Diamagnetic response and phase stiffness for interacting isolated narrow bands.

Superconductivity is a macroscopic manifestation of a quantum phenomenon where pairs of electrons delocalize and develop phase coherence over a long distance. A long-standing quest has been to address the underlying microscopic mechanisms that fundamentally limit the superconducting transition temperature, Tc. A platform which serves as an ideal playground for realizing "high"-temperature superconductors are materials where the electrons' kinetic energy is quenched and interactions provide the only energy scale in the problem. However, when the noninteracting bandwidth for a set of isolated bands is small compared to the interactions, the problem is inherently nonperturbative. In two spatial dimensions, Tc is controlled by superconducting phase stiffness. Here, we present a theoretical framework for computing the electromagnetic response for generic model Hamiltonians, which controls the maximum possible superconducting phase stiffness and thereby Tc, without resorting to any mean-field approximation. Our explicit computations demonstrate that the contribution to the phase stiffness arises from i) "integrating out" the remote bands that couple to the microscopic current operator and ii) the density-density interactions projected on to the isolated narrow bands. Our framework can be used to obtain an upper bound on the phase stiffness and relatedly Tc for a range of physically inspired models involving both topological and nontopological narrow bands with density-density interactions. We discuss a number of salient aspects of this formalism by applying it to a specific model of interacting flat bands and compare the upper bound against the known Tc from independent numerically exact computations.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (µSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field µSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Evidence for even parity unconventional superconductivity in Sr2RuO4.

Unambiguous identification of the superconducting order parameter symmetry in [Formula: see text] has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

Atomic-Scale Andreev Probe of Unconventional Superconductivity.

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Superconducting Sr2RuO4 Thin Films without Out-of-Phase Boundaries by Higher-Order Ruddlesden-Popper Intergrowth.

Ruddlesden-Popper (RP) phases (An+1BnO3n+1, n = 1, 2,···) have attracted intensive research with diverse functionalities for device applications. However, the realization of a high-quality RP-phase film is hindered by the formation of out-of-phase boundaries (OPBs) that occur at terrace edges, originating from lattice mismatch in the c-axis direction with the A'B'O3 (n = ∞) substrate. Here, using strontium ruthenate RP-phase Sr2RuO4 (n = 1) as a model system, an experimental approach for suppressing OPBs was developed. By tuning the growth parameters, the Sr3Ru2O7 (n = 2) phase was formed in a controlled manner near the film-substrate interface. This higher-order RP-phase then blocked the subsequent formation of OPBs, resulting in nearly defect-free Sr2RuO4 layer at the upper region of the film. Consequently, the Sr2RuO4 thin films exhibited superconductivity up to 1.15 K, which is the highest among Sr2RuO4 films grown by pulsed laser deposition. This work paves the way for synthesizing pristine RP-phase heterostructures and exploring their unique physical properties.

Concealed d-wave pairs in the s± condensate of iron-based superconductors.

A central question in iron-based superconductivity is the mechanism by which the paired electrons minimize their strong mutual Coulomb repulsion. In most unconventional superconductors, Coulomb repulsion is minimized through the formation of higher angular momentum Cooper pairs, with Fermi surface nodes in the pair wavefunction. The apparent absence of such nodes in the iron-based superconductors has led to a belief they form an s-wave ([Formula: see text]) singlet state, which changes sign between the electron and hole pockets. However, the multiorbital nature of these systems opens an alternative possibility. Here, we propose a new class of [Formula: see text] state containing a condensate of d-wave Cooper pairs, concealed by their entanglement with the iron orbitals. By combining the d-wave ([Formula: see text]) motion of the pairs with the internal angular momenta [Formula: see text] of the iron orbitals to make a singlet ([Formula: see text]), an [Formula: see text] superconductor with a nontrivial topology is formed. This scenario allows us to understand the development of octet nodes in potassium-doped Ba1-x KXFe2As2 as a reconfiguration of the orbital and internal angular momentum into a high spin ([Formula: see text]) state; the reverse transition under pressure into a fully gapped state can then be interpreted as a return to the low-spin singlet. The formation of orbitally entangled pairs is predicted to give rise to a shift in the orbital content at the Fermi surface, which can be tested via laser-based angle-resolved photoemission spectroscopy.

Nematic quantum critical point without magnetism in FeSe1-xSx superconductors.

In most unconventional superconductors, the importance of antiferromagnetic fluctuations is widely acknowledged. In addition, cuprate and iron-pnictide high-temperature superconductors often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. In these materials, however, such nematic correlations are intertwined with antiferromagnetic or charge orders, preventing the identification of the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systematic elastoresistance measurements in FeSe1-xSx superconductors, which, unlike other iron-based families, exhibit an electronic nematic order without accompanying antiferromagnetic order. We find that the nematic transition temperature decreases with sulfur content x; whereas, the nematic fluctuations are strongly enhanced. Near [Formula: see text], the nematic susceptibility diverges toward absolute zero, revealing a nematic quantum critical point. The obtained phase diagram for the nematic and superconducting states highlights FeSe1-xSx as a unique nonmagnetic system suitable for studying the impact of nematicity on superconductivity.

Avoided valence transition in a plutonium superconductor.

The d and f electrons in correlated metals are often neither fully localized around their host nuclei nor fully itinerant. This localized/itinerant duality underlies the correlated electronic states of the high-Tc cuprate superconductors and the heavy-fermion intermetallics and is nowhere more apparent than in the 5f valence electrons of plutonium. Here, we report the full set of symmetry-resolved elastic moduli of PuCoGa5--the highest Tc superconductor of the heavy fermions (Tc = 18.5 K)--and find that the bulk modulus softens anomalously over a wide range in temperature above Tc. The elastic symmetry channel in which this softening occurs is characteristic of a valence instability--therefore, we identify the elastic softening with fluctuations of the plutonium 5f mixed-valence state. These valence fluctuations disappear when the superconducting gap opens at Tc, suggesting that electrons near the Fermi surface play an essential role in the mixed-valence physics of this system and that PuCoGa5 avoids a valence transition by entering the superconducting state. The lack of magnetism in PuCoGa5 has made it difficult to reconcile with most other heavy-fermion superconductors, where superconductivity is generally believed to be mediated by magnetic fluctuations. Our observations suggest that valence fluctuations play a critical role in the unusually high Tc of PuCoGa5.

Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5.

To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high-temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference imaging to reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions of CeCoIn5. Then, by solving the superconducting gap equations on the two heavy-fermion bands Ek(α,ß) with these magnetic interactions as mediators of the Cooper pairing, we derive a series of quantitative predictions about the superconductive state. The agreement found between these diverse predictions and the measured characteristics of superconducting CeCoIn5 then provides direct evidence that the heavy-fermion Cooper pairing is indeed mediated by f-electron magnetism.

Sudden adiabaticity signals reentrant bulk superconductivity in UTe2.

There has been a recent surge of interest in UTe2 due to its unconventional magnetic field (H)-reinforced spin-triplet superconducting phases persisting at fields far above the simple Pauli limit for H∥[010]. Magnetic fields in excess of 35 T then induce a field-polarized magnetic state via a first-order-like phase transition. More controversially, for field orientations close to H∥[011] and above 40 T, electrical resistivity measurements suggest that a further superconducting state may exist. However, no Meissner effect or thermodynamic evidence exists to date for this phase making it difficult to exclude alternative scenarios. In this paper, we describe a study using thermal, electrical, and magnetic probes in magnetic fields of up to 55 T applied between the [010] (b) and [001] (c) directions. Our MHz conductivity data reveal the field-induced state of low or vanishing electrical resistance; our simultaneous magnetocaloric effect measurements (i.e. changes in sample temperature due to changing magnetic field) show the first definitive evidence for adiabaticity and thermal behavior characteristic of bulk field-induced superconductivity.

Bosonic excitation spectra of superconductingBi2Sr2CaCu2O8+δandYBa2Cu3O6+xextracted from scanning tunneling spectra.

A detailed interpretation of scanning tunneling spectra obtained on unconventional superconductors enables one to gain information on the pairing boson. Decisive for this approach are inelastic tunneling events. Due to the lack of momentum conservation in tunneling from or to the sharp tip, those are enhanced in the geometry of a scanning tunneling microscope compared to planar tunnel junctions. This work extends the method of obtaining the bosonic excitation spectrum by deconvolution from tunneling spectra to nodald-wave superconductors. In particular, scanning tunneling spectra of slightly underdopedBi2Sr2CaCu2O8+δwith aTcof 82 K and optimally dopedYBa2Cu3O6+xwith aTcof 92 K reveal a resonance mode in their bosonic excitation spectrum atΩres≈63 meVandΩres≈61 meVrespectively. In both cases, the overall shape of the bosonic excitation spectrum is indicative of predominant spin scattering with a resonant mode atΩres<2Δand overdamped spin fluctuations for energies larger than 2Δ. To perform the deconvolution of the experimental data, we implemented an efficient iterative algorithm that significantly enhances the reliability of our analysis.

Self-doped flat band and spin-triplet superconductivity in monolayer 1T-TaSe2-xTex.

Two-dimensional van der Waals materials have become an established platform to engineer flat bands which can lead to strongly-correlated emergent phenomena. In particular, the family of Ta dichalcogenides in the 1T phase presents a star-of-David charge density wave that creates a flat band at the Fermi level. For TaS2and TaSe2this flat band is at half filling leading to a magnetic insulating phase. In this work, we theoretically demonstrate that ligand substitution in the TaSe2-xTexsystem produces a transition from the magnetic insulator to a non-magnetic metal in which the flat band gets doped away from half-filling. Forx∈[0.846,1.231]the spin-polarized flat band is self-doped and the system becomes a magnetic metal. In this regime, we show that attractive interactions promote three different spin-triplet superconducting phases as a function ofx, corresponding to a nodal f-wave and two topologically-different chiral p-wave superconducting phases. Our results establish monolayer TaSe2-xTexas a promising platform for correlated flat band physics leading to unconventional superconducting states.

Effective model and electron correlations in trilayer nickelate superconductor La4Ni3O10.

Recently, signatures of superconductivity with critical temperature from 20 to 30 K have been reported in pressured trilayer nickelate La4Ni3O10through a pressure-induced structure transition. Here we explore the evolution of electronic structures and electronic correlations in different phases of La4Ni3O10under corresponding pressure regions, by using density functional theory (DFT) combined with dynamical mean-field theory (DMFT). Similar to bilayer superconductor La3Ni2O7, the electronic bands in superconducting La4Ni3O10are dominated by Ni-3dx2-y2and 3dz2orbits near the Fermi level, in contrast, the inner Ni-O plane in La4Ni3O10generates a doublet hole-pocket Fermi surfaces around the Brillouin-zone corner, meanwhile one branch of the Ni-3dz2bands is pushed very close above the Fermi level, which can induce an electron pocket through small electron doping. The DFT+DMFT simulations suggest that the electronic correlations only give minor modification to the Fermi surfaces, meanwhile the Ni-3dz2and 3dx2-y2states on outer Ni-O layers have considerable greater mass enhancements than on the inner layer. The sensitiveness of electronic structure under doping and unique layer dependence of correlation suggest a distinct superconducting mechanism with respect to bilayer La3Ni2O7. Based on the DFT and DFT+DMFT simulations, we eventually derive a trilayer effective tight-binding model, which can produce rather precise electronic bands and Fermi surfaces, hence can serve as an appropriate model to further study the superconducting mechanism and paring symmetry in trilayer La4Ni3O10.

Cuprate-like electronic structures in infinite-layer nickelates with substantial hole dopings.

Superconducting infinite-layer (IL) nickelates offer a new platform for investigating the long-standing problem of high-temperature superconductivity. Many models were proposed to understand the superconducting mechanism of nickelates based on the calculated electronic structure, and the multiple Fermi surfaces and multiple orbitals involved create complications and controversial conclusions. Over the past five years, the lack of direct measurements of the electronic structure has hindered the understanding of nickelate superconductors. Here we fill this gap by directly resolving the electronic structures of the parent compound LaNiO2 and superconducting La0.8Ca0.2NiO2 using angle-resolved photoemission spectroscopy. We find that their Fermi surfaces consist of a quasi-2D hole pocket and a 3D electron pocket at the Brillouin zone corner, whose volumes change upon Ca doping. The Fermi surface topology and band dispersion of the hole pocket closely resemble those observed in hole-doped cuprates. However, the cuprate-like band exhibits significantly higher hole doping in superconducting La0.8Ca0.2NiO2 compared to superconducting cuprates, highlighting the disparities in the electronic states of the superconducting phase. Our observations highlight the novel aspects of the IL nickelates, and pave the way toward the microscopic understanding of the IL nickelate family and its superconductivity.

Evidence of multi-band superconductivity in non-centrosymmetric full Heusler alloy LuPd2Sn.

In this work, evidence of multi-band superconductivity and presence of mixed parity states in full Heusler alloy LuPd2Sn is investigated using the x-ray diffraction, temperature and field dependent resistivity, temperature dependent magnetization, and heat capacity measurements. Our studies reveal that LuPd2Sn is a type II superconductor and undergoes superconducting transition below 2.5 K. Above 2.5 K, the temperature and field dependence of resistivity indicate to the presence of multiple bands and inter-band phonon assisted scattering. The upper critical field,HC2(T) exhibits linear behaviour and deviates from Werthamer, Helfand and Hohenberg model over the measured temperature range. Additionally, the Kadowaki-Woods ratio plot supports the unconventional superconductivity in this alloy. Moreover, a significant deviation from the s-wave behaviour is noted, which is studied using phases fluctuation analysis. It indicates the presence of spin triplet along with spin singlet component arising due to antisymmetric spin orbit coupling.

Pressure-induced linear enhancement of the superconducting transition in Nd0.8Sr0.2NiO2thin films.

We report the pressure (P) effect on the superconducting transition temperatureTcand the upper critical fieldµ0Hc2of infinite-layer Nd0.8Sr0.2NiO2thin films by measuring the electrical transport properties under various hydrostatic pressures to 4.6 GPa. At ambient pressure, it shows the clear superconducting transition withTc∼ 10 K. Based on the evolution of resistanceR(T), we found that theTcis monotonically enhanced to ∼14 K upon increasing pressure to 2.9 GPa. The constructed temperature-pressure phase diagram indicates that the calculated slope dTc/dPis about 1.14 K GPa-1and the superconductingTcshows no signatures of saturation with pressure. It thus gives the possibility to further enhanceTcby employing higher pressures or heterostructure engineering. In addition, the normalized slope of upper critical fieldµ0Hc2(0) implies that the electron correlations are gradually decreasing with pressure, which exhibits an opposite evolution with superconductingTc. Our work further confirms the positive pressure effects in nickelate superconductors and gives more insight to further enhance its superconducting transition temperature.

Upper Critical Field and Tunneling Spectroscopy of Underdoped Na(Fe,Co)As Single Crystals.

A comprehensive study of superconducting properties of underdoped NaFe0.979Co0.021As single crystals by a combination of upper critical field measurements and incoherent multiple Andreev reflection effect (IMARE) spectroscopy is presented. The Hc2(T) temperature dependences are measured at magnetic fields up to 16 T with in-plane and out-of-plane field directions and considered within single-band and two-band models in order to estimate the Hc2(0) value. In IMARE spectroscopy probes, the magnitude, characteristic ratio, and temperature dependence of the superconducting order parameters (ΔL,S(T)) are determined locally and directly. A possible k-space anisotropy of the large superconducting gap is demonstrated. We show that usage of a quadruple of λij0 coupling constants obtained in the IMARE experiment can significantly reduce the number of free parameters required to fit the Hc2(T) dependence within a two-band approach (from six to two).

Evidence of Nodal Superconductivity in Monolayer 1H-TaS2 with Hidden Order Fluctuations.

Unconventional superconductors represent one of the fundamental directions in modern quantum materials research. In particular, nodal superconductors are known to appear naturally in strongly correlated systems, including cuprate superconductors and heavy-fermion systems. Van der Waals materials hosting superconducting states are well known, yet nodal monolayer van der Waals superconductors have remained elusive. Here, using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) experiments, it is shown that pristine monolayer 1H-TaS2 realizes a nodal superconducting state. Non-magnetic disorder drives the nodal superconducting state to a conventional gapped s-wave state. Furthermore, many-body excitations emerge close to the gap edge, signalling a potential unconventional pairing mechanism. The results demonstrate the emergence of nodal superconductivity in a van der Waals monolayer, providing a building block for van der Waals heterostructures exploiting unconventional superconducting states.

Nonunitary superconductivity in complex quantum materials.

We revisit the concept of nonunitary superconductivity and generalize it to address complex quantum materials. Starting with a brief review of the notion of nonunitary superconductivity, we discuss its spectral signatures in simple models with only the spin as an internal degree of freedom. In complex materials with multiple internal degrees of freedom, there are many more possibilities for the development of nonunitary order parameters. We provide examples focusing on d-electron systems with two orbitals, applicable to a variety of materials. We discuss the consequences for the superconducting spectra, highlighting that gap openings of band crossings at finite energies can be attributed to a nonunitary order parameter if this is associated with a finite superconducting fitness matrix. We speculate that nonunitary superconductivity in complex quantum materials is in fact very common and can be associated with multiple cases of recently reported time-reversal symmetry breaking superconductors.

Self-consistent theory of current injection intodandd + issuperconductors.

We present results for the steady-state nonlinear response of adx2-y2superconducting film connected to normal-metal reservoirs under voltage bias, allowing for a subdominants-wave component appearing near the interfaces. Our investigation is based on a current-conserving theory that self-consistently includes the non-equilibrium distribution functions, charge imbalance, and the voltage-dependencies of order parameters and scalar impurity self-energies. For a pured-wave superconductor with [110] orientation of the interfaces to the contacts, the conductance contains a zero-bias peak reflecting the large density of zero-energy interface Andreev bound states. Including a subdominants-wave pairing channel, it is in equilibrium energetically favorable for ans-wave order parameter componentΔsto appear near the interfaces in the time-reversal symmetry breaking combinationd + is. The Andreev states then shift to finite energies in the density of states. Under voltage bias, we find that the non-equilibrium distribution in the contact area causes a rapid suppression of thes-wave component to zero as the voltageeV→Δs. The resulting spectral rearrangements and voltage-dependent scattering amplitudes lead to a pronounced non-thermally broadened split of the zero-bias conductance peak that is not seen in a non-selfconsistent Landauer-Büttiker scattering approach.