Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5.

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.

Mechanical detwinning device for anisotropic resistivity measurements in samples requiring dismounting for particle irradiation.

Uniaxial stress is used to detwin the samples of orthorhombic iron based superconductors to study their intrinsic electronic anisotropy. Here, we describe the development of a new detwinning setup enabling variable-load stress-detwinning with easy sample mounting/dismounting without the need to re-solder the contacts. It enables the systematic study of the anisotropy evolution as a function of an external parameter when the sample is modified between the measurements. In our case, the external parameter is the dose of 2.5 MeV electron irradiation at low temperature. We illustrate the approach by studying resistivity anisotropy in single crystals of Ba1-xKxFe2As2 at x = 0.25, where the much discussed unusual re-entrance of the tetragonal C4 phase, C4 → C2 → C4, is observed on cooling. With the described technique, we found a significant anisotropy increase in the C2 phase after electron irradiation with a dose of 2.35 C/cm2.

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.

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, Tc, varies non-monotonically, whereas the CDW transition temperature, TCDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where Tc 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.

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.

Size-Induced Depression of First-Order Transition Lines and Entropy Jump in Extremely Layered Nanocrystalline Vortex Matter.

We detect the persistence of the solidification and order-disorder first-order transition lines in the phase diagram of nanocrystalline Bi_{2}Sr_{2}CaCu_{2}O_{8} vortex matter down to a system size of less than one hundred vortices. The temperature location of the vortex solidification transition line is not altered by decreasing the sample size although there is a depletion of the entropy jump at the transition with respect to macroscopic vortex matter. The solid order-disorder phase transition field moves upward on decreasing the system size due to the increase of the surface-to-volume ratio of vortices entailing a decrease on the average vortex binding energy.

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

In superconductors with unconventional pairing mechanisms, the energy gap in the excitation spectrum often has nodes, which allow quasiparticle excitations at low energies. In many cases, such as in d-wave cuprate superconductors, the position and topology of nodes are imposed by the symmetry, and thus the presence of gapless excitations is protected against disorder. Here we report on the observation of distinct changes in the gap structure of iron-pnictide superconductors with increasing impurity scattering. By the successive introduction of nonmagnetic point defects into BaFe2(As(1-x)P(x))(2) crystals via electron irradiation, we find from the low-temperature penetration depth measurements that the nodal state changes to a nodeless state with fully gapped excitations. Moreover, under further irradiation the gapped state evolves into another gapless state, providing bulk evidence of unconventional sign-changing s-wave superconductivity. This demonstrates that the topology of the superconducting gap can be controlled by disorder, which is a strikingly unique feature of iron pnictides.

First-order transition in the magnetic vortex matter in superconducting MgB2 tuned by disorder.

The field-driven transition from an ordered Bragg glass to a disordered vortex phase in single-crystalline MgB2 is tuned by an increasing density of point defects, introduced by electron irradiation. The discontinuity observed in magnetization attests to the first-order nature of the transition. The temperature and defect density dependences of the transition field point to vortex pinning mediated by fluctuations in the quasiparticle mean free path, and reveal the mechanism of the transition in the absence of complicating factors such as layeredness or thermal fluctuations.

Microwave surface-impedance measurements of the magnetic penetration depth in single crystal Ba1-xKxFe2As2 superconductors: evidence for a disorder-dependent superfluid density.

We report high-sensitivity microwave measurements of the in-plane penetration depth lambda_{ab} and quasiparticle scattering rate 1/tau in several single crystals of the hole-doped Fe-based superconductor Ba(1-x)K(x)Fe(2)As(2) (x approximately 0.55). While a power-law temperature dependence of lambda_{ab} with a power approximately 2 is found in crystals with large 1/tau, we observe an exponential temperature dependence of the 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 levels of disorder inherent in the crystals. We also find a linear relation between the low-temperature scattering rate and the density of quasiparticles, which shows a clear contrast to the case of d-wave cuprate superconductors with nodes in the gap. These results demonstrate intrinsically nodeless order parameters in the Fe arsenides.

Flux line lattice melting and the formation of a coherent quasiparticle Bloch state in the ultraclean URu2Si2 superconductor.

We find that in the ultraclean heavy-fermion superconductor URu(2)Si(2) (T_{c0}=1.45 K) a distinct flux line lattice melting transition with outstanding characters occurs well below the mean-field upper critical fields. We show that a very small number of carriers with heavy mass in this system results in exceptionally large thermal fluctuations even at sub-Kelvin temperatures, which are witnessed by a sizable region of the flux line liquid phase. The uniqueness is further highlighted by an enhancement of the quasiparticle mean free path below the melting transition, implying a possible formation of a quasiparticle Bloch state in the periodic flux line lattice.

Dynamic and thermodynamic properties of porous vortex matter in Bi(2)Sr(2)CaCu(2)O(8) in an oblique magnetic field.

Vortex matter in Bi(2)Sr(2)CaCu(2)O(8) with a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. It is found that while the dynamic properties are significantly affected by tilting the magnetic field away from the CDs, the thermodynamic transitions are angle independent. The simulations indicate that vortex pancakes remain localized on the CDs even at large tilting angles. This preserves the vortex thermodynamics, while vortex pinning is considerably weakened due to kink sliding.

Vortex redistribution below the first-order transition temperature in the beta-pyrochlore superconductor KOs2O6.

A miniature Hall-sensor array was used to detect magnetic induction locally in the vortex states of the beta-pyrochlore superconductor KOs2O6. Below the first-order transition at T{p} approximately 8 K, which is associated with a change in the rattling motion of K ions, the lower critical field and the remanent magnetization both show a distinct decrease, suggesting that the electron-phonon coupling is weakened below the transition. At high magnetic fields, the local induction shows an unexpectedly large jump at T{p} whose sign changes with position inside the sample. Our results demonstrate a novel redistribution of vortices whose energy is reduced abruptly below the first-order transition at T{p}.

Composite to tilted vortex lattice transition in Bi2Sr2CaCu2O8+delta in oblique fields.

Precision measurements of the vortex phase diagram in single crystals of the layered superconductor Bi2Sr2CaCu2O8+delta in oblique magnetic fields confirm the existence of a second phase transition, in addition to the usual first-order vortex-lattice melting line Hm(T). The transition has a strong first-order character, is accompanied by strong hysteresis, and intersects the melting line in a tricritical point (Hm perpendicular, Hcr parallel). Its field dependence and the changing character of the melting line at the tricritical point strongly suggest that the ground state for magnetic fields closely aligned with the superconducting layers is a lattice of uniformly tilted vortex lines.

Vortex nanoliquid in high-temperature superconductors.

Using a differential magneto-optical technique to visualize the flow of transport currents, we reveal a new delocalization line within the reversible vortex liquid region in the presence of a low density of columnar defects. This line separates a homogeneous vortex liquid, in which all the vortices are delocalized, from a heterogeneous "nanoliquid" phase, in which interconnected nanodroplets of vortex liquid are caged in the pores of a solid skeleton formed by vortices pinned on columnar defects. The nanoliquid phase displays high correlation along the columnar defects but no transverse critical current.

Direct transition from Bose glass to normal state in the (K,Ba)BiO3 superconductor.

The introduction of columnar defects in (K,Ba )Bi O3 single crystals shifts both the irreversibility and thermodynamic transition lines, respectively, deduced from ac susceptibility (and/or transport) and specific heat measurements, upwards. This shift can be attributed to the defect-induced decrease of the difference (Delta F) between the free energies in the superconducting and the normal states, assuming that the position of the superconducting transition is given by the condition absolute value Delta F approximately k(B )T/xi(3 ). This criterion also perfectly reproduces the influence of the angle between the tracks and the external field. This result suggests that no vortex liquid phase exists in this system.

First-order phase transition from the vortex liquid to an amorphous solid.

We present a systematic study of the topology of the vortex solid phase in superconducting Bi2Sr2CaCu2O8 samples with low doses of columnar defects. A new state of vortex matter imposed by the presence of geometrical contours associated with the random distribution of columns is found. The results show that the first-order liquid-solid transition in this vortex matter does not require a structural symmetry change.

Melting of "porous" vortex matter.

Bitter decoration and magneto-optical studies reveal that in heavy-ion irradiated superconductors, a "porous" vortex matter is formed when vortices outnumber columnar defects. In this state ordered vortex crystallites are embedded in the "pores" of a rigid matrix of vortices pinned on columnar defects. The crystallites melt through a first-order transition while the matrix remains solid. The melting temperature increases with density of columnar defects and eventually turns into a continuous transition. At high temperatures a sharp kink in the melting line is found, signaling an abrupt change from crystallite melting to melting of the rigid matrix.

Anisotropic enhancement of superconductivity in heavy-ion irradiated (K, Ba)BiO3.

We have measured the specific heat, resistivity, and ac susceptibility of (K,Ba)BiO3 single crystals before and after introduction of either point or columnar defects by electron (EI) or heavy-ion irradiation (HII). While the magnetic field dependence of these properties remains mainly unaffected by EI, the irreversibility line and the location of the specific heat anomaly are both shifted up in temperature after HII. The shift is apparent only if the magnetic field is applied parallel to the ion tracks. For perpendicularly applied fields, both lines lie at the same field as in the pristine sample. These experiments call the nature of the vortex liquid state into question.

Defect-unbinding and the Bose-glass transition in layered superconductors.

The low-field Bose-glass transition temperature in heavy-ion irradiated Bi(2)Sr(2)CaCu(2)O(8+delta) increases progressively with increasing density n(d) of irradiation-induced columnar defects, but saturates for n(d) greater or = 1.5 x 10(9) cm(-2). The maximum Bose-glass temperature corresponds to that above which diffusion of two-dimensional pancake vortices between vortex lines becomes possible, and the "linelike" character of vortices is lost. We develop a description of the Bose-glass line that quantitatively describes experiments on crystals with widely different track densities and material parameters.

'Inverse' melting of a vortex lattice.

Inverse melting is the process in which a crystal reversibly transforms into a liquid or amorphous phase when its temperature is decreased. Such a process is considered to be very rare, and the search for it is often hampered by the formation of non-equilibrium states or intermediate phases. Here we report the discovery of first-order inverse melting of the lattice formed by magnetic flux lines in a high-temperature superconductor. At low temperatures, disorder in the material pins the vortices, preventing the observation of their equilibrium properties and therefore the determination of whether a phase transition occurs. But by using a technique to 'dither' the vortices, we were able to equilibrate the lattice, which enabled us to obtain direct thermodynamic evidence of inverse melting of the ordered lattice into a disordered vortex phase as the temperature is decreased. The ordered lattice has larger entropy than the low-temperature disordered phase. The mechanism of the first-order phase transition changes gradually from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures.