Superconducting Gap Structure Research Articles

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets.

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Anisotropic s-Wave Gap in the Vicinity of a Quantum Critical Point in Superconducting BaFe2(As1–x P x )2 Single Crystals: A Study of Point-Contact Spectroscopy

We report on soft c-axis point-contact Andreev reflection (PCAR) spectroscopy combining with resistivity measurements on BaFe2(As0.7P0.3)2, to elucidate the superconducting gap structure in the vicinity of the quantum critical point. A double peak at the gap edge plus a dip feature at zero-bias has been observed on the PCAR spectra, indicative of the presence of a nodeless gap in BaFe2(As0.7P0.3)2. Detailed analysis within a sophisticated theoretical model reveals an anisotropic gap with deep gap minima. The PCARs also feature additional structures related to the electron–bosonic coupling mode. Using the extracted superconducting energy gap value, a characteristic bosonic energy Ω b and its temperature dependence are obtained, comparable with the spin-resonance energy observed in neutron scattering experiment. These results indicate a magnetism-driven quantum critical point in the BaFe2(As1−x P x )2 system.

Fully gapped pairing state in spin-triplet superconductor UTe2.

The recently discovered superconductor UTe2 is a promising candidate for spin-triplet superconductors, but the symmetry of the superconducting order parameter remains highly controversial. Here, we determine the superconducting gap structure by the thermal conductivity of ultraclean UTe2 single crystals. We find that the a-axis thermal conductivity divided by temperature κ/T in zero-temperature limit is vanishingly small for both magnetic field H‖a and H‖c axes up to H/Hc2 ∼ 0.2, demonstrating the absence of nodes around the a axis contrary to the previous belief. The present results, combined with the reduction of nuclear magnetic resonance Knight shift, indicate that the superconducting order parameter belongs to the isotropic Au representation with a fully gapped pairing state, analogous to the B phase of superfluid 3He. These findings reveal that UTe2 is likely to be a long-sought three-dimensional strong topological superconductor, hosting helical Majorana surface states on any crystal plane.

Superconducting gap structure of slightly overdoped NaFe$$_{0.955}$$Co$$_{0.045}$$As pnictides: joint SnS-Andreev spectroscopy and specific heat study

Superconducting gap structure of slightly overdoped NaFe$$_{0.955}$$Co$$_{0.045}$$As pnictides: joint SnS-Andreev spectroscopy and specific heat study

Ultralow-temperature heat transport study of noncentrosymmetric superconductor CaPtAs

The noncentrosymmetric superconductor CaPtAs with time-reversal symmetry breaking in its superconducting state was previously proposed to host nodal superconductivity. Here, by employing ultralow-temperature thermal conductivity measurement on CaPtAs single crystal, we study its superconducting gap structure. A negligible residual linear term of thermal conductivity (κ 0/T) in zero magnetic field and the field dependence of κ 0/T indicate that CaPtAs has multiple superconducting gaps with a dominant s-wave component. This is consistent with recent nuclear quadrupole resonance measurements on CaPtAs. Our work puts a strong constraint on the theories to describe the superconducting pairing symmetry of CaPtAs.

Linear magnetic susceptibility of anisotropic superconductors of cuboidal shape

A simplified model of anisotropic magnetic susceptibility in the Meissner–London vortex-free state of cuboidal superconducting samples is presented. Using this model, precision measurements of the magnetic response in three perpendicular directions of a magnetic field with respect to primary crystal axes can be used to extract the components of the London penetration depth, thus enabling the evaluation of the general superfluid density tensor, which is needed in the analysis of the superconducting gap structure.

Andreev Reflection in Scanning Tunneling Spectroscopy of Unconventional Superconductors.

We evaluate the differential conductance measured in an STM setting at arbitrary electron transmission between STM tip and a 2D superconductor with arbitrary gap structure. Our analytical scattering theory accounts for Andreev reflections, which become prominent at larger transmissions. We show that this provides complementary information about the superconducting gap structure beyond the tunneling density of states, strongly facilitating the ability to extract the gap symmetry and its relation to the underlying crystalline lattice. We use the developed theory to discuss recent experimental results on superconductivity in twisted bilayer graphene.

Superconducting Gap Structure of Filled Skutterudite LaOs4As12 Compound through μSR Investigations

Filled skutterudite compounds have gained attention recently as an innovative platforms for studying intriguing low-temperature superconducting properties. Regarding the symmetry of the superconducting gap, contradicting findings from several experiments have been made for LaRu4As12 and its isoelectronic counterpart, LaOs4As12. In this vein, we report comprehensive bulk and microscopic results on LaOs4As12 utilizing specific heat analysis and muon-spin rotation/relaxation (μSR) measurements. Bulk superconductivity with TC = 3.2 K was confirmed by heat capacity. The superconducting ground state of the filled-skutterudite LaOs4As12 compound is found to have two key characteristics: superfluid density exhibits saturation type behavior at low temperature, which points to a fully gapped superconductivity with gap value of 2Δ/kBTC = 3.26; additionally, the superconducting state does not show any sign of spontaneous magnetic field, supporting the preservation of time-reversal symmetry. These results open the door for the development of La-based skutterudites as special probes for examining the interplay of single- and multiband superconductivity in classical electron–phonon systems.

Nodeless electron pairing in CsV3Sb5-derived kagome superconductors.

The newly discovered kagome superconductors represent a promising platform for investigating the interplay between band topology, electronic order and lattice geometry1-9. Despite extensive research efforts on this system, the nature of the superconducting ground state remains elusive10-17. In particular, consensus on the electron pairing symmetry has not been achieved so far18-20, in part owing to the lack of a momentum-resolved measurement of the superconducting gap structure. Here we report the direct observation of a nodeless, nearly isotropic and orbital-independent superconducting gap in the momentum space of two exemplary CsV3Sb5-derived kagome superconductors-Cs(V0.93Nb0.07)3Sb5 and Cs(V0.86Ta0.14)3Sb5-using ultrahigh-resolution and low-temperature angle-resolved photoemission spectroscopy. Remarkably, such a gap structure is robust to the appearance or absence of charge order in the normal state, tuned by isovalent Nb/Ta substitutions of V. Our comprehensive characterizations of the superconducting gap provide indispensable information on the electron pairing symmetry of kagome superconductors, and advance our understanding of the superconductivity and intertwined electronic orders in quantum materials.

Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors

Nonunitary superconductivity has attracted renewed interest as a novel gapless phase of matter. In this study, we investigate the superconducting gap structure of nonunitary odd-parity chiral pairing states in a superconductor involving strong spin-orbit interactions. By applying a group theoretical classification of chiral states in terms of discrete rotation symmetry, we categorized all possible point-nodal gap structures in nonunitary chiral states into four types in terms of the topological number of nodes and node positions relative to the rotation axis. In addition to conventional Dirac and Weyl point nodes, we identify a type of Dirac point nodes unique to nonunitary chiral superconducting states. Such a Dirac point node is a nodal point of two pseudospin excitations, but the dispersions around it depend on the pseudospin. The node type can be identified experimentally based on the temperature dependence of the nuclear magnetic resonance longitudinal relaxation rate. The implication of our results for a nonunitary odd-parity superconductor in ${\mathrm{UTe}}_{2}$ is also discussed.

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and ${B}_{2g}$ (${d}_{xy}$) pairing dominates in the absence of repulsive longer-range Coulomb interactions ${V}_{\mathrm{NN}}$, the latter induces pairing in other symmetry channels, including, e.g., ${A}_{2g}$ ($g$-wave), nodal ${A}_{1g}$ (extended $s$-wave), or nodal ${E}_{u}$ ($p$-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, ${V}_{\mathrm{NN}}<0$, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts ${E}_{u}$ ($p$-wave) spin-triplet or ${B}_{1g}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.

Direct Observation of the Spin Exciton in Andreev Spectroscopy of Iron-Based Superconductors.

Quasiparticle excitations provide viable information on the physics of unconventional superconductors. Higgs and Leggett modes are some of the classic examples. Another important bosonic excitation is the spin exciton originating from the sign-changing superconducting gap structure. Here we report a direct observation of the temperature-dependent spin exciton in the Andreev spectra of iron-based superconductors. Combined with the other experimental evidence, our observation confirms the extended s-wave () order parameter symmetry and indirectly proves the spin-fluctuation mechanism of Cooper pairing.

Superconducting Instabilities in Strongly Correlated Infinite-Layer Nickelates

The discovery of superconductivity in infinite-layer nickelates has added a new family of materials to the fascinating growing class of unconventional superconductors. By incorporating the strongly correlated multiorbital nature of the low-energy electronic degrees of freedom, we compute the leading superconducting instability from magnetic fluctuations relevant for infinite-layer nickelates. Specifically, by properly including the doping dependence of the Ni ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals as well as the self-doping band, we uncover a transition from $d$-wave pairing symmetry to nodal ${s}_{\ifmmode\pm\else\textpm\fi{}}$ superconductivity, driven by strong fluctuations in the ${d}_{{z}^{2}}$-dominated orbital states. We discuss the properties of the resulting superconducting condensates in light of recent tunneling and penetration depth experiments probing the detailed superconducting gap structure of these materials.

Superconducting gap structure in carrier doped BiCh2-based layered superconductors: A [formula omitted]SR study

The layered bismuth oxy-sulfide materials, which are structurally similar to Fe-pnictides/chalcogenides and cuprates superconductors, have sparked a lot of interest in the physics of reduced-dimensional superconductors. The pairing symmetry of the recently discovered BiCh2-based superconductor, La1−xCexOBiSSe with x = 0.3, was investigated using zero-field and transverse field (TF) muon spin measurements, as well as using magnetization and resistivity measurements. Resistivity and magnetization data confirmed bulk superconductivity below 2.7 K for x = 0.3. The temperature dependence of the magnetic penetration depth has been determined from TF-μSR data, which can be described by an isotropic two-gap s+s wave model compared to a single gap s- or anisotropic s-wave model, which resembles with Fe-pnictides/chalcogenides and MgB2. Furthermore, from the TF-μSR data, we have determined the London’s penetration depth λL(0) = 452(3) nm, superconducting carrier’s density ns = 2.18(1) × 1026 carriers/m3 and effective mass enhancement m∗ = 1.66(1) me, respectively. No signature of spontaneous internal field is found down to 100 mK in ZF-μSR measurement, which suggests that time-reversal symmetry is preserved in this system.

Thermal transport in two-dimensional nematic superconductors

We study the thermal transport in a two-dimensional system with coexisting superconducting (SC) and nematic orders. We analyze the nature of the coexistence phase in a tight-binding square lattice where the nematic state is modelled as a $d$-wave Pomeranchuk-type instability and the feedback of the symmetry breaking nematic state on the SC order is accounted for by mixing of the $s, d$ paring interaction. The electronic thermal conductivity is computed within the framework of Boltzmann kinetic theory where the impurity scattering collision integral is treated in the Born and unitary limits. We present qualitative, analytical, and numerical results that show that the heat transport properties of SC states emerging from a nematic background are quite distinct and depend on the degree of anisotropy of the SC gap induced by nematicity. We describe the influence of the Fermi surface topology, the van Hove singularities, and the presence or absence of zero-energy excitations in the coexistence phase on the the low-temperature behavior of the thermal conductivity. Our main conclusion is that the interplay of nematic and SC orders has visible signatures in the thermal transport, which can be used to infer SC gap structure in the coexistence phase.

Low-Temperature Thermal Conductivity of the Two-Phase Superconductor CeRh2As2

CeRh2As2is a rare unconventional superconductor (Tc= 0.26 K) characterized by two adjacent superconducting phases for a magnetic fieldH‖c-axis of the tetragonal crystal structure. Antiferromagnetic order, quadrupole-density-wave order (T0= 0.4 K) and the proximity of this material to a quantum-critical point have also been reported: The coexistence of these phenomena with superconductivity is currently under discussion. Here, we present thermal conductivity and electrical resistivity measurements on a single crystal of CeRh2As2between 60 mK and 200 K and in magnetic fields (H‖c) up to 8 T. Extrapolation of our normal-state data to zero temperature validates the Wiedemann-Franz law within the error bars. TheTdependence of the thermal conductivityκ(T) shows a pronounced drop belowTcwhich is also field dependent and thus interpreted as the signature of superconductivity. However, the large residual resistivity and the lack of sharp anomalies inκ(T) at the expected transition temperatures clearly indicate that samples of much higher purity are required to gain more information about the superconducting gap structure.

Controlling the Superconducting Gap Structure

Controlling the Superconducting Gap Structure

Distorted superconducting nodal line on a single Fermi surface in the anisotropic organic superconductor λ−(BETS)2GaCl4

The superconducting (SC) gap structure appearing in systems with single Fermi surface (FS) is generally described by the single gap function with $s$- or $d$-wave symmetry. The organic superconductor $\ensuremath{\lambda}$-(BETS)${}_{2}{\mathrm{GaCl}}_{4}$ [BETS = (${\mathrm{CH}}_{2}{)}_{2}{\mathrm{S}}_{2}{\mathrm{Se}}_{2}{\mathrm{C}}_{6}{\mathrm{Se}}_{2}{\mathrm{S}}_{2}$(${\mathrm{CH}}_{2}{)}_{2}$] endeavors to examine a novel SC gap structure on the distorted single cylindrical FS. Here, we show an example of the formation of the distorted SC nodal line by using the positive muon spin rotation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) spectroscopy on $\ensuremath{\lambda}$-(BETS)${}_{2}{\mathrm{GaCl}}_{4}$. Our analysis method of the ${\ensuremath{\mu}}^{+}\mathrm{SR}$ data reveals that the nodal line has a narrower width than that of the traditional $d$-wave by the steepness factor of 4.6(2.1), and a flat part with the maximum gap exists. We found that the amplitude of the SC gap is $2\mathrm{\ensuremath{\Delta}}/{k}_{\text{B}}{T}_{c}$ = 3.9(2) and the in-plane penetration depth is ${\ensuremath{\lambda}}_{\text{ac}}$(0) = 560(5) nm. Our present study gives insight into the relation of the FS distortion and the unusual Cooper pair formation mediated by the anisotropic spin fluctuations.

Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor

In superconductors, electrons with spin ${s=1/2}$ form Cooper pairs whose spin structure is usually singlet (${S=0}$) or triplet (${S=1}$). When the electronic structure near the Fermi level is characterized by fermions with angular momentum ${j=3/2}$ due to strong spin-orbit interactions, novel pairing states such as even-parity quintet (${J=2}$) and odd-parity septet (${J=3}$) states become allowed. Prime candidates for such exotic states are half-Heusler superconductors, which exhibit unconventional superconducting properties, but their pairing nature remains unsettled. Here we show that the superconductivity in the noncentrosymmetric half-Heusler LuPdBi can be consistently described by the admixture of isotropic even-parity singlet and anisotropic odd-parity septet pairing, whose ratio can be tuned by electron irradiation. From magnetotransport and penetration depth measurements, we find that carrier concentrations and impurity scattering both increase with irradiation, resulting in a nonmonotonic change of the superconducting gap structure. Our findings shed new light on our fundamental understanding of unconventional superconducting states in topological materials.

Orbital-dependent modulation of the superconducting gap in uniaxially strained Ba0.6K0.4Fe2As2

Pairing symmetry which characterizes the superconducting pairing mechanism is normally determined by measuring the superconducting gap structure ($|\Delta_k|$). Here, we report the measurement of a strain-induced gap modulation ($\partial|\Delta_k|$) in uniaxially strained Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ utilizing angle-resolved photoemission spectroscopy and $in$-$situ$ strain-tuning. We found that the uniaxial strain drives Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ into a nematic superconducting state which breaks the four-fold rotational symmetry of the superconducting pairing. The superconducting gap increases on the $d_{yz}$ electron and hole pockets while it decreases on the $d_{xz}$ counterparts. Such orbital selectivity indicates that orbital-selective pairing exists intrinsically in non-nematic iron-based superconductors. The $d_{xz}$ and $d_{yz}$ pairing channels are balanced originally in the pristine superconducting state, but become imbalanced under uniaxial strain. Our results highlight the important role of intra-orbital scattering in mediating the superconducting pairing in iron-based superconductors. It also highlights the measurement of $\partial|\Delta_k|$ as an effective way to characterize the superconducting pairing from a perturbation perspective.