Isotropic S-wave Research Articles

London penetration depth at zero temperature and near the superconducting transition

A simple relation is established between the zero-$T$ penetration depth $\lambda (0)$ and the slope of $\lambda^{-2}(T)$ near $T_c$, similar to Helfand-Werthamer's relation for $H_{c2}(0)$ and the slope of $H_{c2}(T)$ at $T_c$ for the isotropic s-wave case with non-magnetic scattering.\cite{HW} When the scattering parameter $\rho=\hbar v/2\pi T_c\ell$ ($v$ is the Fermi velocity and $\ell$ is the mean-free path) varies from 1 to 10, the coefficient of proportionality between $\lambda^{-2}(0)$ and $T_c (d\lambda^{-2}/dT)_{T_c}$ changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express $\lambda (0)$ in terms of the slope $(dH_{c2}/dT)_{T_c}$ and the density of states.

Electronic properties of PuNi3-type intermetallic superconductor LaRh3

Electrical resistivity, magnetic susceptibility, and heat capacity of the intermetallic superconductor LaRh3 are systematically studied. LaRh3 crystallizes in the PuNi3-type rhombohedral structure, which displays a sharp superconducting transition at temperature ≈ 2.6 K on both the electrical resistivity and magnetic susceptibility curves. The magnetization hysteresis loop indicates that LaRh3 is a type-II superconductor. The estimated zero-temperature upper critical field μ0Hc2(0) is around 0.8 T, which locates far below the Pauli limit, indicating possible conventional superconductivity. Further analysis on the heat capacity data reveals that LaRh3 is a weak-coupling BCS superconductor with an isotropic s-wave gap.

Symmetry of Order Parameters in Multiband Superconductors LaRu_{4}As_{12} and PrOs_{4}Sb_{12} Probed by Local Magnetization Measurements.

The temperature dependencies of the lower critical field H_{c1}(T) of several filled-skutterudite superconductors were investigated by local magnetization measurements. While LaOs_{4}As_{12} and PrRu_{4}As_{12} exhibit the H_{c1}(T) dependencies consistent with the single-band BCS prediction, for LaRu_{4}As_{12} (the superconducting temperature T_{c}=10.4 K) with a similar three-dimensional Fermi surface, we observe a sudden increase in H_{c1}(T) deep in a superconducting state below about 0.32T_{c}. Remarkably, a rapid rise of H_{c1}(T) at approximately the same reduced temperature 0.27T_{c} is also found for the heavy-fermion compound PrOs_{4}Sb_{12} (T_{c}≃1.78 K), in fair accord with the earlier macroscopic study. We attribute the unusual H_{c1}(T) dependencies of LaRu_{4}As_{12} and PrOs_{4}Sb_{12} to a kink structure in their superfluid densities due to different contributions from two nearly decoupled bands. Whereas LaRu_{4}As_{12} is established as a two-band isotropic s-wave superconductor, nonsaturating behavior of H_{c1}(T) is observed for PrOs_{4}Sb_{12}, indicative of an anisotropic structure of a smaller gap. For this superconductor with broken time-reversal symmetry, our findings suggest a superconducting state with multiple symmetries of the order parameters.

Electronic band structure and superconducting properties of SnAs

We report comprehensive study of physical properties of the binary superconductor compound SnAs. The electronic band structure of SnAs was investigated using both angle-resolved photoemission spectroscopy (ARPES) in a wide binding energy range and density functional theory (DFT) within generalized gradient approximation (GGA). The DFT/GGA calculations were done including spin-orbit coupling for both bulk and (111) slab crystal structures. Comparison of the DFT/GGA band dispersions with ARPES data shows that (111) slab much better describes ARPES data than just bulk bands. Superconducting properties of SnAs were studied experimentally by specific heat, magnetic susceptibility, magnetotransport measurements and Andreev reflection spectroscopy. Temperature dependences of the superconducting gap and of the specific heat were found to be well consistent with those expected for the single band BCS superconductors with an isotropic s-wave order parameter. Despite spin-orbit coupling is present in SnAs, our data shows no signatures of a potential unconventional superconductivity, and the characteristic BCS ratio $2\Delta/T_c = 3.48 - 3.73$ is very close to the BCS value in the weak coupling limit.

Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities

We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The non-linear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in recent experiments is naturally explained by the excitation of Higgs mode mediated by impurity scattering.

Characterizing the Josephson Effect on Ba-122 Single-Crystal Junctions

This paper presents c-direction hybrid Josephson junctions with base electrodes of Co:BaFe2As2 single crystals. To realize Josephson junctions, it applies standard photolithography technologies and a newly developed surface polishing method that was used. As conventional isotropic s-wave superconductor counter electrodes used double layers of Pb/In. The artificial barrier for the tunneling junctions consists of a thin sputtered Ti layer or a thermally evaporated Al layer; both layers were used as an insulator barrier. For characterizing the Josephson effects with TiOx barrier, we could realize IcRN products of about 13.7 μV and unconventional Ic-T dependencies. The formation of Shapiro steps under the influence of microwave irradiation and magnetic field to the junctions will be discussed as well.

Seismic structure beneath the Reykjanes Peninsula, southwest Iceland, inferred from array-derived Rayleigh wave dispersion

The aim is to obtain a site-specific S-wave structure beneath the Reykjanes Peninsula, southwest Iceland. Nine broadband stations of the Reykjanet network are used to find Rayleigh-wave phase velocity dispersion in a relatively wide range of periods (from 3 to 50 s). The records analyzed were made in the years 2013 to 2015 and concern fourteen selected earthquakes whose epicentral distances range from tens of kilometers to almost ten thousand kilometers. Our approach to retrieving Rayleigh phase velocity dispersion involves two partly independent methods allowing for array apertures larger than a wavelength: 1) the zero-crossing point method, and 2) the phase-plane method. The two methods used here work with seismograms decomposed into quasi-harmonic components and implicitly assume a single plane wave propagation. The good match between the dispersion curves obtained by means of the two methods indicates that the assumption has been reasonably fulfilled. The Rayleigh wave phase velocity dispersion data are inverted into a horizontally layered isotropic S-wave velocity model of the Earth's crust and uppermost mantle by a modified method of the single-parameter variation. At shallow depths, the derived model is rather similar to some previous models that were derived predominantly from the arrival times of body waves. At depths exceeding about 20 km, the dispersion data require low S-wave velocities, indicating a noticeable low-velocity zone.

Superconductivity in Ru0.55Rh0.45P and Ru0.75Rh0.25As probed by muon spin relaxation and rotation measurements

Superconductivity in the pseudo-binary pnictides Ru0.55Rh0.45P and Ru0.75Rh0.25As is probed by muon spin relaxation and rotation (muSR) measurements in conjuction with magnetic susceptibility, heat capacity and electrical resistivity measurements. Powder x-ray diffraction confirmed the MnP-type orthorhombic structure (space group Pnma) and showed a nearly single phase nature with small impurity phase(s) of about 5% for both the samples. The occurence of bulk superconductivity is confirmed with Tc = 3.7 K for Ru0.55Rh0.45P and T = 1.6 K for Ru0.75Rh0.25As. The superconducting state electronic heat capacity data reveal weak-coupling single-band isotropic s-wave gap BCS superconductivity. Various normal and superconducting state parameters are determined which reveal a weak-coupling electron-phonon driven type-II dirty-limit superconductivity for both the compounds. The upper critical field shows a linear temperature dependence down to the lowest measured temperatures which is quite unusual for a single-band superconductor. The muSR data confirm the conventional type-II behavior, and show evidence for a single-band s-wave singlet pairing superconductivity with a preserved time reversal symmetry for both the compounds.

Temperature and frequency of complex conductivity, penetration depth and superfluid density of Ba(Fe1−xCox)2As2-superconductor in one- and two-gap models

The temperature and frequency dependence of complex dynamical conductivity $$\sigma = \sigma_{1} + i\sigma_{2}$$ , penetration depth, and superfluid density of Ba(Fe1−xCox)2As2 are calculated in the framework of one- and two-gap models at terahertz frequencies for a temperature range of 2 K < T < TC (TC = 22 K). In the single-gap model, an isotropic s-wave gap without any node and a d-wave gap with possible nodes are considered. In the two-gap model, one of the gaps was considered isotropic s-wave gap with amplitude $$\varDelta_{A} = 3\;{\text{meV}}$$ , while the other gap was supposed to be an anisotropic d-wave gap with possible nodes, and its rms amplitude was $$\varDelta_{0} = 8\;{\text{meV}}$$ . The interaction between the gaps is waived, since it is small, and its description is problematic. Comparing the result with the experimental data proves that the two-gap model consistently describes the optical characteristics of Ba(Fe1−xCox)2As2. In the two-gap model, the temperature dependence of $$\sigma_{1}$$ demonstrated a coherence peak at frequencies below 15 cm−1. The temperature dependence of the penetration depth calculated from $$\sigma_{2}$$ shows power-law behavior at low temperatures, and the superfluid density varies steeply near TC.

Magnetic Exchange Fields and Domain Wall Superconductivity at an All-Oxide Superconductor-Ferromagnet Insulator Interface.

At a superconductor-ferromagnet (S/F) interface, the F layer can introduce a magnetic exchange field within the S layer, which acts to locally spin split the superconducting density of states. The effect of magnetic exchange fields on superconductivity has been thoroughly explored at S-ferromagnet insulator (S/FI) interfaces for isotropic s-wave S and a thickness that is smaller than the superconducting coherence length. Here we report a magnetic exchange field effect at an all-oxide S/FI interface involving the anisotropic d-wave high temperature superconductor praseodymium cerium copper oxide (PCCO) and the FI praseodymium calcium manganese oxide (PCMO). The magnetic exchange field in PCCO, detected via magnetotransport measurements through the superconducting transition, is localized to the PCCO/PCMO interface with an average magnitude that depends on the presence or absence of magnetic domain walls in PCMO. The results are promising for the development of all-oxide superconducting spintronic devices involving unconventional pairing and high temperature superconductors.

Superconducting pairing of topological surface states in bismuth selenide films on niobium.

A topological insulator film coupled to a simple isotropic s-wave superconductor substrate can foster helical pairing of the Dirac fermions associated with the topological surface states. Experimental realization of such a system is exceedingly difficult, however using a novel "flip-chip" technique, we have prepared single-crystalline Bi2Se3 films with predetermined thicknesses in terms of quintuple layers (QLs) on top of Nb substrates fresh from in situ cleavage. Our angle-resolved photoemission spectroscopy (ARPES) measurements of the film surface disclose superconducting gaps and coherence peaks of similar magnitude for both the topological surface states and bulk states. The ARPES spectral map as a function of temperature and film thickness up to 10 QLs reveals key characteristics relevant to the mechanism of coupling between the topological surface states and the superconducting Nb substrate; the effective coupling length is found to be much larger than the decay length of the topological surface states.

Superconducting properties of molybdenum ruthenium alloy Mo0.63Ru0.37

Resistance, magnetization and specific heat measurements were performed on Mo0.63Ru0.37 alloy. All of them confirm that Mo0.63Ru0.37 becomes superconducting at about 7.0 K with bulk nature. Its upper critical field behavior fits to Werthamer-Helfand-Hohenberg (WHH) model quite well, with an upper critical field of μ0Hc2(0) = 8.64 T, less than its Pauli limit. Its electronic specific heat is reproduced by Bardeen-Cooper-Schriffer (BCS)-based α-model with a gap ratio Δ0 = 1.88k B T c , which is a little larger than the standard BCS value of 1.76. We concluded that Mo0.63Ru0.37 is a fully gapped isotropic s-wave superconductor, with its features are mostly consistent with the conventional theory.

Band structure and Fermi surfaces of the reentrant ferromagnetic superconductor Eu(Fe0.86Ir0.14)2As2

The electronic structure of the reentrant superconductor Eu(Fe$_{0.86}$Ir$_{0.14}$)$_{2}$As$_{2}$ (T$_c$ = 22 K) with coexisting ferromagnetic order (T$_M$ = 18 K) is investigated using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS). We study the in-plane and out-of-plane band dispersions and Fermi surface (FS) of Eu(Fe$_{0.86}$Ir$_{0.14}$)$_{2}$As$_{2}$. The near E$_F$ Fe 3d-derived band dispersions near the $\Gamma$ and X high-symmetry points show changes due to Ir substitution, but the FS topology is preserved. From momentum dependent measurements of the superconducting gap measured at T = 5 K, we estimate an essentially isotropic s-wave gap ($\Delta\sim5.25\pm 0.25$ meV), indicative of strong-coupling superconductivity with 2$\Delta$/k$_{B}$T$_{c}\simeq$ 5.8. The gap gets closed at temperatures T $\geq$ 10 K, and this is attributed to the resistive phase which sets in at T$_M$ = 18 K due to the Eu$^{2+}$-derived magnetic order. The modifications of the FS with Ir substitution clearly indicates an effective hole doping with respect to the parent compound.

Specific heat of FeSe: Two gaps with different anisotropy in superconducting state

We present detailed study of specific heat of FeSe single crystals with critical temperature Tc=8.45K at 0.4−200K in magnetic fields 0−9T. Analysis of the electronic specific heat at low temperatures shows the coexistence of isotropic s-wave gap and strongly anisotropic extended s-wave gap without nodes. It was found two possibilities of superconducting gap parameters which give equally description of experimental data: (i) two gaps with approximately equal amplitudes and weight contribution to specific heat: isotropic Δ1=1.7 meV (2Δ1/kBTc=4.7) and anisotropic gap with the amplitude Δ2max=1.8 meV (2Δ2max/kBTc=4.9 and anisotropy parameter m=0.85); (ii) two gaps with substantially different values: isotropic large gap Δ1=1.65 meV (2Δ1/kBTc=4.52) and anisotropic small gap Δ2max=0.75 meV (2Δ2max/kBTc=2) with anisotropy parameter m=0.71. These results are confirmed by the field behavior of the residual electronic specific heat γr.

How does the break-junction quasiparticle tunnel conductance look like for d-wave superconductors?

The bias-voltage, V, dependences of the differential tunnel conductance G(V) = dJ/DV were calculated for the quasiparticle current J flowing in the ab plane across the break junction made of d-wave superconductors. The tunnel directionality effect was taken into account by introducing an effective tunneling cone described by the angle 2θ0. It was shown that G(V) looks like predominantly d-wave or isotropic s-wave ones, depending on the magnitude of θ0 and the rotation angles of the crystal lattices of electrodes with respect to the junction plane. In certain configurations, the G(V) dependences of nominally symmetric S-I-S junctions may turn out similar to those for non-symmetric S–I–N junctions (here, S, I, and N denote superconductors, insulators, and normal metals, respectively) and provide misleading information about the actual energy gap. At finite temperatures, sub-gap structures appear, which possess features appropriate to both d- and s-wave superconductors and are dependent on the problem parameters.

Particular type of a gap in the spectrum of multiband superconductors

We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic orbitals of different symmetries. This gap has composite superconducting-hybridization origin, because it exists only if both the superconductivity and the hybridization between different kinds of orbitals are present. So for many classes of superconductors with multiorbital structure such spectrum changes should take place. These particular changes in the spectrum at some distance from the Fermi level result in slow convergence of the spectral weight of the optical conductivity even in quite conventional superconductors with isotropic s-wave pairing mechanism.

Highly anisotropic superconducting gaps and possible evidence of antiferromagnetic order in FeSe single crystals

Specific heat has been measured in FeSe single crystals down to 0.414 K under magnetic fields up to 16 T. A sharp specific heat anomaly at about 8.2 K is observed and is related to the superconducting transition. Another jump of specific heat is observed at about 1.08 K which may either reflect an antiferromagnetic transition of the system or a superconducting transition arising from Al impurity. We would argue that this anomaly in low temperature region may be the long sought antiferromagnetic transition in FeSe. Global fitting in wide temperature region shows that the models with a single contribution with isotropic s-wave, anisotropic s-wave, and d-wave gap all do not work well, nor the two isotropic s-wave gaps. We then fit the data by a model with two components in which one has the gap function of $\Delta_0(1+\alpha cos2\theta)$. To have a good global fitting and the entropy conservation for the low temperature transition, we reach a conclusion that the gap minimum should be smaller than 0.15 meV ($\alpha$ = 0.9 to 1), indicating that the superconducting gap(s) are highly anisotropic. Our results are very consistent with the gap structure derived recently from the scanning tunneling spectroscopy measurements and yield specific heat contributions of about 32\% weight from the hole pocket and 68\% from the electron pockets.

Nodal Superconducting Gap Structure in the Quasi-One-Dimensional Cs2Cr3As3 Investigated Using μSR Measurements

The superconducting ground state of the newly discovered superconductor Cs$_2$Cr$_3$As$_3$ with a quasi-one-dimensional crystal structure ($T_{\bf c}\sim$ 2.1(1) K) has been investigated using magnetization and muon-spin relaxation or rotation ($\mu$SR), both zero-field (ZF) and transverse-field (TF), measurements. Our ZF $\mu$SR measurements reveal the presence of spin fluctuations below 4 K and the ZF relaxation rate ($\lambda$) shows enhancement below $T_{\bf c}\sim$ 2.1 K, which might indicate that the superconducting state is unconventional. This observation suggests that the electrons are paired via unconventional channels such as spin fluctuations, as proposed on the basis of theoretical models. Our analysis of the TF $\mu$SR results shows that the temperature dependence of the superfluid density is fitted better with a nodal gap structure than an isotropic s-wave model for the superconducting gap. The observation of a nodal gap in Cs$_2$Cr$_3$As$_3$ is consistent with that observed in the isostructural K$_2$Cr$_3$As$_3$ compound through TF $\mu$SR measurements. Furthermore, from our TF $\mu$SR study we have estimated the magnetic penetration depth $\lambda_{\mathrm{L}}$$(0)$ = 954 nm, superconducting carrier density $n_s = 4.98 \times 10^{26}~ $m$^{-3}$, and carrier's effective-mass enhancement $m^*$ = 1.61m$_{e}$.

Fermionic boundary modes in two-dimensional noncentrosymmetric superconductors

We calculate the spectrum of the Andreev boundary modes in a two-dimensional superconductor formed at an interface between two different non-superconducting materials, e.g. insulating oxides. Inversion symmetry is absent in this system, and both the electron band structure and the superconducting pairing are strongly affected by the spin-orbit coupling of the Rashba type. We consider isotropic s-wave pairing states, both with and without time-reversal symmetry breaking, as well as various d-wave states. In all cases, there exist subgap Andreev boundary states, whose properties, in particular, the number and location of the zero-energy modes, qualitatively depend on the gap symmetry and the spin-orbit coupling strength.

An approach to source characterization of tremor signals associated with eruptions and lahars

Tremor signals are observed in association with eruption activity and lahar descents. Reduced displacement (D R) derived from tremor signals has been used to quantify tremor sources. However, tremor duration is not considered in D R, which makes it difficult to compare D R values estimated for different tremor episodes. We propose application of the amplitude source location (ASL) method to characterize the sources of tremor signals. We used this method to estimate the tremor source location and source amplitude from high-frequency (5–10 Hz) seismic amplitudes under the assumption of isotropic S-wave radiation. We considered the source amplitude to be the maximum value during tremor. We estimated the cumulative source amplitude (I s) as the offset value of the time-integrated envelope of the vertical seismogram of tremor corrected for geometrical spreading and medium attenuation in the 5–10-Hz band. For eruption tremor signals, we also estimated the cumulative source pressure (I p) from an infrasonic envelope waveform corrected for geometrical spreading. We studied these parameters of tremor signals associated with eruptions and lahars and explosion events at Tungurahua volcano, Ecuador. We identified two types of eruption tremor at Tungurahua: noise-like inharmonic waveforms and harmonic oscillatory signals. We found that I s increased linearly with increasing source amplitude for lahar tremor signals and explosion events, but I s increased exponentially with increasing source amplitude for inharmonic eruption tremor signals. The source characteristics of harmonic eruption tremor signals differed from those of inharmonic tremor signals. We found a linear relation between I s and I p for both explosion events and eruption tremor. Because I p may be proportional to the total mass involved during an eruption episode, this linear relation suggests that I s may be useful to quantify eruption size. The I s values we estimated for inharmonic eruption tremor were consistent with previous estimates of volumes of tephra fallout. The scaling relations among source parameters that we identified will contribute to our understanding of the dynamic processes associated with eruptions and lahars. This new approach is applicable in analyzing tremor sources in real time and may contribute to early assessment of the size of eruptions and lahars.