Superconducting Pairing Symmetry Research Articles

Pairing correlation of the kagome-lattice Hubbard model with the nearest-neighbor interaction

Abstract A recently discovered family of kagome lattice materials, AV3Sb5 (A = K,Rb,Cs), has attracted great interest, especially in the debate over their dominant superconducting pairing symmetry. To explore this issue, we study the superconducting pairing behavior within the kagome-lattice Hubbard model through the constrained path Monte Carlo method. It is found that doping around the Dirac point generates a dominant next-nearest-neighbor-d pairing symmetry driven by on-site Coulomb interaction U. However, when considering the nearest-neighbor interaction V, it may induce nearest-neighbor-p pairing to become the preferred pairing symmetry. Our results provide useful information to identify the dominant superconducting pairing symmetry in the AV3Sb5 family.

Normal and Superconducting Properties of La3Ni2O7

Abstract This review provides a comprehensive overview of current research on the structural, electronic, and magnetic characteristics of the recently discovered high-temperature superconductor La3Ni2O7 under high pressures. We present the experimental results for synthesizing and characterizing this material, derived from measurements of transport, thermodynamics, and various spectroscopic techniques, and discuss their physical implications. We also explore theoretical models proposed to describe the electronic structures and superconducting pairing symmetry in La3Ni2O7, highlighting the intricate interplay between electronic correlations and magnetic interactions. Despite these advances, challenges remain in growing high-quality samples free of extrinsic phases and oxygen deficiencies and in developing reliable measurement tools for determining diamagnetism and other physical quantities under high pressures. Further investigations in these areas are essential to deepening our understanding of the physical properties of La3Ni2O7 and unlocking its superconducting pairing mechanism.

Magnetic fluctuations and dominant superconducting pairing symmetry near the tunable Van Hove singularity

Magnetic fluctuations and dominant superconducting pairing symmetry near the tunable Van Hove singularity

Evidence for d-wave superconductivity of infinite-layer nickelates from low-energy electrodynamics.

The discovery of superconductivity in infinite-layer nickelates established another category of unconventional superconductors that shares structural and electronic similarities with cuprates. However, key issues of the superconducting pairing symmetry, gap amplitude and superconducting fluctuations are yet to be addressed. Here we utilize static and ultrafast terahertz spectroscopy to address these. We demonstrate that the equilibrium terahertz conductivity and non-equilibrium terahertz responses of an optimally Sr-doped nickelate film (superconducting transition temperature of Tc = 17 K) are in line with the electrodynamics of d-wave superconductivity in the dirty limit. The gap-to-Tc ratio (2Δ/kBTc) is found to be 3.4, indicating that the superconductivity falls in the weak coupling regime. In addition, we observed substantial superconducting fluctuations near Tc that do not extend into the deep normal state as the optimally hole-doped cuprates do. Our results support a d-wave system that closely resembles the electron-doped cuprates.

Investigation on Magnetotransport Properties and Specific Heat Capacity of FeTe0.58Se0.42 Single Crystals Grown by Self‐Flux Method

A comprehensive study of magnetotransport and field‐dependent specific heat of FeTe0.58Se0.42 single crystals synthesized using the self‐flux method is reported. The transport measurement reveals the presence of Fermi liquid behavior in the normal state resistivity of the single crystals. Furthermore, the grown single crystals exhibit anisotropy and demonstrate a high value of upper critical magnetic field (HC2). The magnetoresistance exhibits a linear behavior as the magnetic field increases, suggesting the possible presence of a Dirac‐cone state. Anisotropy is also observed in magnetoresistance near the superconducting transition temperature (TC). The sign reversal of the Hall coefficient and the violation of Kohler's rules are observed, which provide evidence of the presence of multiband effects in FeTe0.58Se0.42 single crystals. Specific heat measurements confirm the bulk superconductivity in the grown single crystals. Additionally, the specific heat jump is estimated, which is approximately equal to . The magnetic field‐dependent specific heat also suggests multiband superconductivity and offers insights into the upper critical field. Furthermore, the electronic specific heat is best fitted with a two‐band model. Moreover, the field‐dependent residual Sommerfeld coefficient gives information about the superconducting pairing symmetry.

Effects of carrier density and interactions on pairing symmetry in a t2g model

By utilizing the fluctuation exchange approximation method, we perform a study on the superconducting pairing symmetry in a t2g three-orbital model on the square lattice. Although the tight-binding parameters of the model are based on Sr2RuO4, we have systematically studied the evolution of superconducting pairing symmetry with the carrier density and interactions, making our findings relevant to a broader range of material systems. Under a moderate Hund’s coupling, we find that spin fluctuations dominate the superconducting pairing, leading to a prevalent spin-singlet pairing with a d x 2–y 2 -wave symmetry for the carrier density within the range of n = 1.5–4 per site. By reducing the Hund’s coupling, the charge fluctuations are enhanced and play a crucial role in determining the pairing symmetry, leading to a transition of the pairing symmetry from the spin-singlet d x 2–y 2 -wave to the spin-triplet p-wave. Furthermore, we find that the superconducting pairings are orbital dependent. As the carrier density changes from n = 4 to n = 1.5, the active orbitals for superconducting pairing shift from the quasi-two-dimensional orbital d xy to the quasi-one-dimensional orbitals d xz and d yz .

Rotational symmetry breaking in superconducting nickelate Nd0.8Sr0.2NiO2 films

The infinite-layer nickelates, isostructural to the high-Tc cuprate superconductors, have emerged as a promising platform to host unconventional superconductivity and stimulated growing interest in the condensed matter community. Despite considerable attention, the superconducting pairing symmetry of the nickelate superconductors, the fundamental characteristic of a superconducting state, is still under debate. Moreover, the strong electronic correlation in the nickelates may give rise to a rich phase diagram, where the underlying interplay between the superconductivity and other emerging quantum states with broken symmetry is awaiting exploration. Here, we study the angular dependence of the transport properties of the infinite-layer nickelate Nd0.8Sr0.2NiO2 superconducting films with Corbino-disk configuration. The azimuthal angular dependence of the magnetoresistance (R(φ)) manifests the rotational symmetry breaking from isotropy to four-fold (C4) anisotropy with increasing magnetic field, revealing a symmetry-breaking phase transition. Approaching the low-temperature and large-magnetic-field regime, an additional two-fold (C2) symmetric component in the R(φ) curves and an anomalous upturn of the temperature-dependent critical field are observed simultaneously, suggesting the emergence of an exotic electronic phase. Our work uncovers the evolution of the quantum states with different rotational symmetries in nickelate superconductors and provides deep insight into their global phase diagram.

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.

Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities.

Recent studies have attracted intense attention on the quasi-2D kagome superconductors AV_{3}Sb_{5} (A=K, Rb, and Cs) where the unexpected chiral flux phase (CFP) associates with the spontaneous time-reversal symmetry breaking in charge density wave states. Here, commencing from the 2-by-2 charge density wave phases, we bridge the gap between topological superconductivity and time-reversal asymmetric CFP in kagome systems. Several chiral topological superconductor (TSC) states featuring distinct Chern numbers emerge for an s-wave or a d-wave superconducting pairing symmetry. Importantly, these CFP-based TSC phases possess unique gapless edge modes with mixed chiralities (i.e., both positive and negative chiralities), but with the net chiralities consistent with the Bogoliubov-de Gennes Chern numbers. We further study the transport properties of a two-terminal junction, using Chern insulator or normal metal leads via atomic Green's function method with Landauer-Büttiker formalism. In both cases, the normal electron tunneling and the crossed Andreev reflection oscillate as the chemical potential changes, but together contribute to plateau transmissions (1 and 3/2, respectively) that exhibit robustness against disorder. These behaviors can be regarded as the signature of a TSC hosting edge states with mixed chiralities.

Fractional magnetoresistance oscillations in spin-triplet superconducting rings

Half-quantum vortices in spin-triplet superconductors are predicted to host Majorana zero modes and may provide a viable platform for topological quantum computation. Recent works also suggested that, in thin mesoscopic rings, the superconducting pairing symmetry can be probed via Little-Parks-like magnetoresistance oscillations of periodicity Φ0 = h/2e that persist below the critical temperature. Here we use the London limit of Ginzburg-Landau theory to study these magnetoresistance oscillations resulting from thermal vortex tunneling in spin-triplet superconducting rings. For a range of temperatures in the presence of disorder, we find magnetoresistance oscillations with an emergent fractional periodicity Φ0/n, where the integer n ≥ 3 is entirely determined by the ratio of the spin and charge superfluid densities. These fractional oscillations can unambiguously confirm the spin-triplet nature of superconductivity and directly reveal the tunneling of half-quantum vortices in real-world candidate materials.

Single magnetic impurity effects in graphene based superconductors

The magnetic impurity effects and the existence of bound states (i.e. Yu-Shiba-Rusinov states) in superconductors have been a topic of great interest. Recently, the existence of Yu-Shiba-Rusinov states in graphene-based superconducting materials has been successfully observed in the laboratory. In this work, an effective Hamiltonian in real space is established to describe the superconducting state of graphene materials by considering a single magnetic impurity. Thus the Bogoliubov-de Gennes (BdG) equation is constructed and the self-consistency calculations of the superconducting order parameter are conducted. On this basis, the effects of magnetic impurities on graphene-like superconductors are investigated theoretically. The numerical results show that the Yu-Shiba-Rusinov state can only appear in the symmetry of the superconducting pair of the traditional <i>s</i>-wave coupling. The position and strength of the bound state are related to the magnetic moment of the impurity, showing a notable electron-hole asymmetry. There are no bound states in the energy gap for other pairing symmetries. This theoretical calculation not only provides a reasonable explanation for experimental phenomena, but also demonstrates that the heterojunction system composed of graphene and traditional superconductors has an <i>s</i>-wave superconducting pairing induced by the proximity effect in the graphene layer.

Superconductivity and density-wave fluctuations in an extended triangular Hubbard model: an application to SnSe2

We employ the fluctuation-exchange approximation to study the relation of superconducting pairing symmetries and density-wave fluctuations based on the extended triangular Hubbard model upon electron doping and interactions, with an possible application to the layered metal dichalcogenide SnSe2. For the case where the interactions between electrons contain only the on-site Hubbard term, the superconducting pairings are mainly mediated by spin fluctuations, and the spin-singlet pairing with the d-wave symmetry robustly dominates in the low and moderate doping levels, and a d-wave to extended s-wave transition is observed as the electron doping reaches n = 1. When the near-neighbor site Coulomb interactions are also included, the charge fluctuations are enhanced, and the spin-triplet pairings with the p-wave and f-wave symmetries can be realized in the high and low doping levels, respectively.

Identifying topological superconductivity in two-dimensional transition-metal dichalcogenides

We study the superconducting pairing instabilities and gap functions for prototypical two-dimensional (2D) transition-metal dichalcogenides (TMDCs) WS$_2$, MoTe$_2$, and MoS$_2$ in the 2H phase under both hole and electron doping at 10 K. Our first-principles quantum many-body Green's function approach allows us to treat the full $d$ and $p$ manifold of orbitals with strong spin-orbit coupling, yielding pairing predictions with material specific detail. The resulting gap functions exhibit a variety of mixed-parity superconducting states, including $s$, $p$, $d$, $f$, $d\pm id$, and $p\pm ip$ pairing modes. In particular, we predict 3% and 4% hole-doped WS$_2$ to be a chiral $p\pm ip$ topological superconductor. For 1% hole-doped MoS$_2$, we find a competition between three doubly degenerate chiral and non-chiral instabilities. Overall, the relative pairing strengths are found to follow the Fermi surface topology, due to nesting between the Fermi surface sheets. Finally, we discuss our predictions in relation to available experimental data and classify the topology of the predicted superconducting pairing symmetries.

Multipole-fluctuation pairing mechanism of dx2−y2 + ig superconductivity in Sr2RuO4

Despite of many experimental and theoretical efforts, the pairing symmetry of superconductivity in Sr$_2$RuO$_4$ remains undecided. The accidentally degenerate $d_{x^2-y^2}+ig$ is consistent with most current experiments and seems to be one of the most probable candidates, but we still lack a satisfactory theoretical mechanism for its appearance. Here we construct a phenomenological model combining realistic electronic band structures and all symmetry-allowed multipole fluctuations as potential pairing glues, and make a systematic survey of major pairing states within the Eliashberg framework. Our calculations show that $d_{x^2-y^2}+ig$ can arise naturally from the interplay of antiferromagnetic, ferromagnetic, and electric multipole fluctuations whose coexistence is manifested in previous experiments and calculations. Our work provides a physically reasonable basis supporting the possibility of $d_{x^2-y^2}+ig$ pairing in superconducting Sr$_2$RuO$_4$.

Testing superconducting pairing symmetry in multiterminal junctions

An approach to distinguish p-wave from s-wave superconducting pairing symmetry and thus to select potential platforms for Majorana fermions is proposed in terms of electronic transport differences in a four terminal junction consisting of superconducting (S) and normal (N) terminals in the diffusive regime. The Keldysh Green’s function equations are derived in the θ-parametrisation, incorporating terms previously neglected in the literature. A stable procedure to solve these equations is presented. The supercurrent and differential conductance between two superconducting electrodes were calculated in the Keldysh–Usadel approximation. The N-terminals can be used to manipulate the energy distribution functions of electrons in the junction in order to control the overall charge transport. Our results provide a new experimental test to detect potential p-wave superconductivity. In fact, we show that the differential conductance of junctions containing p-wave superconductors is distinctly different from the differential conductance in junctions with s-wave superconductors, whereas the supercurrent through the junction is qualitatively similar. This is of importance for the search for Majorana fermions since it may help to design experiments to detect signatures of p-wave symmetry, which may lead to potential platforms for Majorana fermions.

Superconducting pairing symmetry in the kagome-lattice Hubbard model

The dominating superconducting pairing symmetry of the kagome-lattice Hubbard model is investigated using the determinant quantum Monte Carlo method. The superconducting instability occurs when doping the correlated insulators formed by the Hubbard interaction near the Dirac filling, and the superconducting state exhibits an electron-hole asymmetry. Among the pairing symmetries allowed, we demonstrate that the dominating channel is d-wave in the hole-doped case. This opens the possibility of condensation into an unconventional $d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer topological invariant and gapless edge states. In contrast, the $s^*$-wave channel, which has no change of sign in the pairing function, is favored by electron doping. We further find the dominating $s^*$-wave pairing persists up to the Van Hove singularity. The results are closely related to the recent experimental observations in kagome compounds AV3Sb5(A: K, Rb, Cs), and provide insight into the pairing mechanism of their superconducting states.

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

Dispersion of neutron spin resonance mode in Ba0.67K0.33Fe2As2 * *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0704200, 2018YFA0305602, 2017YFA0303100, and 2017YFA0302900), the National Natural Science Foundation of China (Grant Nos. 11822411 and 11961160699), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (CAS) (Grant Nos. XDB25000000 and XDB07020300), K.C.Wong Education

We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba0.67K0.33Fe2As2 with Tc= 38.2 K. Although the resonance is nearly two-dimensional with peak energy E R ≈ 14 meV, it splits into two incommensurate peaks along the longitudinal direction ([H,0,0]) and shows an upward dispersion persisting to 26 meV. Such dispersion breaks through the limit of total superconducting gaps Δ tot = |Δk | + |Δ k+Q | (about 11–17 meV) on nested Fermi surfaces measured by high resolution angle resolved photoemission spectroscopy (ARPES). These results cannot be fully understood by the magnetic exciton scenario under s±-pairing symmetry of superconductivity, and suggest that the spin resonance may not be restricted by the superconducting gaps in the multi-band systems.

Local magnetism induced by non-magnetic impurities in FeSe in proximity to s-wave superconductivity

The response of non-magnetic impurities to superconductivity is useful to characterize the superconducting pairing symmetry. The s-wave superconductivity is not affected by the presence of non-magnetic impurities. However, the unconventional superconductivity responds to the non-magnetic impurities, inducing in-gap states in the superconducting gap. However, this characterization fails if non-magnetic impurities could induce magnetic moments in superconductors. Here, we used scanning tunneling microscopy/spectroscopy to elucidate if non-magnetic impurities are irrelevant to magnetism in FeSe. To study this, we have grown FeSe films on the Pb(111) substrate. We find that the FeSe films are proximity-induced s-wave superconductors. By investigating various non-magnetic impurities and native defects of FeSe, we explicitly show that these impurities and defects can directly induce local magnetism in FeSe.

Lattice distortion induced first- and second-order topological phase transition in a rectangular high- Tc superconducting monolayer

We theoretically study the lattice distortion induced first and second order topological phase transition in rectangular FeSe$_{x}$Te$_{1-x}$ monolayer. When compressing the lattice constant in one direction, our first principles calculation shows that the FeSe$_x$Te$_{1-x}$ undergoes a band inversion at $\Gamma$ point in a wide dopping range, say $x\in(0.0,0.7)$, which ensures coexistence of the topological band state and the high-T$_{\rm c}$ superconductivity. This unidirectional pressure also leads to the C$_4$ symmetry breaking which is necessary for the monolayer FeSe$_x$Te$_{1-x}$ to support Majorana corner states in the either presence or absence of time-reversal symmetry. Particularly, we use $k\cdot p$ methods to fit the band structure from the first principles calculation and found that the edge states along the $(100)$ and $(010)$ directions have different Dirac energy due to C$_4$ symmetry breaking. This is essential to obtain Majorana corner states in D class without concerning the details of the superconducting pairing symmetries and Zeeman form, which can potentially bring advantages in the experimental implementation.