D-wave Pairing State Research Articles

Multiorbital singlet pairing and d\u2009+\u2009d superconductivity

Recent experiments in multiband Fe-based and heavy-fermion superconductors have challenged the long-held dichotomy between simple s- and d-wave spin-singlet pairing states. Here, we advance several time-reversal-invariant irreducible pairings that go beyond the standard singlet functions through a matrix structure in the band/orbital space, and elucidate their naturalness in multiband systems. We consider the sτ3 multiorbital superconducting state for Fe-chalcogenide superconductors. This state, corresponding to a d + d intra- and inter-band pairing, is shown to contrast with the more familiar d + id state in a way analogous to how the B- triplet pairing phase of 3He superfluid differs from its A- phase counterpart. In addition, we construct an analog of the sτ3 pairing for the heavy-fermion superconductor CeCu2Si2, using degrees-of-freedom that incorporate spin-orbit coupling. Our results lead to the proposition that d-wave superconductors in correlated multiband systems will generically have a fully-gapped Fermi surface when they are examined at sufficiently low energies.

Flux-dependent evolution of mixed pairing orders in mesoscopic superconducting square loops

Based on a model Hamiltonian including the on-site repulsive interaction among the electrons, we investigate the flux-dependent evolution of mixed pairing orders in mesoscopic superconducting square loops by numerically solving the Bogoliubov-de Gennes equations. The influence of centered hole size on the order modulation is mainly discussed. For the emergent spin-triplet p-wave and subdominant spin-singlet d-wave pairing states in the present loop system with an enlarged hole size, the order-parameter patterns always behave the diagonal symmetry. In addition, the obtained vortical and skyrmionic configurations inside the sample along one of diagonal directions can be effectively tuned by the chosen chemical potential and the next-nearest-neighbor hopping effect.

Insulator-to-superconductor transition by exciting half-filled d-wave pairing state beyond Mott gap

In connection with recent tera-Hertz photoexcitation experiments in which strongly correlated materials are changed from Mott-insulating to metallic, we statically study the properties of excited states beyond the Mott gap in the -wave superconducting (d-SC) branch at half filling, by applying a variational Monte Carlo method to a two-dimensional Hubbard model. It is found that the first-order Mott transition previously found at U = U c for the lowest-energy state vanishes for the excited states. As a result, an insulator-to-d-SC transition occurs as the strength of excitation (corresponding to light intensity) is increased for U/t (> U c /t) fixed. As a mechanism, this conduction is led by newly created free carriers (unbound doublons and holons) in the excited states.

Quasiparticle interference and symmetry of superconducting order parameter in strongly electron-doped iron-based superconductors

Motivated by recent experimental reports of significant spin–orbit coupling (SOC) and a sign-changing order-parameter in the Li1−xFex(OHFe)1−yZnySe superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states—s-wave, d-wave and helical p-wave—can have a fully gapped density of states consistent with angle-resolved photoemission spectroscopy experiments and, due to SOC, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity A1g (s-wave) and B2g (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

Strange superconductivity near an antiferromagnetic heavy-fermion quantum critical point

The heavy fermion CeMIn5 family with M = Co, Rh, Ir provide a prototypical example of strange superconductors with unconventional d-wave pairing and strange metal normal state, emerged near an antiferromagnetic quantum critical point. The microscopic origin of strange superconductor and its link to antiferromagnetic quantum criticality and strange metal state are still open issues. We propose a microscopic mechanism for strange superconductor, based on the coexistence and competition between the Kondo correlation and the quasi-2d short-ranged antiferromagnetic resonating-valence-bond spin-liquid near the antiferromagnetic quantum critical point via a large-N Kondo-Heisenberg model and renormalization group analysis beyond the mean-field level. We find the coexistence (competition) between the two types of correlations well explains the overall features of superconducting and strange metal state. The interplay of these two effects provides a qualitative understanding on how superconductivity emerges from the SM state and the observed superconducting phase diagrams for CeMIn5 near the anti-ferromagnetic quantum critical point.

Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states

We report a theoretical study on the phase transition between superconducting states with and without spontaneous surface current. The phase transition takes place due to the formation of surface Andreev bound states in unconventional superconductors. Based on the quasiclassical theory of superconductivity, we examine the influence of atomic-scale surface roughness on the surface phase transition temperature $T_s$. To describe the surface effect, the boundary condition for the quasiclassical Green's function is parameterized in terms of specularity (the specular reflection probability in the normal state at the Fermi level). This boundary condition allows systematic study of the surface effect ranging from the specular limit to the diffuse limit. We show that diffuse quasiparticle scattering at a rough surface causes substantial reduction of $T_s$ in the d-wave pairing state of high-$T_c$ cuprate superconductors. We also consider a p-wave pairing state in which Andreev bound states similar to those in the d-wave state are generated. In contrast to the d-wave case, $T_s$ in the p-wave state is insensitive to the specularity. This is because the Andreev bound states in the p-wave superconductor are robust against diffuse scattering, as implied from symmetry consideration for odd-frequency Cooper pairs induced at the surface; the p-wave state has odd-frequency pairs with s-wave symmetry, while the d-wave state does not.

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO2 grown on the Bi2Sr2CaCu2O8+δ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional model in proximity to an antiferromagnetic (AF) insulator. We found that i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity-induced AF field. ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a Z2 topological superconductor protected by valley symmetry, exhibiting robust gapless nonchiral edge modes. These findings strongly suggest that the high-Tc superconductors in proximity to antiferromagnets can realize fully gapped symmetry-protected topological SC.

Consistent picture of the octet-nodal gap and its evolution with doping in heavily overdoped Ba1−xKxFe2As2

We investigate the pairing symmetry in heavily overdoped Ba1−xKxFe2As2 based on the spin-fluctuation mechanism. We propose a Fermi-patch mechanism that is different from the conventional Fermi-surface-nesting picture. The exotic octet nodes of the superconducting gap and the unusual evolution of the gap with doping observed by the recent experiments are well explained in a unified manner. We demonstrate that the scattering of electrons on the Fermi patches is mainly responsible for the incommensurate spin fluctuations and consequently the Fermi-surface-dependent multi-gap structure, since the Fermi level is close to the flat band. In addition, we find that a d-wave pairing state will prevail over the s-wave pairing state around the Lifshitz transition point.

From d-wave to s-wave pairing in the iron-pnictide superconductor (Ba,K)Fe2As2

The nature of the pairing state in iron-based superconductors is the subject of much debate. Here we argue that in one material, the stoichiometric iron pnictide KFe2As2, there is overwhelming evidence for a d-wave pairing state, characterized by symmetry-imposed vertical line nodes in the superconducting gap. This evidence is reviewed, with a focus on thermal conductivity and the strong impact of impurity scattering on the critical temperature Tc. We then compare KFe2As2 to Ba0.6K0.4Fe2As2, obtained by Ba substitution, where the pairing symmetry is s-wave and the Tc is ten times higher. The transition from d-wave to s-wave within the same crystal structure provides a rare opportunity to investigate the connection between band structure and the pairing mechanism. We also compare KFe2As2 with the nodal iron-based superconductor LaFePO, for which the pairing symmetry is probably not d-wave, but more likely s-wave with accidental line nodes.

Effect of hole–phonon interaction on [formula omitted] superconducting phase in 2D t-J model with phonon mediated interaction

Ground-state properties of the 2D t-J model with phonon mediated interaction are examined by an exact diagonalization method, following the idea that a local lattice distortion occurs in association with hole upon doping. Effect of this phonon mediated interaction on d-wave pairing over the pure t-J model has been shown. Results show an influence of phonon mediated interaction on d-wave pairing state. Formation of a less mobile quasi-particle made of hole–polaron accompanied by a hole at nearest-neighbor site, eventually supports d-wave pairing. It is also shown that increase in coupling strength forms inter-site hole–bipolaron which gradually decrease d-wave pairing strength. Results show that role of phonons in the mechanism of high temperature superconductivity is very much relevant.

Existence of Majorana Fermions and Topological Order in Nodal Superconductors with Spin-Orbit Interactions in External Magnetic Fields

We demonstrate that Majorana fermions exist in edges of systems and in a vortex core even for superconductors with nodal excitations such as the d-wave pairing state under a particular but realistic condition in the case with an antisymmetric spin-orbit interaction and a nonzero magnetic field below the upper critical field. We clarify that the Majorana fermion state is topologically protected in spite of the presence of bulk gapless nodal excitations, because of the existence of a nontrivial topological number. Our finding drastically enlarges target systems where we can explore the Majorana fermion state.

Interplane penetration depth and coherent transport in organic superconductors

Measurements of the interlayer penetration depth {lambda}{sub {perpendicular}} have been performed on single crystals of the organic superconductors {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br and {kappa}-(ET){sub 2}Cu(NCS){sub 2}. We find that {lambda}{sub {perpendicular}}(0){approx}130 {micro}m for both materials. The normalized superfluid density {rho}{sub {perpendicular}} = [{lambda}{sub {perpendicular}}(0)/{lambda}{sub {perpendicular}} (T)]{sup 2} may be fit equally well to a power law 1{rho}{sub {perpendicular}} {approx} T{sup n} with n = 1.3-1.5 or to the form 1{rho}{sub {perpendicular}} = {alpha}(t{sup 2}/T{sub c})/(T+T*), consistent with a d-wave pairing state with impurity scattering. The data imply coherent transport between conducting planes, in agreement with recent magnetoresistive measurements [J. Singleton, P. A. Goddard, A. Ardavan, N. Harrison, S. J. Blundell, J. A. Schlueter, and A. M. Kini, Phys. Rev. Lett. 88, 037001 (2002)] and in contrast to the copper oxides.

A d-wave pairing state in terms of the Zhang–Rice singlets

In cuprate superconductors doping is believed to create holes on the O-sites, which couple antiferromagnetically with holes on the Cu-sites to form the so-called Zhang–Rice singlets. Here we study a d-wave pairing state based on the Zhang–Rice singlet states. Upper and lower bounds of an off-diagonal long-range order parameter with d-wave symmetry for this state are estimated. We also introduce a concrete model with on-site Coulomb repulsion and kinds of antiferromagnetic interactions whose ground state is this d-wave pairing state.

Magnetic excitations in La-based cuprate superconductors: Slave-boson mean-field analysis of the two-dimensionalt−Jmodel

Motivated by recent inelastic neutron scattering experiments up to a high-energy region for La-based cuprates, we compute (q,omega) maps of the imaginary part of the dynamical magnetic susceptibility chi(q,omega) in the slave-boson mean-field approximation to the two-dimensional t-J model. While the strong spectral weight appears at incommensurate positions, namely at q neq Q =(pi,pi), for low energy, the incommensurate signals disperse with increasing omega and finally merge into a commensurate signal at a particular energy omega=omega_Q. These features are seen in both the d-wave pairing state and the normal state. In particular, the incommensurate signals below omega_Q in the normal state are due to the Fermi surface geometry, which we expect for La-based cuprates because of a tendency to d-wave type Fermi surface deformations. Above omega_Q, strong signals appear to trace an upward dispersion especially for a low doping rate in the d-wave pairing state while typically broad spectral weight is obtained around q=Q in the normal state. Salient features of magnetic excitations in La-based cuprates are thus naturally captured in terms of particle-hole excitations. Global understanding of magnetic excitations in high-Tc cuprates is discussed through a comparison with magnetic excitations in YBa_2Cu_3O_y.

µSR Studies of Pu Metal and the Pu-based Superconductor PuCoGa5

We present recent measurements of the magnetic properties of Pu metal and the superconducting properties of PuCoGa 5 using the µSR technique. Our measurements set the most stringent upper limits to date on the magnitude of the ordered moments µ ord in α-Pu and δ-stabilized Pu (alloyed with 4.3 at. % Ga) in zero applied field: µ ord ≤10 -3 µ B at T \cong4 K. Measurements of the in-plane magnetic-field penetration depth λ( T ) in PuCoGa 5 ( T c =18.5 K) for 0.06 T applied field (≈2-5 × H c1 ) show that the temperature dependence of the superfluid density, and therefore Δλ( T )=λ( T )-λ(0), are ∝ T for T / T c ≤0.5. We estimate that λ(0)=241(3) nm. We also find no evidence for a time-reversal-symmetry violating superconducting order parameter. Taken together the measurements in PuCoGa 5 are, therefore, consistent with an even-parity (pseudo-spin singlet), d-wave pairing state.

Formula omitted] studies of the superconducting order parameter in [formula omitted

We present transverse-field (TF) measurements of the in-plane magnetic-field penetration depth λ ( T ) in single-crystalline PuCoGa 5 ( T c = 18.5 K ) for 0.06 T applied field ( ≈ 2 – 5 × H c 1 ) . We find that the temperature dependence of the superfluid density, and therefore Δ λ ( T ) = λ ( T ) - λ ( 0 ) , is ∝ T for T / T c ⩽ 0.5 . We estimate that the measured λ ( 0 ) = 241 ( 3 ) nm . ZF measurements find no evidence for time-reversal symmetry violation. The ZF and TF measurements are consistent with an even-parity (pseudo-spin singlet), d-wave pairing state.

Electron transport, penetration depth, and the upper critical magnetic field in ZrB12 and MgB2

We report on the synthesis and measurements of the temperature dependence of resistivity, R(T), the penetration depth, l(T), and upper critical magnetic field, Hc2(T), for polycrystalline samples of dodecaboride ZrB12 and diboride MgB2. We conclude that ZrB12 as well as MgB2 behave like simple metals in the normal state with usual Bloch-Gruneisen temperature dependence of resistivity and with rather low resistive Debye temperature, TR=280 K, for ZrB12 (as compared to MgB2 with TR=900 K). The R(T) and l(T) dependencies of ZrB12 reveal a superconducting transition at Tc=6.0 K. Although a clear exponential l(T)dependence in MgB2 thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB12 below Tc/2. These features indicate s-wave pairing state in MgB2, whereas a d-wave pairing state is possible in ZrB12. A fit to the data gives a reduced energy gap 2D(0)/kTc=1.6 for MgB2 films and pellets, in good agreement with published data for 3D \pi - sheets of the Fermi surface. Contrary to conventional theories we found a linear temperature dependence of Hc2(T) for ZrB12 (Hc2(0)=0.15 T).

Excitation Spectrum ofd-Wave Fermi Surface Deformation

Several instabilities competing with the d-wave singlet pairing were proposed for high-Tc cuprates. One of them is the d-wave Fermi surface deformation (dFSD), which is generated by forward scattering. In this Letter, correlation functions of the dFSD are calculated within the random phase approximation. In the normal state, the excitation spectrum shows a low energy peak, which smoothly connects to critical fluctuations of the dFSD at lower temperature. The competition with the d-wave pairing, however, blocks the critical fluctuations. The whole spectral weight is transferred to high energy and a pronounced peak appears there in the d-wave pairing state. This peak is an overdamped collective mode of the dFSD and can grow to become a resonance mode at moderate finite wave vectors.

Theory of Superconductivity in PuCoGa5

Recently, superconductivity in PuCoGa5 was discovered. It has the same crystal structure as CeMIn5(M=Ir, Co, Rh). The electron correlation in PuCoGa5 is estimated to be weak compared with CeMIn5, and the filling number of electrons is considered to be far from 0.5/spin in the band which plays an important role in realizing the superconductivity. Nevertheless, the superconducting transition temperature Tc in PuCoGa5 is almost by an order of magnitude higher than that in CeMIn5. In order to explain the superconductivity with high Tc, we adopt the periodic Anderson model and calculate Tc by solving the Dyson-Gor'kov equation derived by the third order perturbation theory with respect to U. By this calculation, we indicate that the superconducting state of PuCoGa5 is a d-wave pairing state, and show that the good location of two Fermi surfaces results in the high Tc in PuCoGa5.

Order parameter and current-phase relation in Josephson junctions composed ofg+s-wave superconductors

Based on the analyses of bulk sensitive experimental data on penetration depths, Raman spectra, electron photoemission spectra, etc., G. M. Zhao concluded in a recent paper [Phys. Rev. B 64, 024503 (2001)] that the symmetry of high-T c superconductors belongs to the g+s-wave type. To explore the common and uncommon features of the g+s-wave pairing state with respect to the d-wave pairing state, both superconductor-insulator-superconductor junction and superconductor-normal metal-superconductor junction have been studied self-consistently in this paper using the quasiclassical theory. The current phase relation for g+s-wave superconductors Δ(s,θ)=Δ 0 (s+cos4θ) is investigated systematically as functions of s-wave component, crystal orientation angle β, as well as roughness p of the interface layer. Our results show that there exists a critical β C for a given s and p so that the current phase relation approaches asymptotically to I(φ)=I C sin(2φ) from I(φ)=I C sin(φ) as β→β C . The order parameter and β C -s relation are calculated self-consistently as interface roughness varies. Our results are compared with their counterparts in Josephson junctions with the d-wave pairing state obtained using a similar method.