S-wave Pairing Symmetry Research Articles

Cyclic superconducting refrigerators using guided fluxon propagation

We propose cyclic refrigeration in solid state, employing a gas of magnetic field vortices in a type-II superconductor—also known as fluxons—as the cooling agent. Refrigeration cycles are realized by envisioning a racetrack geometry consisting of both adiabatic and isothermal arms, etched into a type-II superconductor. The guided propagation of fluxons in the racetrack is achieved by applying an external electrical current, in a Corbino geometry, through the sample. A gradient of magnetic field is set across the racetrack allowing one to adiabatically cool down and heat up the fluxons, which subsequently exchange heat with the cold and hot reservoirs, respectively. We characterize the steady state of refrigeration cycles thermodynamically for both s-wave and d-wave pairing symmetries, and present their figures of merit such as the cooling power delivered, and the coefficient of performance. Our cooling principle can offer significant cooling for on-chip microrefrigeration purposes, by locally cooling below the base temperatures achievable in a conventional dilution refrigerator. We estimate nW/mm2 of cooling power per unit area assuming a tunnel coupling with ∼MΩµm2 specific resistance. Integrating the fluxon fridge to quantum circuits can enhance their coherence time by locally suppressing thermal fluctuations, and improve the efficiency of single photon detectors and charge sensors. Published by the American Physical Society 2024

Identifying s-wave pairing symmetry in single-layer FeSe from topologically trivial edge states

Determining the pairing symmetry of single-layer FeSe on SrTiO3 is the key to understanding the enhanced pairing mechanism. It also guides the search for superconductors with high transition temperatures. Despite considerable efforts, it remains controversial whether the symmetry is the sign-preserving s- or the sign-changing s±-wave. Here, we investigate the pairing symmetry of single-layer FeSe from a topological point of view. Using low-temperature scanning tunneling microscopy/spectroscopy, we systematically characterize the superconducting states at edges and corners of single-layer FeSe. The tunneling spectra collected at edges and corners show a full energy gap and a substantial dip, respectively, suggesting the absence of topologically non-trivial edge and corner modes. According to our theoretical calculations, these spectroscopic features can be considered as strong evidence for the sign-preserving s-wave pairing in single-layer FeSe.

Density of states in antiferromagnetic nanowire superconductors

The coexistence of different order parameters and the pairing symmetry is the major issue in the study of one dimensional wires. We adopt a tight-binding model, for the coexistence of superconductivity and antiferromagnetism in s-wave pairing symmetry, which is consistent and most favourable for the nearest-neighbour pairing interaction, and derive a set of gap equations which are solved numerically and self-consistently. The effects of the order parameters on one another are studied. We have also calculated the density of states and band energies. The density of states shows the defined interference peaks on either side of the Fermi level corresponding to the order parameters with van Hove singularities.

Spectroscopic evidence of mixed angular momentum symmetry in non-centrosymmetric Ru_7B_3

Superconducting crystals with a lack of inversion symmetry can potentially host unconventional pairing. However, till today, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both s-wave (singlet) and p-wave (triplet) pairing symmetries in non-centrosymmetric Ru_7B_3. Our temperature and magnetic field-dependent studies also indicate that the relative amplitudes of the singlet and triplet components change differently with temperature.

Impurity effect on order modulations in superconducting systems with mixed singlet-triplet pairing

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the effect induced by nonmagnetic impurities in bulk superconducting systems with mixed singlet-triplet pairing by numerically solving the Bogoliubov-de Gennes equations. For the emergent spin-triplet p-wave as well as coexisted spin-singlet s-wave and d-wave pairing symmetries, the order-parameter patterns for the quantized vortex states with point-like cores can be effectively tuned by the located sites of nonmagnetic impurities. The next-nearest-neighbor hopping effect on the evolution of vortex configurations is also discussed in the presence of vortex pinning by the impurity. Besides the unconventional vortex lattice, several types of topological defects, including the unclosed domain walls and enclosed skyrmionic modes, can be obtained when the impurity position is varied. All these configurations can be resolved by the zero-energy peaks in the local density of states.

Vortical patterns in bulk superconducting systems with mixed pairing orders

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the spatial configurations of mixed spin-triplet (dominant p-wave) and spin-singlet (coexisted s-wave and d-wave) pairing symmetries in bulk superconducting systems by numerically solving the Bogoliubov–de Gennes equations. The influences of the Zeeman field and the next-nearest-neighbor hopping on the order-parameter modulations are mainly discussed. Besides the quantized vortex states with point-like cores, the unclosed vortex chains and enclosed skyrmionic modes can remain stable in the present bulk sample. Furthermore, nonuniform patterns of the vortex lattice and the elliptical-like vortices can be obtained at appropriate applied flux. The corresponding zero-energy local density of states as well as the relative phase differences useful to display the skyrmionic texture are provided

Impurity effect as a probe for the pairing symmetry of graphene-based superconductors

We study theoretically the single impurity effect on graphene-based superconductors. Four different pairing symmetries are discussed. Sharp in-gap resonant peaks are found near the impurity site for the d + id pairing symmetry and the p + ip pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the d + id pairing symmetry while they disappear for the p + ip pairing symmetry. Such in-gap peaks are absent for the fully gapped extended s-wave pairing symmetry and the nodal f-wave pairing symmetry. The existence of the ingap resonant peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the T-matrix. All of the features may be checked by the experiments, providing a useful probe for the pairing symmetry of graphene-based superconductors.

Probing physical properties and superconductivity of noncentrosymmetric superconductors LaPtGe and LaPtGe3: A first-principles study

In this study, both scalar and full-relativistic ab initio pseudopotential calculations have been actualized on the physical and superconducting properties of noncentrosymmetric superconductors LaPtGe and LaPtGe3 in order to discern the effect of spin-orbit coupling. The spin-orbit coupling makes slightly more effect on the physical properties of LaPtGe than those of LaPtGe3 since the near-Fermi band structure of the former is dominated by d shell electrons rather than p shell electrons as observed in the latter. For both compounds, the splitting into sub-bands arising from the antisymmetric spin-orbit effect remains small around the Fermi level. The phonon spectrum and Eliashberg spectral function of LaPtGe are weakly affected by the inclusion of spin-orbit coupling, while this coupling makes almost no effect on them for LaPtGe3. Therefore, we can conclude that superconductivity in both noncentrosymmetric superconductors has s-wave pairing symmetry and its mechanism arises from the electron-phonon interaction in the medium coupling limit for LaPtGe and the weak-coupling limit for LaPtGe3.

Novel attractive pairing interaction in strongly correlated superconductors

Conventional and unconventional superconductivity, respectively, arise from attractive (electron-phonon) and repulsive (many-body Coulomb) interactions with fixed-sign and sign-reversal pairing symmetries. Although heavy-fermions, cuprates, and pnictides are widely believed to be unconventional superconductors, recent evidence in one of the heavy fermion superconductor (CeCu_22Si_22) indicate the presence of a novel conventional type pairing symmetry beyond the electron-phonon coupling. We present a new mechanism of attractive potential between electrons, mediated by emergent boson fields (vacuum or holon) in the strongly correlated mixed valence compounds. In the strong coupling limit, localized electron sites are protected from double occupancy, which results in an emergent holon fields. The holon states can, however, attract conduction electrons through valence fluctuation channel, and the resulting doubly occupied states with local and conduction electrons condenseas Cooper pairs with onsite, fixed-sign, s-wave pairing symmetry. We develop the corresponding self-consistent theory of superconductivity, and compare the results with experiments. Our theory provides a new mechanism of superconductivity whose applicability extends to the wider class of intermetallic/mixed-valence materials and other flat-band metals.

Nodeless High-T_{c} Superconductivity in the Highly Overdoped CuO_{2} Monolayer.

We study the electronic structure and superconductivity in a CuO_{2} monolayer grown recently on the d-wave cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Density functional theory calculations indicate a significant charge transfer across the interface such that the CuO_{2} monolayer is heavily overdoped into the hole-rich regime yet inaccessible in bulk cuprates. We show that both the Cu d_{x^{2}-y^{2}} and d_{3z^{2}-r^{2}} orbitals become important and the Fermi surface contains one electron and one hole pocket associated with the two orbitals, respectively. Constructing a minimal correlated two-orbital model for the e_{g} complex, we show that the spin-orbital exchange interactions produce a nodeless superconductor with extended s-wave pairing symmetry and a pairing energy gap comparable to the bulk d-wave gap, in agreement with recent experiments. The findings point to a direction of realizing new high-T_{c} superconductors in ozone grown transition-metal-oxide monolayer heterostructures.

A single full gap in noncentrosymmetric superconductor Re6Hf by point-contact spectroscopy

We report a point-contact spectroscopy study on the noncentrosymmetric superconductor Re6Hf with a superconducting transition temperature Tc ∼ 6.0 K. The point-contact conductance spectra can be well fitted by an s-wave Blonder-Tinkham-Klapwijk (BTK) model, where the superconducting gap follows a standard BCS behavior as a function of temperature or magnetic field. The gap at 0 K is estimated to be Δ0 ∼ 0.92 meV, yielding 2Δ0/kBTc ∼ 3.56. Hence, our results are consistent with a fully gaped s-wave pairing symmetry with a negligible spin-triplet superconducting component in Re6Hf.

A possible family of Ni-based high temperature superconductors

We suggest that a family of Ni-based compounds, which contain [Ni2M2O]2− (M = chalcogen) layers with an antiperovskite structure constructed by mixed-anion Ni complexes, NiM4O2, can be potential high temperature superconductors (high-Tc) upon doping or applying pressure. The layer structures have been formed in many other transitional metal compounds such as La2B2Se2O3 (B = Mn, Fe, Co). For the Ni-based compounds, we predict that the parental compounds host collinear antiferromagnetic states similar to those in iron-based high temperature superconductors. The electronic physics near Fermi energy is controlled by two egd-orbitals with completely independent in-plane kinematics. We predict that the superconductivity in this family is characterized by strong competition between extended s-wave and d-wave pairing symmetries.

Dirty two-band superconductivity with interband pairing order

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature Tc in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. Because of the two-band degree of freedom, it is possible to define a spin-triplet s-wave pairing order parameter as well as a spin-singlet s-wave order parameter. The former belongs to odd-band-parity symmetry class, whereas the latter belongs to even-band-parity symmetry class. In a spin-singlet superconductor, Tc is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, Tc decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.

Probing the superconducting ground state of the rare-earth ternary boride superconductors RRuB2 ( R= Lu,Y) using muon-spin rotation and relaxation

The superconductivity in the rare-earth transition metal ternary borides $R$RuB$_2$ (where $R$ = Lu and Y) has been investigated using muon-spin rotation and relaxation. Measurements made in zero-field suggest that time-reversal symmetry is preserved upon entering the superconducting state in both materials; a small difference in depolarization is observed above and below the superconducting transition in both compounds, however this has been attributed to quasistatic magnetic fluctuations. Transverse-field measurements of the flux-line lattice indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. The electronic properties of the charge carriers in the superconducting state have been calculated, with effective masses $m^*/ m_\mathrm{e} = $ $9.8\pm0.1$ and $15.0\pm0.1$ in the Lu and Y compounds, respectively, with superconducting carrier densities $n_\mathrm{s} = $ ($2.73\pm0.04$) $\times 10^{28}$ m$^{-3}$ and ($2.17\pm0.02$) $\times 10^{28}$ m$^{-3}$. The materials have been classified according to the Uemura scheme for superconductivity, with values for $T_\mathrm{c}/T_\mathrm{F}$ of $1/(414\pm6)$ and $1/(304\pm3)$, implying that the superconductivity may not be entirely conventional in nature.

Multiple odd-frequency superconducting states in buckled quantum spin Hall insulators with time-reversal symmetry

We consider a buckled quantum spin Hall insulator (QSHI), such as silicene, proximity-coupled to a conventional spin-singlet, s-wave superconductor. Even limiting the discussion to the disorder-robust s-wave pairing symmetry, we find both odd-frequency ($\omega$), spin-singlet and spin-triplet pair amplitudes and where both preserve time-reversal symmetry. Our results show that there are two unrelated mechanisms generating these different odd-$\omega$ pair amplitudes. The spin-singlet state is due to the strong inter-orbital processes present in the QSHI. It is exists generically at the edges of the QSHI, but also in the bulk in heavily doped regime if an electric field is applied. The spin-triplet state requires a finite gradient in the proximity-induced superconducting order along the edge, which we find is automatically generated at the atomic scale for armchair edges but not at zigzag edges. In combination these results make superconducting QSHIs a very exciting venue for investigating not only the existence of odd-$\omega$ superconductivity, but also the interplay between different odd-$\omega$ states.

Quantum gas microscopy of an attractive Fermi–Hubbard system

The attractive Fermi-Hubbard model is the simplest theoretical model for studying pairing and superconductivity of fermions on a lattice. Although its s-wave pairing symmetry excludes it as a microscopic model for high-temperature superconductivity, it exhibits much of the relevant phenomenology, including a short-coherence length at intermediate coupling and a pseudogap regime with anomalous properties. Here we study an experimental realization of this model using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Our site-resolved measurements on the normal state reveal checkerboard charge-density-wave correlations close to half-filling. A "hidden" SU(2) pseudo-spin symmetry of the Hubbard model at half-filling guarantees superfluid correlations in our system, the first evidence for such correlations in a single-band Hubbard system of ultracold fermions. Compared to the paired atom fraction, we find the charge-density-wave correlations to be a much more sensitive thermometer, useful for optimizing cooling into superfluid phases in future experiments.

Robustness of s-wave pairing symmetry in iron-based superconductors and its implications for fundamentals of magnetically driven high-temperature superconductivity

Based on the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we propose that the pairing symmetry in all measured iron-based superconductors is generally consistent with the A1g s-wave. Robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high-Tc superconducting mechanisms: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-Tc superconductivity and determine pairing symmetries; (ii) the magnetic-selection pairing rule: superconductivity is only induced by the magnetic-exchange couplings from the super-exchange mechanism through cation-anion-cation chemical bonding. These principles explain why unconventional high-Tc superconductivity appears to be such a rare but robust phenomena, with its strict requirements regarding the electronic environment. The results will help us to identify new electronic structures that can support high-Tc superconductivity.

Identifying the genes of unconventional high temperature superconductors

We elucidate a recently emergent framework in unifying the two families of high temperature (high Tc) superconductors, cuprates and iron-based superconductors. The unification suggests that the latter is simply the counterpart of the former to realize robust extended s-wave pairing symmetries in a square lattice. The unification identifies that the key ingredients (gene) of high Tc superconductors is a quasi two dimensional electronic environment in which the d-orbitals of cations that participate in strong in-plane couplings to the p-orbitals of anions are isolated near Fermi energy. With this gene, the superexchange magnetic interactions mediated by anions could maximize their contributions to superconductivity. Creating the gene requires special arrangements between local electronic structures and crystal lattice structures. The speciality explains why high Tc superconductors are so rare. An explicit prediction is made to realize high Tc superconductivity in Co/Ni-based materials with a quasi two dimensional hexagonal lattice structure formed by trigonal bipyramidal complexes.

Relationship between pairing symmetries and interaction parameters in iron-based superconductors from functional renormalization group calculations

Pairing symmetries of iron-based superconductors are investigated systematically in a five-orbital model within the different regions of interaction parameters by functional renormalization group (FRG). Even for a fixed Fermi surface with both hole and electron pockets, it is found that depending on interaction parameters, a variety of pairing symmetries, including two types of d-wave and two types of s-wave pairing symmetries, can emerge. Only the - and the s±-waves are robustly supported by the nearest-neighbor (NN) intra-orbital J1 and the next-nearest-neighbor (NNN) intra-orbital J2 antiferromagnetic (AFM) exchange couplings, respectively. This study suggests that the accurate initial input of the interaction parameters is essential to make FRG a useful method to determine the leading channel of superconducting instability.

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

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