Nodal d + id pairing and topological phases on the triangular lattice of Na(x)CoO(2).yH(2)O: evidence for an unconventional superconducting state

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density x(c) where the normal state Fermi surface crosses the isolated zeros. For spin-singlet pairing, we show that the second-nearest-neighbor (d+id)-wave pairing can be the dominant pairing channel. The gapless critical state at x (c) approximately 0.25 has six Dirac points and is topologically nontrivial with a T3 spin relaxation rate below T(c). This picture provides a possible explanation for the unconventional superconducting state of Na(x)Co O(2). yH(2)O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.     

Effect of Fermi surface nesting on resonant spin excitations in Ba(1-x)K(x)Fe2As2

We report inelastic neutron scattering measurements of the resonant spin excitations in Ba(1-x)K(x)Fe(2)As(2) over a broad range of electron band filling. The fall in the superconducting transition temperature with hole doping coincides with the magnetic excitations splitting into two incommensurate peaks because of the growing mismatch in the hole and electron Fermi surface volumes, as confirmed by a tight-binding model with s(±)-symmetry pairing. The reduction in Fermi surface nesting is accompanied by a collapse of the resonance binding energy and its spectral weight, caused by the weakening of electron-electron correlations.     

Broad peak in the dx2-y2 superconducting correlation length as a function of hole concentration in the two-dimensional t-J model

We have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D t-J model with s, dx2-y2, and dxy symmetry pairs. Our calculations differ from previous work by removing disconnected pieces from the original four-point correlator and by treating the resulting pairing correlator as a matrix. We find the correlation length for dx2-y2 pairing grows significantly with decreasing temperature and develops a broad peak as a function of doping around delta=0.25 for T/J=0.25 at J/t=0.4. The correlation lengths for s and dxy symmetry remain small and do not display peaks. Antiferromagnetic spin correlations at low doping act to suppress the dx2-y2 and dxy superconducting correlation lengths.     

High-energy spin dynamics in La1.69Sr0.31NiO4

To test the prediction that the dispersion of the magnetic resonance in superconducting YBa2Cu3O(6+x) is similar to magnons in an incommensurate antiferromagnet, we have mapped out the spin dynamics in a stripe-ordered nickelate, La(2-x)SrxNiO4, with x approximately equal to 0.31, using inelastic neutron scattering. We observe spin-wave excitations up to 80 meV emerging from the incommensurate magnetic peaks with a surprisingly large and almost isotropic spin velocity: variant Planck's over 2 pi c(s) approximately 0.32 eV A. A comparison indicates that the inferred spin-excitation spectrum is not, by itself, an adequate model for the magnetic resonance feature of the superconductor.     

Phenomenological theory of the s-wave state in superconductors without an inversion center

In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairing states. Consequently, the superconducting order parameter is generally a mixture of spin singlet and triplet pairing states. In this paper we investigate the structure of the order parameter and its response to disorder for the most symmetric pairing state (A₁). Using the example of the heavy Fermion superconductor CePt₃Si, we determine characteristic properties of the superconducting instability. Depending on the type of the pairing interaction, the gap function is characterized by the presence of line nodes. We show that this line nodes move in general upon temperature. Such nodes would be essential to explain recent low-temperature data of thermodynamic quantities such as the NMR-T₁ ^-1, London penetration depth, and heat conductance. Moreover, we study the effect of (non-magnetic) impurity on the superconducting state.     

Dispersion of neutron spin resonance mode in Ba0.67K0.33Fe2As2

We report an inelastic neutron scattering investigation on the spin resonance mode in the optimally hole-doped iron-based superconductor Ba_0.67K_0.33Fe₂As₂ with T_c=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 ∆_tot=|∆_k|+|∆_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.     

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

We review the normal and superconducting state properties of the unconventional triplet superconductor Sr₂RuO₄ with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru d‐orbitals and a strong magnetic anisotropy occurs (χ^+‐ < χ^zz) due to spin‐orbit coupling. The latter results mainly from different values of the g‐factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation‐induced Cooper‐pairing scenario in application to Sr₂RuO₄ we show how p‐wave Cooper‐pairing with line nodes between neighboring RuO₂‐planes may occur. We also discuss the open issues in Sr₂RuO₄ like the influence of magnetic and non‐magnetic impurities on the superconducting and normal state of Sr₂RuO₄. It is clear that the physics of triplet superconductivity in Sr₂RuO₄ is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy‐fermion systems exhibiting spin fluctuations.     

Pairing symmetry in monolayer of orthorhombic CoSb

Ferromagnetism and superconductivity are generally considered to be antagonistic phenomena in condensed matter physics. Here, we theoretically study the interplay between the ferromagnetic and superconducting orders in a recent discovered monolayered CoSb superconductor with an orthorhombic symmetry and net magnetization, and demonstrate the pairing symmetry of CoSb as a candidate of non-unitary superconductor with time-reversal symmetry breaking. By performing the group theory analysis and the first-principles calculations, the superconducting order parameter is suggested to be a triplet pairing with the irreducible representation of ³B_2u, which displays intriguing nodal points and non-zero periodic modulation of Cooper pair spin polarization on the Fermi surface topologies. These findings not only provide a significant theoretical insight into the coexistence of superconductivity and ferromagnetism, but also reveal the exotic spin polarized Cooper pairing driven by ferromagnetic spin fluctuations in a triplet superconductor.     

Spin and charge pumping by ferromagnetic-superconductor order parameters

We study transport in ferromagnetic-superconductor/normal-metal systems. It is shown that charge and spin currents are pumped from ferromagnetic superconductors into adjacent normal metals by adiabatic changes in the order parameters induced by external electromagnetic fields. Spin and charge pumping identify the symmetry of the superconducting order parameter, e.g., singlet pairing or triplet pairing with opposite or equal spin pairing. Consequences for ferromagnetic-resonance experiments are discussed.     

HighT c superconductivity in the itinerant Ising model II. Spin triplet pairing

We study the spin triplet pairing superconducting states of the itinerant Ising model. The spin and spatial symmetries of the states are explored. We find that only a restricted set of spin symmetry states are allowed, while an infinite number of spatial symmetry states exist. The spin triplet pairing states can either be gapless or have finite energy gaps, but all spin triplet pairing states have the sameT _c .The free energies of spin triplet and spin singlet pairing states are calculated and compared.     

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.     

A Theory on the Mixture of Fermi-Liquid and Spin-Liquid

The delocalization of the doped holes in a CuO₂ sheet of the superconducting oxides is investigated. It leads to the formation of a mixture of Fermi-liquid and spin-liquid. The exchange interaction between them is proven to be weak and the Fermi-liquid feature of the itinerant holes is ensured. This exchange leads to the long-range RKKY interaction among the isolated spins embedded in the spin-liquid, and under certain condition can produce an incommensurate spin configuration. For the Fermi-liquid, the spin-flip part of this exchange provides a pairing mechanism of the singlet type in high frequency window. It is found that the Coulomb repulsion within a pair is suppressed by the pseudopotential effect in the unscreened case. The relation to other mechanisms which also produce the pairing in high frequency window is discussed. The possibility of co-appearance of superconductivity and incommensurate spin configuration is analyzed. Several critical doping concentrations are estimated.     

Incommensurate spin fluctuations in hole-overdoped superconductor KFe2As2

A neutron scattering study of heavily hole-overdoped superconducting KFe2As2 revealed a well-defined low-energy incommensurate spin fluctuation at [π(1 ± 2 δ),0] with δ = 0.16. The incommensurate structure differs from the previously observed commensurate peaks in electron-doped AFe2As2 (A = Ba, Ca, or Sr) at low energies. The direction of the peak splitting is perpendicular to that observed in Fe(Te,Se) or in Ba(Fe,Co)2As2 at high energies. A band structure calculation suggests interband scattering between bands around the Γ and X points as an origin of this incommensurate peak. The perpendicular direction of the peak splitting can be understood within the framework of multiorbital band structure. The results suggest that spin fluctuation is more robust in hole-doped than in electron-doped samples, which can be responsible for the appearance of superconductivity in the heavily hole-doped samples.     

Topological superconductivity in Janus monolayer transition metal dichalcogenides

The Janus monolayer transition metal dichalcogenides (TMDs) $MXY$ ($M={\rm Mo}$, W, $etc$. and $X, Y={\rm S}$, Se, $etc$.) have been successfully synthesized in recent years. The Rashba spin splitting in these compounds arises due to the breaking of out-of-plane mirror symmetry. Here we study the pairing symmetry of superconducting Janus monolayer TMDs within the weak-coupling framework near critical temperature $T_{\rm c}$, of which the Fermi surface (FS) sheets centered around both $ărGamma$ and $K (K')$ points. We find that the strong Rashba splitting produces two kinds of topological superconducting states which differ from that in its parent compounds. More specifically, at relatively high chemical potentials, we obtain a time-reversal invariant $s + f + p$-wave mixed superconducting state, which is fully gapped and topologically nontrivial, $i.e.$, a $\mathbb{Z}_2$ topological state. On the other hand, a time-reversal symmetry breaking $d + p + f$-wave superconducting state appears at lower chemical potentials. This state possess a large Chern number $|C|=6$ at appropriate pairing strength, demonstrating its nontrivial band topology. Our results suggest the Janus monolayer TMDs to be a promising candidate for the intrinsic helical and chiral topological superconductors.     

Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3

TbMnO3 is an orthorhombic insulator where incommensurate spin order for temperature T(N)<41 K is accompanied by ferroelectric order for T<28 K. To understand this, we establish the magnetic structure above and below the ferroelectric transition using neutron diffraction. In the paraelectric phase, the spin structure is incommensurate and longitudinally modulated. In the ferroelectric phase, however, there is a transverse incommensurate spiral. We show that the spiral breaks spatial inversion symmetry and can account for magnetoelectricity in TbMnO3.     

Hidden quasi-one-dimensional superconductivity in Sr₂RuO₄

We show that the interplay between spin and charge fluctuations in Sr?RuO? leads unequivocally to triplet pairing which has a hidden quasi-one-dimensional character. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form Δ ~(p(x)+ip(y))z(^) with sharp gap minima and a d vector that is only weakly pinned. The superconductor lacks robust chiral Majorana fermion modes along the boundary. The absence of topologically protected edge modes could explain the surprising absence of experimentally detectable edge currents in this system.     

Effects of strong coupling on pairing fluctuations in layered superconductors

The influence of short inelastic lifetimes due to strong coupling of fermionic quasiparticles to bosons on superconducting fluctuation effects aboveT _c is calculated. Considering a strong-coupling model for a layered superconducting metal, it is shown that pairing fluctuation corrections to the spin-lattice relaxation rate in weak coupling and very strong coupling are qualitatively different if the pairing fluctuation spectrum has s-wave symmetry. For weak coupling the corrections are positive, whereas for very strong coupling γ = 2? d ω α² F(ω)/ω > 2 the corrections are negative. In contrast, the Pauli spin susceptibility is insensitive to strong-coupling corrections.     

A brief review on <Emphasis Type="Italic">μ</Emphasis>SR studies of unconventional Fe- and Cr-based superconductors

Muon spin relaxation/rotation (μSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super- conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on μSR studies of the newly discovered superconductors ACa₂Fe₄As₄F₂ (A = K, Rb, and Cs), ThFeAsN, and A₂Cr₃As₃ (A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of μSR investigations of the superconductivity in hole and electron doped BaFe₂As₂.     

Normal-state hourglass dispersion of the spin excitations in FeSexTe(1-x)

We use cold neutron spectroscopy to study the low-energy spin excitations of superconducting (SC) FeSe0.4Te0.6 and essentially nonsuperconducting (NSC) FeSe0.45Te0.55. In contrast with BaFe2-x(Co,Ni)xAs2, where the low-energy spin excitations are commensurate both in the SC and normal state, the normal-state spin excitations in SC FeSe0.4Te0.6 are incommensurate and show an hourglass dispersion near the resonance energy. Since similar hourglass dispersion is also found in the NSC FeSe0.45Te0.55, we argue that the observed incommensurate spin excitations in FeSe(1-x)Tex are not directly associated with superconductivity. Instead, the results can be understood within a picture of Fermi surface nesting assuming extremely low Fermi velocities and spin-orbital coupling.     

Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in s(±) pairing; the higher energy peak appears around the commensurate momenta due to scattering between α-FS to γ/δ-FS pockets. The second resonance is incommensurate, coming from β-FS to γ/δ-FS scatterings, and its q vector is doping-dependent and, hence, on the FS topology. Energies of both resonances ω(res)(1,2) are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.