiparticles. The results imply that the rattling phonons help to enhanc…
We show that the field dependence of the magnetic penetration depth ($λ$), for which muon spin rotation ($μ$SR) is an excellent microscopic probe, provides useful information on the degree of anisotropy for the superconducting order parameter. In type II superconductors associated with anisotropic order parameters, $λ$ is sensitive to the quasiparticle excitation induced by the Doppler shift due to a supercurrent around magnetic vortices. The presence of such low-energy excitations manifests itself in the non-zero slope of $λ$ against an external magnetic field. We review recent results on the…
Transverse-field muon spin rotation ($μ$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $λ(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $λ(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the…
The pressure dependence of the inverse square of the magnetic penetration depth $λ^{- 2}$ in $κ$-$($ET$)_2$Cu(NCS)$_2$ was measured by Larkin, et al According to the paper, $λ^{- 2}$ behaves differently under low pressure and under high pressure. Under low pressure, the development of $λ^{- 2}$ just below $T=T_c$ is rapid compared to the case under high pressure. Moreover, $T_c$ in $κ$-$($ET$)_2$Cu(NCS)$_2$ increases under c-axis pressure up to 1kbar and decreases under higher pressure, while $T_c$ decreases monotonically under the hydrostatic pressure, or under the uniaxial pressure parallel …
CeCoIn5 is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism, and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low temperature microwave spectroscopy to study the charge dynamics of the CeCoIn5 superconducting state. The similarities to cuprates, in particular to ul…
The current-voltage characteristics (IVC) of $S-c-N$ point contacts of superconductors with a small coherence length ${ξ_{0}}$ reveal steps with discrete values of the differential resistance. This peculiarity is associated with a transition of the contact region of the superconductor to a spatially inhomogeneous state under the influence of the current injection of nonequilibrium quasiparticles penetrating the superconductor to a depth ${{l}_{E}}$ . The role of the relaxation of the disbalance between the occupancies of electron- and hole-like branches of the quasiparticle spectrum is manifes…
We measured the optical conductivity of superconducting LiFeAs. In the superconducting state, the formation of the condensate leads to a spectral-weight loss and yields a penetration depth of 225 nm. No sharp signature of the superconducting gap is observed. This suggests that the system is likely in the clean limit. A Drude-Lorentz parametrization of the data in the normal state reveals a quasiparticle scattering rate supportive of spin fluctuations and proximity to a quantum critical point.
The renormalization of the magnetic field penetration depth $λ$ owing to the electron-electron correlation is discussed with its application to high-$T_{\rm c}$ cuprates. The formula for the current carried by quasiparticle with the Umklapp scattering is derived, on the basis of which we investigate how the value of $λ^{-2}$ deviates from that of $n/m^*$ where $n$ and $m^*$ are the carrier density and the effective mass respectively. Although this deviation is small in the case of weak momentum dependence of the vertex, this is large and negative owing to the non-negligible value of the backfl…
We construct a phenomenological superfluid Fermi liquid theory for a two-dimensional d-wave superconductor on a square lattice, and study the effect of quasiparticle interactions on the superfluid density. Using simple models for the dispersion and the Landau interaction function, we illustrate the deviation of these results from those for the isotropic superfluid. This allows us to reconcile the value and doping dependence of the superfluid density slope at low temperature obtained from penetration depth measurements, with photoemission data on nodal quasiparticles.
We describe an experimental protocol to characterize magnetic field dependent microwave losses in superconducting niobium microstrip resonators. Our approach provides a unified view that covers two well-known magnetic field dependent loss mechanisms: quasiparticle generation and vortex motion. We find that quasiparticle generation is the dominant loss mechanism for parallel magnetic fields. For perpendicular fields, the dominant loss mechanism is vortex motion or switches from quasiparticle generation to vortex motion, depending on cooling procedures. In particular, we introduce a plot of the …
A drastic enhancement of the thermal Hall angle in $d$-wave superconductors was observed experimentally in a cuprate superconductor and in CeCoIn$_5$ at low temperatures and very weak magnetic field [Phys. Rev. Lett. $\bf 86$, 890 (2001); Phys. Rev. B $\bf 72$, 214515 (2005)]. However, to the best of our knowledge, its microscopic calculation has not been performed yet. To study this microscopically, we derive the thermal Hall coefficient in extreme type-II superconductors with an isolated pinned vortex based on the augmented quasiclassical equations of superconductivity with the Lorentz force…
In the heavily hole-doped iron-based superconductors $A$Fe$_2$As$_2$ ($A=$ K, Rb, and Cs), the electron effective mass increases rapidly with alkali-ion radius. To study how the mass enhancement affects the superconducting state, we measure the London penetration depth $λ(T)$ in clean crystals of $A$Fe$_2$As$_2$ down to low temperature $T\sim0.1$ K. In all systems, the superfluid stiffness $ρ_s(T)=λ^2(0)/λ^2(T)$ can be approximated by a power-law $T$ dependence at low temperatures, indicating the robustness of strong momentum anisotropy in the superconducting gap $Δ(k)$. The power $α$ increase…
The in-plane thermal conductivity of iron-based superconductor Ca$_{10}$(Pt$_{4-δ}$As$_8$)((Fe$_{1-x}$Pt$_{x}$)$_2$As$_2$)$_5$ single crystal (``10-4-8", $T_c$ = 22 K) was measured down to 80 mK. In zero field, the residual linear term $κ_0/T$ is negligible, suggesting nodeless superconducting gaps in this multiband compound. In magnetic fields, $κ_0/T$ increases rapidly, which mimics those of multiband superconductor NbSe$_2$ and LuNi$_2$B$_2$C with highly anisotropic gap. Such a field dependence of $κ_0/T$ is an evidence for multiple superconducting gaps with quite different magnitudes or hi…
The low temperature surface resistance R_s of d-wave superconductors is calculated as function of frequency assuming normal state quasiparticle mean free paths l in excess of the penetration depth. Results depend strongly on the geometric configuration. In the clean limit, two contributions to R_s with different temperature dependencies are identified: photon absorption by quasiparticles and pair breaking. The size of nonlocal corrections, which can be positive or negative depending on frequency decreases for given l as the scattering phase shift δ_N is increased. However, except in the unitar…
The electromagnetic response of the CuO2-planes is calculated within a strong coupling theory using model tight binding bands and momentum dependent pairing interactions representing spin fluctuations and phonon exchange. The superconducting state resulting from these interactions has d-wave symmetry. With phonon exchange included the order parameter amplitude grows rapidly below Tc at elevated frequencies which leads to improved agreement with the observed temperature dependence of the penetration depth. Good agreement between theory and experiment can only be achieved if it is assumed that t…
We measured the complex conductivity, $σ$, of FeSe$_{1-x}$Te$_x$ ($x=0-0.5$) films in the superconducting state which show a drastic increase of the superconducting transition temperature, $T_\textrm{c}$, when the nematic order disappears. Since the magnetic penetration depth, $λ$ $(>$ 400 nm), of Fe(Se,Te) is longer than the typical thickness of the film ($\sim$100 nm), we combined the coplanar waveguide resonator and cavity perturbation techniques to evaluate both the real and imaginary parts of $σ$. Films with a nematic order showed a qualitatively different temperature dependence in penetr…
In the cuprate superconductor $YBa_2Cu_3O_{6+x}$, hole doping in the $CuO_2$ layers is controlled by both oxygen content and the degree of oxygen-ordering. At the composition $\rm YBa_2Cu_3O_{6.35}$, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from zero to 20 K. Here we exploit this to study the c-axis penetration depth as a function of temperature and doping. The temperature dependence shows the d-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering wi…
Precision measurements of active and reactive components of in-plane microwave surface impedance were performed in single crystals of optimally-doped Fe-based superconductor Ba(Fe1-xCox)2As2 (x = 0.074, Tc = 22.8 K). Measurements in a millimeter wavelength range (Ka band, 35-40 GHz) were performed using whispering gallery mode excitations in the ultrahigh quality factor quasioptical sapphire disk resonator with YBa2Cu2O7 superconducting (Tc = 90 K) end plates. The temperature variation of the London penetration depth is best described by a power-law function, delta λ(T) is proportional to T wi…
In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairing states. Consequently, the superconducting order parameter is generally a mixture of spin singlet and triplet pairing states. In this paper we investigate the structure of the order parameter and its response to disorder for the most symmetric pairing state ($A_1$). Using the example of the heavy Fermion superconductor CePt$_3$Si, we determine ch…
Although quasi-two-dimensional organic superconductors such as $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean systems, with apparent quasiparticle mean-free paths of several thousand Å, the superconducting transition is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K). We propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles. Using a statistical model, we are able to account for the experimental observations. A parameter $\bar{x}$, whi…
We report microwave surface impedances of FeSe$_{0.4}$Te$_{0.6}$ single crystals measured at 12, 19, and 44 GHz. The penetration depth exhibits a power law behavior, $δλ_L=λ_L (T)-λ_L (0) \propto CT^n$ with an exponent $n\simeq 2$, which is considered to result from impurity scattering. This behavior is consistent with $s\pm$-wave pairing symmetry. The temperature dependence of the superfluid density largely deviates from the behavior expected in the BCS theory. We believe that this deviation is caused by the crossover from the dirty regime near $T_c$ to the clean regime at low temperatures, w…
Low-temperature electrical and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor UTe2 to determine the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallographic a- and b-axes reveal a vanishingly small residual fermionic component of the thermal conductivity. The magnetic field dependence of the residual term follows a rapid, quasi-linear increase consistent with the presence of nodal quasiparticles, rising toward the a-axis up…
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…
The in-plane magnetic penetration depth λ_{ab} in optimally doped (BiPb)_2(SrLa)_2CuO_{6+δ} (OP Bi2201) was studied by means of muon-spin rotation. The measurements of λ_{ab}^{-2}(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett {\bf 98}, 267004 (2007)], where it was shown that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. We find that the remaining parts o…
