Disorder-induced topological change of the superconducting gap structure in iron pnictides

Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba0.2K0.8Fe2As2 Superconductor

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba1-xKxFe2As2, x = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting Tc, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

Nodeless Superconductivity in Kagome Metal CsV3Sb5 with and without Time Reversal Symmetry Breaking

The kagome metal CsV₃Sb₅ features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV₃Sb₅ emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional s-wave superconductivity. Moreover, our measurements of the self-field critical current (I_c,sf), which is related to the London penetration depth, also confirm conventional s-wave superconductivity with strong coupling. Finally, we measure I_c,sf where the CDW order is removed by pressure and superconductivity emerges from the pristine normal state. Our results show that s-wave gap symmetry is retained, providing strong evidence for the presence of conventional s-wave superconductivity in CsV₃Sb₅ irrespective of the presence of the TRSB.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV(3)Sb(5)

The recently discovered kagome superconductors AV₃Sb₅ (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV₃Sb₅ is still lacking. Here we report the impurity effects in CsV₃Sb₅ using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV₃Sb₅ is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

Experimental overview on pairing mechanisms of BiCh2-based (Ch: S, Se) layered superconductors

BiCh₂-based (Ch: S, Se) layered superconductors have attracted extensive attentions because of variation of materials and physical characteristics, which include relatively large spin-orbit coupling originating from bismuth 6porbitals, and the possibility of anisotropic superconducting gap. Some of theoretical studies suggested that anisotropic superconductivity is realized in the BiCh₂-based superconductors. In experimental studies, angle-resolved photoemission spectroscopy measurement on the superconducting states of Nd(O,F)BiS₂have revealed the anisotropic structure of the superconducting gap, and the absence of isotope effect have been reported, indicating unconventional superconductivity pairing. Furthermore, two-fold-symmetric in-plane anisotropy of magnetoresistance have been observed in the superconducting states of some of Bi(S,Se)₂-based systems like La(O,F)Bi(S,Se)₂while the crystal structure possesses a tetragonal square plane with four-fold symmetry. Those results indicate nematic superconductivity is emerging in BiCh₂-based superconductors. On the basis of the observations suggesting unconventional superconductivity in BiCh₂-based systems, clarification of pairing mechanisms of superconductivity in BiCh₂-based superconductors have been highly desired. In this article, we review experimental results on the superconducting gap structure, the pairing mechanism, and related phenomena of BiCh₂-based superconductors.

Effect of Controlled Artificial Disorder on the Magnetic Properties of EuFe2(As1-xPx)2 Ferromagnetic Superconductor

Static (DC) and dynamic (AC, at 14 MHz and 8 GHz) magnetic susceptibilities of single crystals of a ferromagnetic superconductor, EuFe2(As1-xPx)2 (x = 0.23), were measured in pristine state and after different doses of 2.5 MeV electron or 3.5 MeV proton irradiation. The superconducting transition temperature, Tc(H), shows an extraordinarily large decrease. It starts at Tc(H=0)≈24K in the pristine sample for both AC and DC measurements, but moves to almost half of that value after moderate irradiation dose. Remarkably, after the irradiation not only Tc moves significantly below the FM transition, its values differ drastically for measurements at different frequencies, ≈16 K in AC measurements and ≈12 K in a DC regime. We attribute such a large difference in Tc to the appearance of the spontaneous internal magnetic field below the FM transition, so that the superconductivity develops directly into the mixed spontaneous vortex-antivortex state where the onset of diamagnetism is known to be frequency-dependent. We also examined the response to the applied DC magnetic fields and studied the annealing of irradiated samples, which almost completely restores the superconducting transition. Overall, our results suggest that in EuFe2(As1-xPx)2 superconductivity is affected by local-moment ferromagnetism mostly via the spontaneous internal magnetic fields induced by the FM subsystem. Another mechanism is revealed upon irradiation where magnetic defects created in ordered Eu2+ lattice act as efficient pairbreakers leading to a significant Tc reduction upon irradiation compared to other 122 compounds. On the other hand, the exchange interactions seem to be weakly screened by the superconducting phase leading to a modest increase of Tm (less than 1 K) after the irradiation drives Tc to below Tm. Our results suggest that FM and SC phases coexist microscopically in the same volume.

Eliashberg Theory of a Multiband Non-Phononic Spin Glass Superconductor

I solved the Eliashberg equations for a multiband non-phononic s± wave spin-glass superconductor, calculating the temperature dependence of the gaps and of superfluid density. Their behaviors were revealed to be unusual: showing non-monotonic temperature dependence and reentrant superconductivity. By considering particular input parameters values that could describe the iron pnictide EuFe2(As1−xPx)2, a rich and complex phase diagram arises, with two different ranges of temperature in which superconductivity appears.

Band-dependent superconducting gap in SrFe2(As0.65P0.35)2 studied by angle-resolved photoemission spectroscopy

The isovalent-substituted iron pnictide compound SrFe₂(As_1−xP_x)₂ exhibits multiple evidence for nodal superconductivity via various experimental probes, such as the penetration depth, nuclear magnetic resonance and specific heat measurements. The direct identification of the nodal superconducting (SC) gap structure is challenging, partly because the presence of nodes is not protected by symmetry but instead caused by an accidental sign change of the order parameter, and also because of the three-dimensionality of the electronic structure. We have studied the SC gaps of SrFe₂(As_0.65P_0.35)₂ in three-dimensional momentum space by synchrotron and laser-based angle-resolved photoemission spectroscopy. The three hole Fermi surfaces (FSs) at the zone center have SC gaps with different magnitudes, whereas the SC gaps of the electron FSs at the zone corner are almost isotropic and k_z-independent. As a possible nodal SC gap structure, we propose that the SC gap of the outer hole FS changes sign around the Z-X [(0, 0, 2π) − (π, π, 2π)] direction.

Disorder-Driven Transition from s_{±} to s_{++} Superconducting Order Parameter in Proton Irradiated Ba(Fe_{1-x}Rh_{x})_{2}As_{2} Single Crystals

Microwave measurements of the London penetration depth and critical temperature T_{c} were used to show evidence of a disordered-driven transition from s_{±} to s_{++} order parameter symmetry in optimally doped Ba(Fe_{1-x}Rh_{x})_{2}As_{2} single crystals, where disorder was induced by means of 3.5 MeV proton irradiation. Signatures of such a transition, as theoretically predicted [V. D. Efremov et al., Phys. Rev. B 84, 180512(R) (2011)PRBMDO1098-012110.1103/PhysRevB.84.180512], are found as a drop in the low-temperature values of the London penetration depth and a virtually disorder-independent superconducting T_{c}. We show how these experimental observations can be described by multiband Eliashberg calculations in which the effect of disorder is accounted for in a suitable way. To this aim, an effective two-band approach is adopted, allowing us to treat disorder in a range between the Born approximation and the unitary limit.

Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2

The interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe₂ is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing long-range orders, and reveal the underlying interactions that give rise to them. Here we introduce disorder by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, the superconducting transition temperature, T_c, varies non-monotonically, whereas the CDW transition temperature, T_CDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where T_c drops sharply. Our results imply that the CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.

Phase-Sensitive Evidence for the Sign-Reversal s_{±} Symmetry of the Order Parameter in an Iron-Pnictide Superconductor Using Nb/Ba_{1-x}Na_{x}Fe_{2}As_{2} Josephson Junctions

Josephson current provides a phase-sensitive tool for probing the pairing symmetry. Here we present an experimental study of high-quality Josephson junctions between a conventional s-wave superconductor Nb and a multiband iron-pnictide Ba_{1-x}Na_{x}Fe_{2}As_{2}. Junctions exhibit a large enough critical current density to preclude the d-wave symmetry of the order parameter in the pnictide. However, the I_{c}R_{n} product is very small ≃3μV, which is not consistent with the sign-preserving s_{++} symmetry either. We argue that the small I_{c}R_{n} value, along with its unusual temperature dependence, provides evidence for the sign-reversal s_{±} symmetry of the order parameter in Ba_{1-x}Na_{x}Fe_{2}As_{2}. We conclude that it is the phase sensitivity of our junctions that leads to an almost complete (below a subpercent) cancellation of supercurrents from sign-reversal bands in the pnictide.

Effects of disorder induced by heavy-ion irradiation on (Ba1-x K x )Fe2As2 single crystals, within the three-band Eliashberg s± wave model

One of the open issues concerning iron-based superconductors is whether the s± wave model is able to account for the overall effects of impurity scattering, including the low rate of decrease of the critical temperature with the impurity concentration. Here we investigate Ba_1-x K _x Fe₂As₂ crystals where disorder is introduced by Au-ion irradiation. Critical temperature, T _c , and London penetration depth, λ _L , were measured by a microwave resonator technique, for different values of the irradiation fluence. We compared experimental data with calculations made on the basis of the three-band Eliashberg equations, suitably accounting for the impurity scattering. We show that this approach is able to explain in a consistent way the effects of disorder both on T _c and on λ _L (T), within the s± wave model. In particular, a change of curvature in the low-temperature λ _L (T) curves for the most irradiated crystals is fairly well reproduced.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.

Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2

In exotic superconductors, including high-Tc copper oxides, the interactions mediating electron Cooper pairing are widely considered to have a magnetic rather than a conventional electron-phonon origin. Interest in this exotic pairing was initiated by the 1979 discovery of heavy-fermion superconductivity in CeCu2Si2, which exhibits strong antiferromagnetic fluctuations. A hallmark of unconventional pairing by anisotropic repulsive interactions is that the superconducting energy gap changes sign as a function of the electron momentum, often leading to nodes where the gap goes to zero. We report low-temperature specific heat, thermal conductivity, and magnetic penetration depth measurements in CeCu2Si2, demonstrating the absence of gap nodes at any point on the Fermi surface. Moreover, electron irradiation experiments reveal that the superconductivity survives even when the electron mean free path becomes substantially shorter than the superconducting coherence length. This indicates that superconductivity is robust against impurities, implying that there is no sign change in the gap function. These results show that, contrary to long-standing belief, heavy electrons with extremely strong Coulomb repulsions can condense into a fully gapped s-wave superconducting state, which has an on-site attractive pairing interaction.

Unconventional Superconductivity in the BiS_{2}-Based Layered Superconductor NdO_{0.71}F_{0.29}BiS_{2}

We investigate the superconducting-gap anisotropy in one of the recently discovered BiS_{2}-based superconductors, NdO_{0.71}F_{0.29}BiS_{2} (T_{c}∼5  K), using laser-based angle-resolved photoemission spectroscopy. Whereas the previously discovered high-T_{c} superconductors such as copper oxides and iron-based superconductors, which are believed to have unconventional superconducting mechanisms, have 3d electrons in their conduction bands, the conduction band of BiS_{2}-based superconductors mainly consists of Bi 6p electrons, and, hence, the conventional superconducting mechanism might be expected. Contrary to this expectation, we observe a strongly anisotropic superconducting gap. This result strongly suggests that the pairing mechanism for NdO_{0.71}F_{0.29}BiS_{2} is an unconventional one and we attribute the observed anisotropy to competitive or cooperative multiple paring interactions.

Vortices in high-performance high-temperature superconductors

The behavior of vortex matter in high-temperature superconductors (HTS) controls the entire electromagnetic response of the material, including its current carrying capacity. Here, we review the basic concepts of vortex pinning and its application to a complex mixed pinning landscape to enhance the critical current and to reduce its anisotropy. We focus on recent scientific advances that have resulted in large enhancements of the in-field critical current in state-of-the-art second generation (2G) YBCO coated conductors and on the prospect of an isotropic, high-critical current superconductor in the iron-based superconductors. Lastly, we discuss an emerging new paradigm of critical current by design-a drive to achieve a quantitative correlation between the observed critical current density and mesoscale mixed pinning landscapes by using realistic input parameters in an innovative and powerful large-scale time dependent Ginzburg-Landau approach to simulating vortex dynamics.

Energy gap evolution across the superconductivity dome in single crystals of (Ba1-x K x )Fe2As2

The mechanism of unconventional superconductivity in iron-based superconductors (IBSs) is one of the most intriguing questions in current materials research. Among non-oxide IBSs, (Ba_1-x K _x )Fe₂As₂ has been intensively studied because of its high superconducting transition temperature and fascinating evolution of the superconducting gap structure from being fully isotropic at optimal doping (x ≈ 0.4) to becoming nodal at x > 0.8. Although this marked evolution was identified in several independent experiments, there are no details of the gap evolution to date because of the lack of high-quality single crystals covering the entire K-doping range of the superconducting dome. We conducted a systematic study of the London penetration depth, λ(T), across the full phase diagram for different concentrations of point-like defects introduced by 2.5-MeV electron irradiation. Fitting the low-temperature variation with the power law, Δλ ~ Tⁿ , we find that the exponent n is the highest and the T_c suppression rate with disorder is the smallest at optimal doping, and they evolve with doping being away from optimal, which is consistent with increasing gap anisotropy, including an abrupt change around x ≃ 0.8, indicating the onset of nodal behavior. Our analysis using a self-consistent t-matrix approach suggests the ubiquitous and robust nature of s_± pairing in IBSs and argues against a previously suggested transition to a d-wave state near x = 1 in this system.

Temperature dependent local atomic displacements in ammonia intercalated iron selenide superconductor

Recently, ammonia-thermal reaction has been used for molecular intercalation in layered FeSe, resulting a new Li_x(NH₃)_yFe₂Se₂ superconductor with T_c ~ 45 K. Here, we have used temperature dependent extended x-ray absorption fine structure (EXAFS) to investigate local atomic displacements in single crystals of this new superconductor. Using polarized EXAFS at Fe K-edge we have obtained direct information on the local Fe-Se and Fe-Fe bondlengths and corresponding mean square relative displacements (MSRD). We find that the Se-height in the intercalated system is lower than the one in the binary FeSe, suggesting compressed FeSe₄ tetrahedron in the title system. Incidentally, there is hardly any effect of the intercalation on the bondlengths characteristics, revealed by the Einstein temperatures, that are similar to those found in the binary FeSe. Therefore, the molecular intercalation induces an effective compression and decouples the FeSe slabs. Furthermore, the results reveal an anomalous change in the atomic correlations across T_c, appearing as a clear decrease in the MSRD, indicating hardening of the local lattice mode. Similar response of the local lattice has been found in other families of superconductors, e.g., A15-type and cuprates superconductors. This observation suggests that local atomic correlations should have some direct correlation with the superconductivity.

A study of temperature dependent local atomic displacements in a Ba(Fe(1-x)Co(x))2As2 superconductor

We have studied the local structure of a Ba(Fe(1-x)Co(x))2As2 superconductor using temperature dependent extended X-ray absorption fine structure (EXAFS) measurements. Polarized EXAFS at the Fe K-edge on an optimally doped (x = 0.06) single crystal has permitted us to determine atomic displacements across the superconducting transition temperature (T(c)). The Fe-As bondlength hardly shows any change with temperature; however, the Fe-Fe sublattice reveals a sharp anomaly across T(c), indicated by a significant drop in mean square relative displacements, similar to the one known for cuprates and A15-type superconductors. We have also found a large atomic disorder around the substituted Co, revealed by polarized Co K-edge EXAFS measurements. The Co-Fe/Co bonds are more flexible than the Fe-Fe bonds with the As-height in Co-containing tetrahedra being larger than the one in FeAs4. The results suggest that the local Fe-Fe bondlength fluctuations and the atomic disorder in this sub-lattice should have some important role in the superconductivity of Ba(Fe(1-x)Co(x))2As2 pnictides.