Testing the sign-changing superconducting gap in iron-based superconductors with quasiparticle interference and neutron scattering

We present a phenomenological calculation of the quasiparticle interference (QPI) pattern and inelastic neutron scattering (INS) spectra in iron-pnictide and layered iron-selenide compounds by using material specific band structure and superconducting (SC) gap properties. As both the QPI and the INS spectra arise due to scattering of the Bogolyubov quasiparticles, they exhibit a one-to-one correspondence of the scattering vectors and the energy scales. We show that these two spectroscopies complement each other in such a way that a comparative study allows one to extract quantitative and unambiguous information about the underlying pairing structure and the phase of the SC gap. Due to the nodeless and isotropic nature of the SC gaps, both the QPI and INS maps are concentrated at only two energies in pnictide (two SC gaps) and one energy in iron-selenide, while the associated scattering vectors q for scattering of sign-changing and same sign of the SC gaps change between these spectroscopies. The results presented, particularly for the newly discovered iron-selenide compounds, can be used to test the nodeless d-wave pairing in this class of high temperature superconductor.     

Magnetic resonant mode in the low-energy spin-excitation spectrum of superconducting Rb2Fe4Se5 single crystals

We have studied the low-energy spin-excitation spectrum of the single-crystalline Rb(2)Fe(4)Se(5) superconductor (T(c)=32 K) by means of inelastic neutron scattering. In the superconducting state, we observe a magnetic resonant mode centered at an energy of ?ω(res)=14 meV and at the (0.5 0.25 0.5) wave vector (unfolded Fe-sublattice notation), which differs from the ones characterizing magnetic resonant modes in other iron-based superconductors. Our finding suggests that the 245-iron selenides are unconventional superconductors with a sign-changing order parameter, in which bulk superconductivity coexists with the √5×√5 magnetic superstructure. The estimated ratios of ?ω(res)/k(B)T(c)≈5.1±0.4 and ?ω(res)/2Δ≈0.7±0.1, where Δ is the superconducting gap, indicate moderate pairing strength in this compound, similar to that in optimally doped 1111 and 122 pnictides.     

Pair-density-wave pseudogap and superconducting states in cuprates

Bogoliubov quasiparticle interference and localized high-energy excitations observed in cuprates in nodal and antinodal regions of the momentum space, respectively, would lead to a conclusion that only the nodal region might give rise to superconductivity whereas the antinodal one might be associated with the pseudogap. We argue that both pseudogap and superconducting states arise exactly in the antinodal region with pronounced nesting feature of the Fermi contour as spatially inhomogeneous incoherent and coherent states of pairs with large momentum. The nodal region gives rise to conventional superconducting pairing with zero momentum which, together with the pairing with large momentum in the antinodal region, forms a biordered superconducting state in the whole of the Brillouin zone. This coherent state with complicated momentum dependence of the order parameter manifests itself as a pair-density wave that can exist without any driving insulating order. We believe that quasiparticle interference, other than observed in the nodal region, should be observable in the antinodal region as well.     

Measurement of a sign-changing two-gap superconducting phase in electron-doped Ba(Fe(1-x)Co(x))2As2 single crystals using scanning tunneling spectroscopy

Scanning tunneling spectroscopic studies of Ba(Fe(1-x)Co(x))(2)As(2) (x=0.06, 0.12) single crystals reveal direct evidence for predominantly two-gap superconductivity. These gaps decrease with increasing temperature and vanish above the superconducting transition T(c). The two-gap nature and the slightly doping- and energy-dependent quasiparticle scattering interferences near the wave vectors (±π, 0) and (0, ±π) are consistent with sign-changing s-wave superconductivity. The excess zero-bias conductance and the large gap-to-T(c) ratios suggest dominant unitary impurity scattering.     

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.     

Sign reversal of the order parameter near <Emphasis Type="Italic">s</Emphasis><Subscript>±</Subscript>-superconductor surface

The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of self-consistent calculations for a two band superconductor with nodeless extended s-wave order parameter symmetry, as possibly realized in Fe-based high-temperature superconductors. It is found that for a wide range of parameters the spatial behavior of the order parameter at a surface is not reduced to a trivial suppression. If the interband scattering at a surface is of the order of the intraband one or dominates it, it can be energetically favorable to change the symmetry of the superconducting state near the surface from s _± to conventional s-wave. The range of existing of this surface conventional superconductivity is very sensitive to the relative values of interband and intraband pairing potentials. It is shown that the LDOS spectra near the surface can qualitatively differ upon calculating with and without taking into account the self-consistency of the order parameter.     

Specific heat in superconductors

Specific heat is a powerful tool to investigate the physical properties of condensed materials. Superconducting state is achieved through the condensation of paired electrons, namely, the Cooper pairs. The condensed Cooper pairs have lower entropy compared with that of electrons in normal metal, thus specific heat is very useful in detecting the low lying quasiparticle excitations of the superconducting condensate and the pairing symmetry of the superconducting gap. In this brief overview, we will give an introduction to the specific heat investigation of the physical properties of superconductors.We show the data obtained in cuprate and iron based superconductors to reveal the pairing symmetry of the order parameter.     

Topology of the superconducting order under pairing repulsion

The superconducting state with a large momentum of a pair in a doped insulator is controlled by the features of Coulomb pairing associated with the suppression of small momentum transfers during scattering owing to electron-phonon interaction and of large transfers due to redistribution of the spectral weight among the superconducting or the insulating branches of the elementary excitation spectrum. Superconductivity emerges when the characteristic energy of the pairing interaction has an upper bound. The solutions obtained for a self-consistent equation with a simple structure of the degenerate kernel are antisymmetric and symmetric relative to inversion of the momentum of relative motion of a pair. The orbital symmetry of the singlet superconducting order is analyzed.     

Nodal versus nodeless behaviors of the order parameters of LiFeP and LiFeAs superconductors from magnetic penetration-depth measurements

High-precision measurements of magnetic penetration depth λ in clean single crystals of LiFeAs and LiFeP superconductors reveal contrasting behaviors. In LiFeAs the low-temperature λ(T) shows a flat dependence indicative of a fully gapped state, which is consistent with previous studies. In contrast, LiFeP exhibits a T-linear dependence of superfluid density infinity λ(-2), indicating a nodal superconducting order parameter. A systematic comparison of quasiparticle excitations in the 1111, 122, and 111 families of iron-pnictide superconductors implies that the nodal state is induced when the pnictogen height from the iron plane decreases below a threshold value of ~1.33 ?.     

Doubly ordered superconducting state in a doped antiferromagnet

In a weakly doped quasi-two-dimensional antiferromagnet with a Fermi contour in the form of small pockets, the Coulomb repulsion gives rise to a doubly ordered superconducting state of coexisting condensates with a large pair momentum and a zero one. The pairing with the large momentum determines the superconducting transition temperature, below which the order with zero momentum coexists as an induced order until the temperature corresponding to the initiation of the phonon pairing mechanism is reached. The superconductivity-induced orbital current density wave eliminates the pairing-repulsion-caused zero points from the two-gap quasiparticle spectrum and leads to a deviation of the relative phase of the superconducting order parameter components from π.     

Effect of electron correlation on superconducting pairing symmetry

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure s or pure d wave pairing symmetry, the electronic correlation suppresses the s wave gap magnitude (as well as the ) at a faster rate than that for the d wave gap. On the other hand, a complex order parameter of the form () shows anomalous temperature dependence. For example, if the temperature () at which the d wave component of the complex order parameter vanishes happens to be larger than that for the s wave component (), then the growth of the d wave component is arrested with the onset of the s wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding due to coulomb correlation are very sensitive to the relative pairing strengths of s and d channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of )the gap magnitude of the d wave component increases with electron correlation but not for certain values of electron correlation. However, this never happens in case of the s wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ( and ) in a mixed symmetry pairing state and the thermal variation of the gap anisotropy [0pt][0pt] with electron correlation. The results are discussed with reference to experimental observations. Received: 26 August 1997 / Revised: 31 December 1997 / Accepted: 28 January 1998     

Surface Majorana flat bands in j=3/2 superconductors with singlet-quintet mixing

Recent experiments [Science Advances 4 eaao4513(2018)] have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g., YPt Bi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the(111) surface of half-Heusler superconductors.Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. We study the effect of the surface order parameter and the surface impurity on the surface Majorana flat bands of half-Heusler superconductors based on the Luttinger model. To be specific, we consider the topological nodal-line superconducting phase induced by the singlet-quintet pairing mixing, classify all the possible translationally invariant order parameters for the surface states according to irreducible representations of C_(3v)point group, and demonstrate that any energetically favorable order parameter needs to break the time-reversal symmetry. We further discuss the energy splitting in the energy spectrum of surface Majorana flat bands induced by different order parameters and non-magnetic or magnetic impurities. We propose that the splitting in the energy spectrum can serve as the fingerprint of the pairing symmetry and mean-field order parameters. Our theoretical prediction can be examined in the future scanning tunneling microscopy experiments.     

配对对称性与带间作用

研究d p模型的超导性质.可出现d p配对占主导的情形，配对对称性取决于CuO2面内空穴作用的各向异性，可以是纯d波配对，也可以是纯s波配对.CuO2面内各向排斥作用不能导致空穴配对.欠掺杂区域可以出现“预配对”.当库伯对是局域的则不能根据配对函数求超导临界温度.空穴的退局域以及配对参量对称性的演化也能得到理解. 关键词： d波对称性 d p配对 超导电性     

Superconducting properties of “111” type LiFeAs iron arsenide single crystals

LiFeAs single crystal has been grown with superconducting transition temperature Tc comparable to that of polycrystals.A magnetic transition is found at about 160 K,which suggests the correlation of superconductivity with spin wave density.     

Evolution of the superconducting state of Fe-based compounds with doping

We introduce an effective low-energy pairing model for Fe-based superconductors with s- and d-wave interaction components and a small number of input parameters and use it to study the doping evolution of the symmetry and the structure of the superconducting gap. We argue that the model describes the entire variety of pairing states found so far in the Fe-based superconductors and allows one to understand the mechanism of the attraction in s(±) and d(x(2)-y(2)) channels, the competition between s- and d-wave solutions, and the origin of superconductivity in heavily doped systems, when only electron or only hole pockets are present.     

Triplet versus singlet superconductivity in quasi-one-dimensional conductors

Quasi-one-dimensional organic conductors are highly unconventional materials, which exhibit a wide variety of phenomena, including spin density waves, quantum Hall effect, and superconductivity. In this paper, we review some experimental and theoretical developments concerning the superconducting state of these systems, where a particular emphasis is placed on the possibility of triplet superconductivity. This possibility is supported by various experiments including upper critical field, Knight shift and NMR relaxation time measurements on the Bechgaard salt bistetramethyltetraselenafulvalene hexafluorophosphate [(TMTSF)₂PF₆]. However, similar NMR results are still lacking for another compound (TMTSF)₂ClO₄ and other members of the Bechgaard salts family. Furthermore, the pairing mechanism and order parameter symmetry are not yet fully known. Therefore, we include a discussion of both triplet and singlet pairing states, and analyse briefly the possibility that the symmetries of the superconducting order parameters are different for various compounds. Finally, we also discuss some open questions regarding the superconducting state of these systems.     

Kinetic energy driven pairing in cuprate superconductors

Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.     

Origin of Bragg-Coulomb high-Tc superconductivity Green''s function and diagram method for umklapp e-e scattering

The Green's function method and diagram technique for umklapp electron-electron scattering mediated by the screened Coulomb interaction in layered anisotropic conductors are examined. Gor'kov-type equations and their general solution for anomalous and normal temperature Green's functions are derived taking into account umklapp scattering of all orders. Explicit equations for dielectric and superconducting order parameters, including coexistent Bragg and BCS pairing, are found. The possibility of the first-order phase transition to the superconducting state is discussed. The theory elucidates the origin of Bragg-Coulomb high-T_c superconductivity, proposed by the authors.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.