Unconventional Pairing Symmetry Research Articles

Electronic and superconducting properties of CoSi[formula omitted] films on silicon — An unconventional superconductor with technological potential

We report the observation of unusual normal-state electronic conduction properties and superconducting characteristics of high-quality CoSi2/Si films grown on silicon Si(100) and Si(111) substrates. A good understanding of these features shall help to address the underlying physics of the unconventional pairing symmetry recently discovered in transparent CoSi2/TiSi2 heterojunctions (Chiu et al., 2021; Chiu et al., 2023), where CoSi2/Si is a superconductor with a superconducting transition temperature Tc≃ (1.1–1.5) K, dependent on its dimensions, and TiSi2 is a normal metal. In CoSi2/Si films, we find a pronounced positive magnetoresistance caused by the weak-antilocalization effect, indicating a strong Rashba spin–orbit coupling (SOC). This SOC generates two-component superconductivity in CoSi2/TiSi2 heterojunctions. The CoSi2/Si films are stable under ambient conditions and have ultralow 1/f noise. Moreover, they can be patterned via the standard lithography techniques, which might be of considerable practical value for future scalable superconducting and quantum device fabrication.

Intrinsic surface p-wave superconductivity in layered AuSn4

The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.

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.

Superconductivity of K‐Intercalated Epitaxial Bilayer Graphene

AbstractGraphene‐based materials are among the most promising candidates for studying superconductivity arising from reduced dimensionality. Apart from doping by twisted stacking, superconductivity can also be achieved by metal‐intercalation of stacked graphene sheets, where the properties depend on the choice of the metal atoms and the number of graphene layers. Many different and even unconventional pairing mechanisms and symmetries are predicted in the literature for graphene monolayers and few‐layers. However, those theoretical predictions have yet to be verified experimentally. Here, it is shown that potassium‐intercalated epitaxial bilayer graphene is a superconductor with a critical temperature of Tc = 3.6 ± 0.1 K. By scanning‐tunneling microscopy and angle‐resolved photoelectron spectroscopy, the physical mechanisms are analyzed in great detail, using laboratory equipment. The data demonstrate that electron–phonon coupling is the driving force enabling superconductivity. Although the consideration of an s‐wave pairing symmetry is sufficient to explain the experimental data, evidence is found for the existence of multiple energy gaps. Furthermore, it is shown that low‐dimensional effects are most likely the cause of a gap ratio of 6.1 ± 0.2 that strongly exceeds the Bardeen‐Cooper‐Schrieffer (BCS) value of 3.52 for conventional superconductors. These results highlight the importance of reduced dimensionality yielding unusual superconducting properties of K‐intercalated epitaxial bilayer graphene.

Strong Correlation Between Superconductivity and Ferromagnetism in an Fe-Chalcogenide Superconductor.

The interplay among topology, superconductivity, and magnetism promises to bring a plethora of exotic and unintuitive behaviors in emergent quantum materials. The family of Fe-chalcogenide superconductors FeTexSe1-x are directly relevant in this context due to their intrinsic topological band structure, high-temperature superconductivity, and unconventional pairing symmetry. Despite enormous promise and expectation, the local magnetic properties of FeTexSe1-x remain largely unexplored, which prevents a comprehensive understanding of their underlying material properties. Exploiting nitrogen vacancy (NV) centers in diamond, here we report nanoscale quantum sensing and imaging of magnetic flux generated by exfoliated FeTexSe1-x flakes, demonstrating strong correlation between superconductivity and ferromagnetism in FeTexSe1-x. The coexistence of superconductivity and ferromagnetism in an established topological superconductor opens up new opportunities for exploring exotic spin and charge transport phenomena in quantum materials. The demonstrated coupling between NV centers and FeTexSe1-x may also find applications in developing hybrid architectures for next-generation, solid-state-based quantum information technologies.

Possible multiband superconductivity in the quaternary carbide YRe2SiC

We report for the first time the occurrence of superconductivity in the quaternary silicide carbide YRe2SiC with T c ≈ 5.9 K. The emergence of superconductivity was confirmed by means of magnetic susceptibility, electrical resistivity, and heat capacity measurements. The presence of a well-developed heat capacity feature at T c confirms that superconductivity is a bulk phenomenon, while a second feature in the heat capacity near 0.5T c combined with the unusual temperature dependence of the upper critical field H c2(T) indicate the presence of a multiband superconducting state. Additionally, the linear dependence of the lower critical field H c1 with temperature resemble the behavior found in compounds with unconventional pairing symmetry. Band structure calculations reveal that YRe2SiC could harbor a non-trivial topological state and that the low-energy states occupy multiple disconnected sheets at the Fermi surface, with different degrees of hybridization, nesting, and screening effects, therefore making unconventional multiband superconductivity plausible.

Two-band superconductivity with unconventional pairing symmetry in HfV2Ga4

In this letter, we have examined the superconducting ground state of the HfV$_2$Ga$_4$ compound using resistivity, magnetization, zero-field (ZF) and transverse-field (TF) muon-spin relaxation and rotation ($\mu$SR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with $T_{\bf c}\sim$ 3.9~K, while TF-$\mu$SR measurements show that the temperature dependence of the superfluid density is well described by a nodal two-gap $s$+$d$-wave order parameter model. In addition, ZF muon relaxation rate increases with decreasing temperature below 4.6 K, indicating the presence of weak spin fluctuations. These observations suggest an unconventional multiband nature of the superconductivity possibly arising from the distinct $d$-bands of V and Hf ions with spin fluctuations playing an important role. To better understand these findings, we carry out first-principles electronic-structure calculations, further highlighting that the Fermi surface consists of multiple disconnected sheets with very different orbital weights and spin-orbit coupling, bridging the way for a nodal multiband superconductivity scenario. In this vein, therefore, HfV$_2$Ga$_4$-family stands out as an open avenue to novel unexplored unconventional superconducting compounds, such as ScV$_2$Ga$_4$ and ZrV$_2$Ga$_4$, and other many rare earths based materials.

Observation of half-quantum flux in the unconventional superconductor β-Bi2Pd.

Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi2Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of β-Bi2Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.

Majorana Multipole Response of Topological Superconductors.

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify unconventional pairing symmetry via the magnetic response of helical MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but those on superconductors with spin-3/2 electrons may display a magnetic-octupole response in leading order, which uniquely characterizes high-spin superconductors. Detection of such an octupole response provides direct evidence of high-spin superconductivity, such as in half-Heusler superconductors.

Anomalous isotope effect in iron-based superconductors

The role of electron-phonon interactions in iron-based superconductor is currently under debate with conflicting experimental reports on the isotope effect. To address this important issue, we employ the renormalization-group method to investigate the competition between electron-electron and electron-phonon interactions in these materials. The renormalization-group analysis shows that the ground state is a phonon-dressed unconventional superconductor: the dominant electronic interactions account for pairing mechanism while electron-phonon interactions are subdominant. Because of the phonon dressing, the isotope effect of the critical temperature can be normal or reversed, depending on whether the retarded intra- or inter-band interactions are altered upon isotope substitutions. The connection between the anomalous isotope effect and the unconventional pairing symmetry is discussed at the end.

Tunneling conductance and twofold spin-singlet Andreev reflections in ferromagnet/ferromagnet/iron pnictide superconductor hybrid structures with collinear magnetizations

Iron-based superconductors, as some other high-temperature superconducting materials such as the cuprates, are confronted with uncovering the unconventional pairing symmetry, although most researchers favor the so-called s±-wave pairing state. Herein, we theoretically investigate the tunneling conductance of clean ferromagnet (FM)/FM/iron pnictide superconductor (SC) hybrid structures with the SC having s±(two energy gaps have phase difference) pairing symmetry. Novel twofold spin-singlet pairing states near the FM/SC interface in collinear magnetizations emerge due to the presence of two bands in the SC. Conversions of the differential conductance in the ferromagnetic alignment of the two FMs between the peak and valley are shown to be much different from those in the antiferromagnetic alignment. More importantly, two rather different properties in contrast with tunneling into a conventional s-wave SC and an s++-wave SC (two energy gaps have the same sign) are also exhibited, which can be experimentally used to probe and identify the s±pairing symmetry in the iron pnictide SC.

First-Principles Correlated Approach to the Normal State of Strontium Ruthenate

The interplay between multiple bands, sizable multi-band electronic correlations and strong spin-orbit coupling may conspire in selecting a rather unusual unconventional pairing symmetry in layered Sr2RuO4. This mandates a detailed revisit of the normal state and, in particular, the T-dependent incoherence-coherence crossover. Using a modern first-principles correlated view, we study this issue in the actual structure of Sr2RuO4 and present a unified and quantitative description of a range of unusual physical responses in the normal state. Armed with these, we propose that a new and important element, that of dominant multi-orbital charge fluctuations in a Hund’s metal, may be a primary pair glue for unconventional superconductivity. Thereby we establish a connection between the normal state responses and superconductivity in this system.

Twofold Andreev reflections and coherent transport in ferromagnetic semiconductor/d-wave superconductor/ferromagnetic semiconductor double tunneling junctions

Coherent transport in a ferromagnetic semiconductor (FS)/d-wave superconductor (SC)/FS structure with {110} interfaces is studied by extending Bogoliubov-de Gennes equation into eight components, in which the interband coupling of heavy and light hole bands in the FS, the strengths of potential scattering at the interfaces, and the mismatches in the effective mass and Fermi vector between the FS and SC are taken into account. Twofold Andreev reflections exist due to the existence of two bands in the FS, in which the incident hole and the two Andreev-reflected electrons, belonging to the different spin subbands, form twofold spin-singlet pairing states near the FS/SC interface. It is shown that due to the interplay of the SC with unconventional d-wave pairing symmetry and FS, the differential conductance and tunneling magnetoresistance exhibit an abundant dependence on not only the interband coupling in the FS but also the strengths of potential scattering at the interfaces. More importantly, the properties are found to be quite different from those in the FS/s-wave SC/FS structure with conventional pairing symmetry for the SC.

Calorimetric study of single-crystal CsFe2As2

We measured resistivity and specific heat of high-quality CsFe$_2$As$_2$ single crystals, which were grown by using a self-flux method. The CsFe$_2$As$_2$ crystal shows sharp superconducting transition at 1.8 K with the transition width of 0.1 K. The sharp superconducting transition and pronounced jump in specific heat indicate high quality of the crystals. Analysis on the superconducting-state specific heat supports unconventional pairing symmetry in CsFe$_2$As$_2$.

Comparative studies of the scanning tunneling spectra in cuprate and iron-arsenide superconductors

We report scanning tunneling spectroscopic studies of cuprate and iron-arsenic superconductors, including YBa2Cu3O7-δ (Y-123, Tc = 93 K), Sr0.9La0.1CuO2 (La-112, Tc = 43 K), and the “122” compounds Ba(Fe1-xCox)2As2 (Co-122 with x = 0.06, 0.08, 0.12 for Tc = 14, 24, 20 K). In zero field (H = 0), spatially homogeneous coherence peaks at energies ω = ± ΔSC flanked by spectral “shoulders” at ±Δeff are found in hole-type Y-123. In contrast, only a pair of spatially homogeneous peaks is seen in electron-type La-112 at ± Δeff. For H > 0, pseudogap (ΔPG) features are revealed inside the vortices, with ΔPG = [(Δeff)2-(ΔSC)2]1/2 > ΔSC in Y-123 and ΔPG < ΔSC in La-112, suggesting that the physical origin of ΔPG is a competing order coexisting with superconductivity. Additionally, Fourier transformation (FT) of the Y-123 spectra exhibits two types of spectral peaks, one type is associated with ω-dependent quasiparticle interference (QPI) wave-vectors and the other consists of ω-independent wave-vectors due to competing orders and (π,π) magnetic resonances. For the multi-band Co-122 compounds, two-gap superconductivity is found for all doping levels. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps are also identified. These findings, together with the ω- and x-dependent QPI spectra, are consistent with a sign-changing s-wave pairing symmetry in the Co-122 iron arsenides. Our comparative studies suggest that the commonalities among the cuprate and the ferrous superconductors include the proximity to competing orders, antiferromagnetic (AFM) spin fluctuations and magnetic resonances in the superconducting (SC) state, and the unconventional pairing symmetries with sign-changing order parameters on different parts of the Fermi surface.

Quantum oscillations in the vortex state of underdoped YBa2Cu3O6.5and other multiband superconductors

We argue that the low-frequency quantum oscillations observed recently in the vortex state of underdoped ortho-II YBa${}_{2}$Cu${}_{3}$O${}_{6,5}$ have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several leading Fermi surfaces creates the proximity gaps on the other. The gap that is transferred on a small-sized pocket from larger Fermi surfaces is small. In the case of unconventional pairing symmetry the induced gap is proportional to the ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to the mass enhancement on the latter. We share the view that small pockets in and of themselves exist as a certain band feature among all Fermi surfaces.

Integer and half-integer flux-quantum transitions in a niobium–iron pnictide loop

Measurements of integer and half-integer transitions of the quantized magnetic flux through a superconducting niobium–iron pnictide ring provide strong evidence to support predictions that the Cooper pairs within iron-based superconductors show an unconventional ‘reversed s-wave symmetry’. The recent discovery of iron-based superconductors1,2,3 challenges the existing paradigm of high-temperature superconductivity. Owing to their unusual multi-orbital band structure4,5, magnetism6 and electron correlation7, theories propose a unique sign-reversed s-wave pairing state, with the order parameter changing sign between the electron and hole Fermi pockets8,9,10,11,12,13,14. However, because of the complex Fermi surface topology and materials-related issues, the predicted sign reversal remains unconfirmed. Here we report a new phase-sensitive technique for probing unconventional pairing symmetry in the polycrystalline iron pnictides. Through the observation of both integer and half-integer flux-quantum transitions in composite niobium–iron pnictide loops, we provide the first phase-sensitive evidence of the sign change of the order parameter in NdFeAsO0.88F0.12, lending strong support for microscopic models predicting unconventional s-wave pairing symmetry9,10,11,12,13,14. These findings have important implications on the mechanism of iron pnictide superconductivity, and lay the groundwork for future studies of new physics arising from the exotic order in the FeAs-based superconductors.

Measurement of the nonlinear Meissner effect in superconducting Nb films using a resonant microwave cavity: A probe of unconventional pairing symmetries

We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in superconductors.

Weak-link behavior of grain boundaries in superconducting Ba(Fe1−xCox)2As2 bicrystals

We show that despite the low anisotropy, strong vortex pinning, and high irreversibility field Hirr close to the upper critical field Hc2 of Ba(Fe1−xCox)2As2, the critical current density Jgb across [001] tilt grain boundaries (GBs) of thin film Ba(Fe1−xCox)2As2 bicrystals is strongly depressed, similar to high-Tc cuprates. Our results suggest that weak-linked GBs are characteristic of both cuprates and pnictides because of competing orders, low carrier density, and unconventional pairing symmetry.

Josephson current in graphene: Role of unconventional pairing symmetries

We investigate the Josephson current in a graphene superconductor/normal/superconductor junction, where superconductivity is induced by means of the proximity effect from external contacts. We take into account the possibility of anisotropic pairing by also including singlet nearest-neighbor interactions, and investigate how the transport properties are affected by the symmetry of the superconducting order parameter. This corresponds to an extension of the usual on-site interaction assumption, which yields an isotropic $s$-wave order parameter near the Dirac points. Here, we employ a full numerical solution as well as an analytical treatment, and show how the proximity effect may induce exotic types of superconducting states near the Dirac points, e.g., ${p}_{x}$- and ${p}_{y}$-wave pairing or a combination of $s$- and $p+\text{i}p$-wave pairing. We find that the Josephson current exhibits a weakly damped, oscillatory dependence on the length of the junction when the graphene sheet is strongly doped. The analytical and numerical treatments are found to agree well with each other in the $s$-wave case when calculating the critical current and current-phase relationship. For the scenarios with anisotropic superconducting pairing, there is a deviation between the two treatments, especially for the effective ${p}_{x}$-wave order parameter near the Dirac cones which features zero-energy states at the interfaces. This indicates that a numerical, self-consistent approach becomes necessary when treating anisotropic superconducting pairing in graphene.