Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor

Unveiling nodeless unconventional superconductivity proximate to honeycomb-vacancy ordering in the Ir-Sb binary system

Vacancies in solid-state physics are underexplored in materials with strong electron-electron correlations. Recent research on the Ir-Sb binary system revealed an extended buckled-honeycomb vacancy (BHV) order. Superconductivity arises by suppressing BHV ordering through high-pressure growth with excess Ir atoms or Rh substitution, yet the superconducting pairing nature remains unknown. To explore this, we conducted muon spin rotation experiments on Ir1-δ Sb (synthesized at 5.5 GPa, T c = 4.2 K) and ambient pressure synthesized optimally Rh-doped Ir1-x Rh x Sb (x=0.3, T c = 2.7 K). The exponential temperature dependence of the superfluid density suggests a fully gapped superconducting state exists in both samples. The ratio of T c to the superfluid density resembles that of unconventional superconductors. A significant increase in the superfluid density in the high-pressure synthesized sample correlates with T c, indicating that unconventional superconductivity is intrinsic to the Ir-Sb binary system. These findings, along with the dome-shaped phase diagram, highlight IrSb as the first unconventional superconducting parent phase with ordered vacancies, requiring further theoretical investigations.

Tuning of the flat band and its impact on superconductivity in Mo5Si3-xPx

The superconductivity in systems containing dispersionless (flat) bands is seemingly paradoxical, as traditional Bardeen-Cooper-Schrieffer theory requires an infinite enhancement of the carrier masses. However, the combination of flat and steep (dispersive) bands within the multiple band scenario might boost superconducting responses, potentially explaining high-temperature superconductivity in cuprates and metal hydrides. Here, we report on the magnetic penetration depths, the upper critical field, and the specific heat measurements, together with the first-principles calculations for the Mo5Si3-xPx superconducting family. The band structure features a flat band that gradually approaches the Fermi level as a function of phosphorus doping x, reaching the Fermi level at x ≃ 1.3. This leads to an abrupt change in nearly all superconducting quantities. The superfluid density data placed on the 'Uemura plot' results in two separated branches, thus indicating that the emergence of a flat band enhances correlations between conducting electrons.

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015  K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7  K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3)  nm agrees with λ_{ab}≃130  nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Time-reversal symmetry-breaking charge order in a kagome superconductor

The kagome lattice¹, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders^2-8 and, most rarely, to unconventional superconductivity^6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV₃Sb₅ (A = K, Rb, Cs)^9-11 exhibit unconventional chiral charge order^12-19, which is analogous to the long-sought-after quantum order in the Haldane model²⁰ or Varma model²¹. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV₃Sb₅. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV₃Sb₅ and that the [Formula: see text] ratio (where T_c is the superconducting transition temperature and λ_ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Superconductivity and the Jahn–Teller Polaron

In this article, we review the essential properties of high-temperature superconducting cuprates, which are unconventional isotope effects, heterogeneity, and lattice responses. Since their discovery was based on ideas stemming from Jahn–Teller polarons, their special role, together with the Jahn–Teller effect itself, is discussed in greater detail. We conclude that the underlying physics of cuprates cannot stem from purely electronic mechanisms, but that the intricate interaction between lattice and charge is at its origin.

Coexistence ofs- andd-wave gaps due to pair-hopping and exchange interactions

I investigate the superconductivity of the three-bandt-J-Umodel derived from the three-band Hubbard model using the Schrieffer-Wolff transformation. My model is designed considering the hole-doped high-T_csuperconducting cuprate. The model does not exclude the double occupancy of Cu sites bydelectrons, and there is a pair-hopping interaction between thedandpbands together with the exchange interaction. I analyse the superconducting transition temperature, electronic state, and superconducting gap function based on strong coupling theory and find that the superconductivity emerges due to the pair-hopping and exchange interactions via the Suhl-Kondo mechanism. In the superconducting state, the extendeds- anddx2-y2-wave superconducting gaps coexist, where both charge fluctuations andd-pband hybridization are key ingredients.

From SrTiO3 to Cuprates and Back to SrTiO3: A Way Along Alex Müller’s Scientific Career

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.

Suppression of the s-Wave Order Parameter Near the Surface of the Infinite-Layer Electron-Doped Cuprate Superconductor Sr0.9La0.1CuO2

The temperature dependencies of the in-plane (λab) and out-of-plane (λc) components of the magnetic field penetration depth were investigated near the surface and in the bulk of the electron-doped superconductor Sr0.9La0.1CuO2 by means of magnetization measurements. The measured λab(T) and λc(T) were analyzed in terms of a two-gap model with mixed s+d-wave symmetry of the order parameter. λab(T) is well described by an almost pure anisotropic d-wave symmetry component (≃96%), mainly reflecting the surface properties of the sample. In contrast, λc(T) exhibits a mixed s+d-wave order parameter with a substantial s-wave component of more than 50%. The comparison of λab−2(T) measured near the surface with that determined in the bulk by means of the muon-spin rotation/relaxation technique demonstrates that the suppression of the s-wave component of the order parameter near the surface is associated with a reduction of the superfluid density by more than a factor of two.

Unconventional Magnetism in Layered Transition Metal Dichalcogenides

In this contribution to the MDPI Condensed Matter issue in Honor of Nobel Laureate Professor K.A. Müller I review recent experimental progress on magnetism of semiconducting transition metal dichalcogenides (TMDs) from the local-magnetic probe point of view such as muon-spin rotation and discuss prospects for the creation of unique new device concepts with these materials. TMDs are the prominent class of layered materials, that exhibit a vast range of interesting properties including unconventional semiconducting, optical, and transport behavior originating from valley splitting. Until recently, this family has been missing one crucial member: magnetic semiconductor. The situation has changed over the past few years with the discovery of layered semiconducting magnetic crystals, for example CrI 3 and VI 2 . We have also very recently discovered unconventional magnetism in semiconducting Mo-based TMD systems 2H-MoTe 2 and 2H-MoSe 2 [Guguchia et. al., Science Advances 2018, 4(12)]. Moreover, we also show the evidence for the involvement of magnetism in semiconducting tungsten diselenide 2H-WSe 2 . These results open a path to studying the interplay of 2D physics, semiconducting properties and magnetism in TMDs. It also opens up a host of new opportunities to obtain tunable magnetic semiconductors, forming the basis for spintronics.

Exotic superconducting states in the extended attractive Hubbard model

We show that the extended attractive Hubbard model on a square lattice allows for a variety of superconducting phases, including exotic mixed-symmetry phases with [Formula: see text] and [Formula: see text] symmetries, and a novel [Formula: see text] state. The calculations are performed within the Hartree-Fock Bardeen-Cooper-Schrieffer framework. The ground states of the mean-field Hamiltonian are obtained via a minimization scheme that relaxes the symmetry constraints on the superconducting solutions, hence allowing for a mixing of s-, p- and d-wave order parameters. The results are obtained within the assumption of uniform-density states. Our results show that extended attractive Hubbard model can serve as an effective model for investigating properties of exotic superconductors.

Direct evidence for a pressure-induced nodal superconducting gap in the Ba0.65Rb0.35Fe2As2 superconductor

The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. In contrast to other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba0.65Rb0.35Fe2As2. Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

Signatures of new d-wave vortex physics in overdoped Tl2Ba2CuO(6+x) revealed by TF-µ(+)SR

The spontaneous expulsion of applied magnetic field, the Meissner effect, is a defining feature of superconductors; in Type-II superconductors above the lower critical field, this screening takes the form of a lattice of magnetic flux vortices. Using implanted spin-1/2 positive muons, one can measure the vortex lattice field distribution through the spin precession and deduce key parameters of the superconducting ground state, and thereby fundamental properties of the superconducting pairing. Muon spin rotation/relaxation (µSR) experiments have indeed revealed much interesting physics in the underdoped cuprates, where superconductivity is closely related to, or coexistent with, disordered or fluctuating magnetic and charge excitations. Such complications should be absent in overdoped cuprates, which are believed to exhibit conventional Fermi liquid behaviour. These first transverse field (TF)-µ⁺SR experiments on heavily-overdoped single crystals reveal a superfluid density exhibiting a clear inflection point near 0.5T_c , with a striking doping-independent scaling. This reflects hitherto unrecognized physics intrinsic to d-wave vortices, evidently generic to the cuprates, and may offer fundamentally new insights into their still-mysterious superconductivity.

Isotope and multiband effects in layered superconductors

In this review we consider three classes of superconductors, namely cuprate superconductors, MgB(2) and the new Fe based superconductors. All of these three systems are layered materials and multiband compounds. Their pairing mechanisms are under discussion with the exception of MgB(2), which is widely accepted to be a 'conventional' electron-phonon interaction mediated superconductor, but extending the Bardeen-Cooper-Schrieffer (BCS) theory to account for multiband effects. Cuprates and Fe based superconductors have higher superconducting transition temperatures and more complex structures. Superconductivity is doping dependent in these material classes unlike in MgB(2) which, as a pure compound, has the highest values of T(c) and a rapid suppression of superconductivity with doping takes place. In all three material classes isotope effects have been observed, including exotic ones in the cuprates, and controversial ones in the Fe based materials. Before the area of high-temperature superconductivity, isotope effects on T(c) were the signature for phonon mediated superconductivity-even when deviations from the BCS value to smaller values were observed. Since the discovery of high T(c) materials this is no longer evident since competing mechanisms might exist and other mediating pairing interactions are discussed which are of purely electronic origin. In this work we will compare the three different material classes and especially discuss the experimentally observed isotope effects of all three systems and present a rather general analysis of them. Furthermore, we will concentrate on multiband signatures which are not generally accepted in cuprates even though they are manifest in various experiments, the evidence for those in MgB(2), and indications for them in the Fe based compounds. Mostly we will consider experimental data, but when possible also discuss theoretical models which are suited to explain the data.

Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.

Concerning the superconducting gap symmetry in YBa₂Cu₃O₇- δ, YBa₂Cu₄O, and La₂ - xSrxCuO₄ determined from muon spin rotation in mixed states of crystals and powders

Muon spin rotation (μ(+)SR) measurements of square-root second moments of local magnetic fields σ in superconducting mixed states, as published for oriented crystals and powder samples of YBa(2)Cu(3)O(7 - δ) (δ≈0.05), YBa(2)Cu(4)O(8) and La(2 - x)Sr(x)CuO(4) (x ∼ 0.15-0.17), are subjected to comparative analysis for superconducting gap symmetry. For oriented crystals it is shown that anomalous dependences of σ on temperature T and applied field H, as-measured and extracted a- and b-axial components, are attributable to fluxon depinning and disorder that obscure the intrinsic character of the superconducting penetration depth. Random averages derived from oriented crystal data differ markedly from corresponding non-oriented powders, owing to the weaker influence of pinning in high-quality crystals. Related indicators for pinning perturbations, such as non-monotonic H dependence of σ, irreproducible data and strong H dependence of apparent transition temperatures, are also evident. Strong intrinsic pinning suppresses thermal anomalies in c-axis components of σ, which reflect nodeless gap symmetries in YBa(2)Cu(3)O(7 - δ) and YBa(2)Cu(4)O(8). For YBa(2)Cu(3)O(7 - δ), the crystal (a-b components, corrected for depinning) and powder data all reflect a nodeless gap (however, a-b symmetries remain unresolved for crystalline YBa(2)Cu(4)O(8) and La(1.83)Sr(0.17)CuO(4)). Inconsistencies contained in multiple and noded gap interpretations of crystal data, and observed differences between bulk μ(+)SR and surface-sensitive measurements are discussed.

Anomalous magnetic field dependence of Y Ba(2)Cu(3)O(7 - δ): effect of orthorhombic distortion

In this work an attempt has been made to ascertain the origin of the mixed symmetry state of the order parameters in the high-T(c) superconductor Y Ba(2)Cu(3)O(7 - δ), with the contesting candidates being the orthorhombic distortion associated with the CuO(2) planes and an s-wave order parameter component originating from the CuO chains present in the system. Due to its applicability over the entire range of applied magnetic field H(c1) < H < H(c2) the present theoretical model has been employed to study various unusual properties which are signatures of the unconventional pairing state symmetry of this material. The results presented in this paper and their agreement with the relevant experimental data suggest that the origin of the mixed symmetry state of pairing and the various experimentally observed unusual properties of Y Ba(2)Cu(3)O(7 - δ) including the anomalous magnetic field dependence of the vortex lattice structure, unusual upward curvature of the H(c2)(T) plot, etc, can be attributed to the orthorhombic distortion of the CuO(2) planes present in this material. However, the effect discussed in the present work pertains to the orthorhombic distortion arising only through a second-order coupling; the distortion arising from other possible sources, namely anisotropic mixed gradient coupling, has not been taken into account here. Hence this discussion is restricted to a qualitative explanation of the effect due to orthorhombic distortion arising from the second-order coupling only.

London penetration depth in the tight binding approximation: orthorhombic distortion and oxygen isotope effects in cuprates

We present a simple derivation of an expression for the superfluid density n(s) α 1/λ(2) in superconductors with the tight binding energy dispersion. The derived expression is discussed in detail because of its distinction from the known expressions for ordinary superconductors with parabolic energy dispersion. We apply this expression for the experimental data analysis of the isotope effect in London penetration depth parameter λ in the BiSrCuO and YBaCuO family compounds near optimal doping, taking into account the orthorhombic distortion of crystal structure, and estimate the isotopic change of hopping parameters from the experimental data. We point out that 1/λ(2) temperature behaviour is very sensitive to the ratio 2Δ(m)(T = 0)/k(B)T(c) and estimate this quantity for a number of compounds.

The effect of in-plane mass anisotropy on the properties of high temperature superconductors in states of mixed symmetry

Experiments have suggested that the high- T(c) cuprate YBCO shows marked anisotropy in penetration depth and coherence length measurements. In order to take into account the presence of this anisotropy in the system and its corresponding effect on the various properties of the high- T(c) superconducting materials, we have developed an anisotropic two-order parameter Ginzburg-Landau (GL) theory involving a mixed symmetry state of the order parameter components. For this we have generalized a two-order parameter GL theory, recently developed for the isotropic high- T(c) superconductors involving a mixed symmetry state of the order parameter components (Karmakar and Dey 2008 J. Phys. Condens. Matter 20 255218), in which the effect of the presence of in-plane anisotropy has been taken into account by an effective mass approximation, with the anisotropy being characterized by the parameter γ = m(x)/m(y). The work goes beyond the limitations of the earlier studies in this field as it enables us to carry out a detailed study of the various properties of the system over the entire range of applied magnetic field and wide range of temperature for arbitrary values of the GL parameter κ(y) and vortex lattice symmetry. The model successfully explains not only the observed oblique vortex lattice structure in the presence of in-plane anisotropy but also the experimentally observed angle between the primitive axes of the vortex lattice. The generation of two-fold symmetry of the vortices in the presence of in-plane anisotropy, for a very low applied magnetic field can also be analyzed by our model. We have also compared our theoretical results with various other experiments on high- T(c) cuprate YBCO.

Comparative study of the pressure effects on the magnetic penetration depth in electron- and hole-doped cuprate superconductors

The effect of pressure on the magnetic penetration depth λ was tested for the hole-doped superconductor YBa(2)Cu(3)O(7-δ) and in the electron-doped one Sr(0.9)La(0.1)CuO(2) by means of magnetization measurements. Whereas a large change of λ was found in YBa(2)Cu(3)O(7-δ), confirming the non-adiabatic character of the electron-phonon coupling in hole-doped superconductors, the same quantity is not affected by pressure in electron-doped Sr(0.9)La(0.1)CuO(2), suggesting a close similarity of the latter to conventional adiabatic Bardeen-Cooper-Schrieffer superconductors. The present results imply a remarkable difference between the electronic properties of hole-doped cuprates and electron-doped Sr(0.9)La(0.1)CuO(2), giving a strong contribution to the long debated asymmetric consequences of hole and electron doping in cuprate superconductors.

Two-gap superconductivity in Ba1-xKxFe2As2: a complementary study of the magnetic penetration depth by muon-spin rotation and angle-resolved photoemission

We investigate the magnetic penetration depth lambda in superconducting Ba1-xKxFe2As2 (Tc approximately 32 K) with muon-spin rotation (microSR) and angle-resolved photoemission (ARPES). Using microSR, we find the penetration-depth anisotropy gamma lambda=lambda c/lambda ab and the second-critical-field anisotropy gammaHc2 to show an opposite T evolution below Tc. This dichotomy resembles the situation in the two-gap superconductor MgB2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth lambda ab around 7 K. The complementarity of microSR and ARPES allows us to pinpoint the values of the two gaps and to arrive to a remarkable agreement between the two techniques concerning the full T evolution of lambdaab. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.

Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors

A detailed analysis of muon-spin rotation (μSR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact solution of the GL model were used. The limits of the validity of these models and the reliability for extracting parameters such as the magnetic penetration depth λ and the coherence length ξ from the experimental μSR spectra were investigated. The analysis of the simulated μSR spectra showed that at high magnetic fields there is a strong correlation between λ and ξ obtained for any value of the Ginzburg-Landau parameter κ = λ/ξ. The smaller the applied magnetic field, the smaller the possibility of finding the correct value of ξ. A simultaneous determination of λ and ξ without any restrictions is very problematic, regardless of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of λ is practically independent of ξ. The second-moment method frequently used to analyze μSR spectra by means of a multi-component Gaussian fit generally yields reliable values of λ over the whole range of applied fields [Formula: see text] (H(c1) and H(c2) are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering experiments on the vortex state in type-II superconductors.

Electron-phonon interactions in superconducting La1.84Sr0.16CuO4 films

We have measured quasiparticle tunneling across a junction perpendicular to the superconducting copper oxide planes. The tunneling spectra show peaks in the density of states. There are 11 minima in the second derivative d2I/dV2, where I is the current and V the voltage, suggesting multiple boson-quasiparticle interactions. These minima match precisely with the published Raman scattering data, leading us to conclude that the relevant bosons in superconducting La1.84Sr0.16CuO4 films are phonons.

Evidence for a competition between the superconducting state and the pseudogap state of (BiPb)2(SrLa)2CuO6+delta from muon spin rotation experiments

The in-plane magnetic penetration depth lambda ab in optimally doped (BiPb)2(SrLa)2CuO6+delta (OP Bi2201) was studied by means of muon-spin rotation. The measurements of lambda 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. 98, 267004 (2007)], which suggest that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. The remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate.

Multiple gap symmetries for the order parameter of cuprate superconductors from penetration depth measurements

The temperature dependence of the London penetration depth lambda was measured for an untwinned single crystal of YBa_{2}Cu_{3}O_{7-delta} along the three principal crystallographic directions (a, b, and c). Both in-plane components (lambda_{a};{-2} and lambda_{b};{-2}) show an inflection point in their temperature dependence which is absent in the component along the c direction (lambda_{c};{-2}). The data provide convincing evidence that the in-plane superconducting order parameter is a mixture of (s+d)-wave symmetry whereas it is mainly s wave along the c direction. In conjunction with previous results it is concluded that coupled s+d-order parameters are universal and intrinsic to cuprate superconductors.