Strong-coupling Superconductivity Research Articles

Emergence of Non-Axisymmetric Vortex in Strong-Coupling Chiral p-Wave Superconductor

We studied strong-coupling effect upon an isolated vortex in a two-dimensional chiral p-wave superconductor. We solved the Eilenberger equation for the quasiclassical Green's functions and the Eliashberg equation with single mode Einstein boson self-consistently. We calculated the free-energy of each obtained vortex, and found that a non-axisymmetric vortex metastably exists in some situation.

Strong-coupling superconductivity revealed by scanning tunneling microscope in tetragonal FeS

We investigate the electronic properties of the tetragonal FeS superconductor by using scanning tunneling microscope/spectroscopy. It is found that the typical tunneling spectrum on the top layer of sulfur can be nicely fitted with an anisotropic s-wave or a combination of two superconducting components in which one may have a highly anisotropic or nodal like superconducting gap. The fittings lead to the maximum superconducting gap $\Delta_{max}\approx$ 0.90$\;$meV, which yields a ratio of 2$\Delta_{max}/k_BT_c\approx$ 4.65. This value is larger than that of the predicted value 3.53 by the BCS theory in the weak coupling limit, indicating a strong coupling superconductivity. Two kinds of defects are observed on the surface, which can be assigned to the defects on the S sites (four-fold image) and Fe sites (dumbbell shape). Impurity induced resonance states are found only for the former defects and stay at zero-bias energy.

Effects of electron correlation, electron-phonon coupling, and spin-orbit coupling on the isovalent Pd-substituted superconductorSrPt3P

We present a systematical study on the roles of electron correlation and spin-orbit coupling in the isovalent Pd-doped superconductor SrPt$_3$P. By using solid state reaction method, we fabricated the strong spin-orbit coupling superconductors Sr(Pt$_{1-x}$Pd$_x$)$_3$P with strong electron correlated Pd dopant of the $4d$ orbital. As increasing the isovalent Pd concentrations without introducing any extra electron/hole carriers, the superconducting transition temperature $T_c$ decreases monotonously, which suggests the existence of competition between spin-orbit coupling and electron correlation in the superconducting state. In addition, the electronic band structure calculations demonstrate that the strength of electron susceptibility is suppressed gradually by the Pd dopant suggesting the incompatible relation between spin-orbit coupling and electron correlation, which is also consistent with experimental measurements. Our results provide significant insights in the natures of the interplay between the spin-orbit coupling and the electron correlation in superconductivity, and may pave a way for understanding the mechanism of superconductivity in this 5d-metal-based compound.

Composition-induced structural instability and strong-coupling superconductivity inAu1−xPdxTe2

The physical properties and structural evolution of the MX$_2$-type solid solution Au$_{1-x}$Pd$_x$Te$_2$ are reported. The end member AuTe$_2$ is a normal metal with a monoclinic distorted CdI$_2$-type structure with preformed Te-Te dimers. A monoclinic--trigonal structural phase transition at a finite temperature occurs upon Pd substitution and is suppressed to zero temperature near $x$ = 0.55, and a superconducting phase with a maximum $T_{\rm c}$ = 4.65 K emerges. A clear indication of strong coupling superconductivity is observed near the composition of the structural instability. The competitive relationship between Te-Te dimers and superconductivity is proposed.

Strong superconducting strength in ε-PbBi microcubes

Single phase ε-PbBi microcubes were synthesized using a simple thermal evaporation method. Synchrotron x-ray measurement of the crystal structure of the ε-PbBi microcubes revealed a space group of P63/mmc. Enhanced superconducting transitions were observed from the temperature dependent magnetization, showing a main diamagnetic Meissner state below a TC of ~8.66(2)K. An extremely strong superconducting strength (α=2.51(1)) and electron-phonon constant (λEP=2.25) are obtained from the modified Allen and Dynes theory, which give rise to higher TC superconductivity in this type of structure. The electron–phonon coupling to low lying phonons is found to be the leading mechanism for the observed strong-coupling superconductivity in the PbBi system.

Electron pairing in the presence of incipient bands in iron-based superconductors

Recent experiments on certain Fe-based superconductors have hinted at a role for paired electrons in "incipient" bands that are close to, but do not cross the Fermi level. Related theoretical works disagree on whether or not strong-coupling superconductivity is required to explain such effects, and whether a critical interaction strength exists. In this work, we consider various versions of the model problem of pairing of electrons in the presence of an incipient band, within a simple multiband weak-coupling BCS approximation. We categorize the problem into two cases: case(I) where superconductivity arises from the "incipient band pairing" alone, and case(II) where it is induced on an incipient band by pairing due to Fermi-surface based interactions. Negative conclusions regarding the importance of incipient bands have been drawn so far largely based on case(I), but we show explicitly that models under case(II) are qualitatively different, and can explain the non-exponential suppression of Tc, as well as robust large gaps on an incipient band. In the latter situation, large gaps on the incipient band do not require a critical interaction strength. We also model the interplay between phonon and spin fluctuation driven superconductivity and describe the bootstrap of electron-phonon superconductivity by spin fluctuations coupling the incipient and the regular bands. Finally, we discuss the effect of the dimensionality of the incipient band on our results. We argue that pairing on incipient bands may be significant and important in several Fe-based materials, including LiFeAs, FeSe intercalates and FeSe monolayers on strontium titanate, and indeed may contribute to high critical temperatures in some cases.

Strong Coupling Superconductivity in the Vicinity of the Structural Quantum Critical Point in (Ca(x)Sr(1-x))₃Rh₄Sn₁₃.

The family of the superconducting quasiskutterudites (Ca(x)Sr(1-x))(3)Rh(4)Sn(13) features a structural quantum critical point at x(c)=0.9, around which a dome-shaped variation of the superconducting transition temperature T(c) is found. Using specific heat, we probe the normal and the superconducting states of the entire series straddling the quantum critical point. Our analysis indicates a significant lowering of the effective Debye temperature on approaching x(c), which we interpret as a result of phonon softening accompanying the structural instability. Furthermore, a remarkably large enhancement of 2Δ/k(B)T(c) and ΔC/γT(c) beyond the Bardeen-Cooper-Schrieffer values is found in the vicinity of the structural quantum critical point. The phase diagram of (Ca(x)Sr(1-x))(3)Rh(4)Sn(13) thus provides a model system to study the interplay between structural quantum criticality and strong electron-phonon coupling superconductivity.

Tunneling Spectroscopy in Organic Superconductor κ-(BEDT-TTF-d[3,3])2Cu[N(CN)2]Br

We performed tunneling spectroscopy (STS) measurement in an organic superconductor, partially deuterated κ-(BEDT-TTF-d[3,3])2Cu[N(CN)2]Br. We carried out angle-resolved STS on cut lateral surfaces by the focused ion beam (FIB) method as well as as-grown single-crystal surfaces. It was found that the d[3,3]-Br salt is a strong-coupling d-wave superconductor and that the nodal direction is at an angle of π/4 from the a*-axis, corresponding to the \(d_{x^{2} - y^{2}}\) symmetry in the bulk superconducting phase. It is understood that the electron correlation in the d[3,3]-Br salt is not strong enough on the basis of the spin fluctuation mechanism. On the other hand, we also observed two types of superconducting gap. This suggests the coexistence of the \(d_{x^{2} - y^{2}}\) and dxy symmetries. This indicates a change in the symmetry from \(d_{x^{2} - y^{2}}\) in the bulk superconducting phase to dxy around the insulating region with increasing electron correlation.

Thermodynamics of the hydrogen dominant potassium hydride superconductor at high pressure

In the present paper we report comprehensive analysis of the thermodynamic properties of novel hydrogen dominant potassium hydride superconductor (KH6). Our computations are conducted within the Eliashberg theory which yields quantitative estimations of the most important thermodynamic properties of superconducting phase. In particular, we observe that together with the increasing pressure all the thermodynamic properties decrease, e.g. TC∈〈72.91,55.50〉 K for p∈〈166,300〉 GPa. It is predicted that such decreasing behavior corresponds to the decreasing hydrogen lattice molecularization with increasing pressure value. Furthermore, by calculating the dimensionless thermodynamic ratios, familiar in the Bardeen–Cooper–Schrieffer (BCS) theory, it is proved that KH6 material is a strong-coupling superconductor and cannot be quantitatively described within the BCS theory.

Size effect of strong-coupled superconducting In2Bi nanoparticles: An investigation of short-range electron phonon coupling

We report the influence of the nanosized effect on the superconducting properties of bimetallic In2Bi nanoparticles. In this study, the temperature- and applied magnetic field-dependence of the magnetization were utilized to investigate the electron-phonon coupling effect while controlling particle sizes 〈d〉 from 21(2) to 42(5) nm. As the particle size decreases, the electron-phonon constant λEP decreases rapidly, signaling the short-range electron-phonon coupling effect which acts to confine the electrons within a smaller volume, thereby giving rise to a higher superconducting transition temperature TC. An enhanced superconducting transition was observed from the temperature dependence of magnetization, revealing a main diamagnetic Meissner state below TC ∼ 5.72(5) K for 〈d〉 = 31(1) nm In2Bi nanoparticles. The variation of the TC is very sensitive to the particle size, which might be due to crystallinity and size uniformity of the samples. The electron-phonon coupling to low lying phonons is found to be the leading mechanism for the observed strong-coupling superconductivity in the In2Bi system.

Nodeless superconductivity in quasi-one-dimensionalNb2PdS5: AμSRstudy

Muon spin relaxation and rotation (muSR) measurements have been performed to study the superconducting and magnetic properties of Nb2PdS5. Zero-field muSR data show that no sizeable spontaneous magnetization arises with the onset of superconductivity in Nb2PdS5 which indicates that the time reversal symmetry is probably preserved in the superconducting state of this system. A strong diamagnetic shift is observed in the transverse-field muSR data practically ruling out a dominant triplet-pairing superconducting state in Nb2PdS5. The temperature dependence of magnetic penetration depth evidences the existence of a single s-wave energy gap with a gap value of 1.07(4) meV at zero temperature. The gap to Tc ratio, 2.02(9), indicates that Nb2PdS5 should be considered as a moderately strong-coupling superconductor. The magnetic penetration depth at zero temperature is 785(20) nm, indicating a very low superfluid density consistent with the quasi-one-dimensional nature of this system.

High-pressure and doping studies of the superconducting antiperovskiteSrPt3P

We report the results of our investigation of SrPt3P, a recently discovered strong-coupling superconductor with Tc = 8.4 K, by application of high physical pressure and by chemical doping. We study hole-doped SrPt3P, which was theoretically predicted to have a higher Tc, resistively, magnetically, and calorimetrically. Here we present the results of these studies and discuss their implications.

What superconducts in sulfur hydrides under pressure and why

The recent discovery of superconductivity at 190~K in highly compressed H$_{2}$S is spectacular not only because it sets a record high critical temperature, but because it does so in a material that appears to be, and we argue here that it is, a conventional strong-coupling BCS superconductor. Intriguingly, superconductivity in the observed pressure and temperature range was predicted theoretically in a similar compound H$_{3}$S. Several important questions about this remarkable result, however, are left unanswered: (1) Does the stoichiometry of the superconducting compound differ from the nominal composition, and could it be the predicted H$_{3}$S compound? (2) Is the physical origin of the anomalously high critical temperature related only to the high H phonon frequencies, or does strong electron-ion coupling play a role? We show that at experimentally relevant pressures H$_2$S is unstable, decomposing into H$_3$S and S, and that H$_3$S has a record high $T_c$ due to its covalent bonds driven metallic. The main reason for this extraordinarily high $T_c$ in H$_3$S as compared with MgB$_2$, another compound with a similar superconductivity mechanism, is the high vibrational frequency of the much lighter H atoms.

Superconducting properties of Ca3Ir4Sn13: a μSR study

Muon spin relaxation and rotation (μSR) measurements have been performed to study the superconducting properties of Ca3Ir4Sn13. Zero-field μSR data shows no sign of any magnetic anomaly in Ca3Ir4Sn13 at the superlattice transition temperature, T* or in the superconducting ground state. Transverse-field μSR measurements in the vortex state provided the temperature dependence of the magnetic penetration depth λ. The dependence of λ−2 with temperature is consistent with the existence of a single s-wave energy gap in the superconducting state of Ca3Ir4Sn13 with a gap value of 1.51(5) meV at absolute zero temperature. The magnetic penetration depth at zero temperature λ(0) is 351(4) nm. The ratio Δ(0)/kBTc = 2.41(8) indicates that Ca3Ir4Sn13 is a strong-coupling superconductor.

Theoretical description of the SrPt3P superconductor in the strong-coupling limit

The thermodynamic properties of a SrPt3P compound in the superconducting state have been investigated by taking the Eliashberg approach. The anti-perovskite SrPt3P is identified as a strong-coupling (λ = 1.33) s-wave superconductor with , where the zero-temperature energy gap () obtained from the Eliashberg calculations is 3.15 meV. The critical temperature TC was recently reported to be 8.4 K and this paper confirms the Coulomb pseudopotential repulsions () to be equal to 0.123. Moreover, the free energy difference between the superconducting and the normal state has been calculated. On the basis of the obtained results, the specific heat for the superconducting and the normal state, as well as the thermodynamic critical field, have been determined. It has been also proved that the electron effective mass is high and reaches its maximum equal to for the critical temperature.

Superconducting and magnetic properties ofSr3Ir4Sn13

Magnetization and muon spin relaxation or rotation (muSR) measurements have been performed to study the superconducting and magnetic properties of Sr3Ir4Sn13. From magnetization measurements the lower and upper critical fields of Sr3Ir4Sn13 are found to be 81(1) Oe and 14.4(2) kOe, respectively. Zero-field muSR data show no sign of any magnetic ordering or weak magnetism in Sr3Ir4Sn13. Transverse-field muSR measurements in the vortex state provided the temperature dependence of the magnetic penetration depth. The dependence of penetration depth with temperature is consistent with the existence of single s-wave energy gap in the superconducting state of Sr3Ir4Sn13 with a gap value of 0.82(2) meV at absolute zero temperature. The magnetic penetration depth at zero temperature is 291(3) nm. The gap to Tc ratio is 2.1(1), indicates that Sr3Ir4Sn13 should be considered as a strong-coupling superconductor.

Strong-coupling superconductivity in CaLi2 under the pressure of 100 GPa

In presented paper the superconducting properties of compressed CaLi2 compounds have been calculated for P21/c phase. Energy gap, critical temperature and electron effective mass are analyzed within the framework of the strong-coupling Eliashberg theory for a wide range of Coulomb pseudopotential μ⋆∈〈0.1,0.3〉. It has been stated that Δ(0) decreases from 6.01meV to 3.62meV, TC decreases from 29.31K to 18.16K and dimensionless ratio 2Δ(0)/kBTC decreases from 4.76 to 4.64 dependently on the assumed value of the Coulomb pseudopotential. Moreover, it has been proved, that the ratio of the electron effective mass to the electron band mass me⋆/me is high in the whole range of the superconducting phase existence and reaches its maximum equal to 3.73 for the critical temperature regardless of the value of Coulomb pseudopotential.

Microscopic properties of the heavy-fermion superconductor PuCoIn5 explored by nuclear quadrupole resonance

We report 115In nuclear quadrupolar resonance (NQR) measurements on the heavy-fermion superconductor PuCoIn5, in the temperature range 0.29K ≤ T ≤ 75K. The NQR parameters for the two crystallographically inequivalent In sites are determined, and their temperature dependence is investigated. A linear shift of the quadrupolar frequency with lowering temperature below the critical value Tc is revealed, in agreement with the prediction for composite pairing. The nuclear spin–lattice relaxation rate T1−1(T) clearly signals a superconducting (SC) phase transition at Tc ≃ 2.3 K, with strong spin fluctuations, mostly in-plane, dominating the relaxation process in the normal state near to Tc. Analysis of the T1−1 data in the SC state suggests that PuCoIn5 is a strong-coupling d-wave superconductor.

Crystal Structure and Superconductivity of BaIr2Ge7 and Ba3Ir4Ge16 with Two-Dimensional Ba-Ge Networks

The Ba-Ir-Ge ternary compounds BaIr2Ge7 and Ba3Ir4Ge16 exhibit superconductivity (SC) at 2.5 and 5.2 K, respectively. Detailed single-crystal structural analysis revealed that these compounds share unique quasi-two-dimensional networks composed of crown-shaped Ge rings that accommodate Ba atoms at the center, referred to as "edge-shared crown-shaped BaGe16 polyhedra". The layered Ba-Ge network yielded a modest anisotropy of 1.3-1.4 in the upper critical field, which is in good agreement with the band structure calculations. The Ba-Ge structural unit is similar to cage structures seen in various clathrates in which the anharmonic vibration of the central atoms, the so-called "rattling" behavior, brings about strong-coupling SC. However, each Ba-Ge unit is relatively small compared to these materials, which likely excludes the possibility of unconventional SC.

Strong Electron–Phonon Coupling Superconductivity Induced by a Low-Lying Phonon in IrGe

The physical properties of the previously reported superconductor IrGe and the Rh1-xIrxGe solid solution are investigated. IrGe has an exceptionally high superconducting transition temperature (\(T_{\text{c}}=4.7\) K) among the isostructural \(1:1\) late-metal germanides \(M\)Ge (\(M=\text{Rh}\), Pd, Ir, and Pt). Specific-heat measurements reveal that IrGe has an anomalously low Debye temperature, originating from a low-lying phonon, compared to the other \(M\)Ge phases. A large jump at \(T_{\text{c}}\) in the specific-heat data clearly indicates that IrGe is a strong coupling superconductor. In the Rh1-xIrxGe solid solution, a relationship between an anomalous change in lattice constants and the Debye temperature is observed. We conclude that the unusually high \(T_{\text{c}}\) for IrGe is likely due to strong electron–phonon coupling derived from the presence of a low-lying phonon.