Unconventional pairing originating from disconnected Fermi surfaces in the iron-based superconductor

For the iron-based high T_c superconductor LaFeAsO_1?xF_x, we construct a minimal model, where all of the five Fe d bands turn out to be involved. We then investigate the origin of superconductivity with a five-band random-phase approximation by solving the Eliashberg equation. We conclude that the spin fluctuation modes arising from the nesting between the disconnected Fermi pockets realise, basically, an extended s-wave pairing, where the gap changes sign across the nesting vector.     

Renormalization group analysis of competing orders and the pairing symmetry in Fe-based superconductors

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0, 0) and (π, π) in the folded Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is A_1g in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.     

Superconductivity enhanced by d-density wave: A weak-coupling theory

Making a revision of mistakes in Ref. [19], we present a detailed study of the competition and interplay between the d-density wave (DDW) and d-wave superconductivity (DSC) within the fluctuation-exchange (FLEX) approximation for the two-dimensional (2D) Hubbard model. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearest-neighbor Coulomb repulsion is included within the Hartree-Fock approximation. We solve the coupled gap equations for the DDW, DSC, and π-pairing as the possible order parameters, which are caused by exchange of spin fluctuations, together with calculating the spin fluctuation pairing interaction self-consistently within the FLEX approximation. We show that even when nesting of the Fermi surface is perfect, as in a square lattice with only nearest-neighbor hopping, there is coexistence of DSC and DDW in a large region of dopings close to the quantum critical point (QCP) at which the DDW state vanishes. In particular, we find that in the presence of DDW order the superconducting transition temperature T_c can be much higher compared to pure superconductivity, since the pairing interaction is strongly enhanced due to the feedback effect on spin fluctuations of the DDW gap. π-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small. In the present work, we have developed a weak-coupling theory of the competition between DDW and DSC in 2D Hubbard model, using the static spin fluctuation obtained within FLEX approximation and ignoring the self-energy effect of spin fluctuations. For our model calculations in the weak-coupling limit we have taken U/t=3.4, since the antiferromagnetic instability occurs for higher values of U/t.     

Two-dimensionality of electronic structure and strong Fermi surface nesting in highly anisotropic iron-based superconductors

We perform first-principle calculations for a newly discovered iron-based superconductor, Sr₂ScFePO₃, whose blocking layer is a thick perovskite-based oxide (Sr₂ScO₃) and compare its result with those of other typical iron-based compounds, in order to make a strategy to explore iron-based compounds with higher superconducting transition temperature T_c. Consequently, we find that the thick blocking layer like Sr₂ScO₃ brings about perfectly cylindrical hole and electron Fermi surfaces. This can give much better nesting condition between disconnected Fermi surfaces compared to other types of iron-based superconductor compounds.     

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.     

Neutron scattering of iron-based superconductors

Low-energy spin excitations have been studied on polycrystalline LaFeAsO_1?xF_x samples by inelastic neutron scattering. The Q-integrated dynamical spin susceptibility χ″(ω) of the superconducting samples is found to be comparable to that of the magnetically ordered parent sample. On the other hand, χ″(ω) almost vanishes at x = 0.158, where the superconducting transition temperature T_c is suppressed to 7 K. In addition, χ″(ω) in optimally doped LaFeAsO_0.918F_0.082 with T_c = 29 K exhibits a spin resonance mode. The peak energy, E_res, when scaled by k_BT_c is similar to the value of about 4.7 reported in other high-T_c iron-based superconductors. This result suggests that there is intimate relationship between the dynamical spin susceptibility and high-T_c superconductivity in iron-based superconductors, and is consistent with a nesting condition between Fermi surfaces at the Γ and M points.     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.     

Anion height as a controlling parameter for the superconductivity in iron pnictides and cuprates

Both families of high T_c superconductors, iron pnictides and cuprates, exhibit material dependence of superconductivity. Here, we study its origin within the spin fluctuation pairing theory based on multiorbital models that take into account realistic band structures. For pnictides, we show that the presence and absence of Fermi surface pockets is sensitive to the pnictogen height measured from the iron plane due to the multiorbital nature of the system, which is reflected to the nodeless/nodal form of the superconducting gap and T_c. Surprisingly, even for the cuprates, which is conventionally modeled by a single orbital model, the multiorbital band structure is shown to play a crucial role in the material dependence of superconductivity. In fact, by adopting a two orbital model that considers the d_z² orbital on top of the d_x²−y² orbital, we can resolve a long standing puzzle of why the single layered Hg cuprate have much higher T_c than the La cuprate. Interestingly, here again the apical oxygen height measured from the CuO₂ plane plays an important role in determining the relative energy difference between d_x²−y² and d_z² orbitals, thereby strongly affecting the superconductivity.     

Unconventional superconductivity pairing induced by antiferromagnetic spin fluctuations in layered organic superconductors

The unconventional character of the superconductivity in organic compounds κ-(ET)₂X is ascribed to an antiferromagnetic spin fluctuation induced pairing. Since the band structure involves two bands (±), we assume that the large amplitude spin fluctuations arise from the band with the best nesting properties (band +), while superconductivity pairing occurs in the other band (-).We show that the nesting properties may mimic either a chemical pressure (deuterization) or a hydrostatic one. Indeed, a change of the nesting ratio t₁/t₂, according to our model, induces a modification of the Fermi surface topology. The spin fluctuations strength in the system is affected and consequently the calculated effective coupling constant of superconductivity for the even-parity singlet pairing channel. Our theory appears to be qualitatively consistent with major experimental reports.     

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ??strange metal phase?? of the doped Mott insulator.     

Angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3: strong coupling behavior and the universality of interband scattering

We have performed angle-resolved photoemission spectroscopy of the iron-chalcogenide superconductor Fe1.03Te0.7Se0.3 to investigate the electronic structure relevant to superconductivity. We observed a holelike Fermi surface (FS) and an electronlike FS at the Brillouin zone center and corner, respectively, which are nearly nested by the Q～(π,π) wave vector. We do not find evidence for the nesting instability with Q～(π+δ,0) reminiscent of the antiferromagnetic order in the parent compound Fe1+yTe. We have observed an isotropic superconducting (SC) gap along the holelike FS with the gap size Δ of ～4 meV (2Δ/kBTc ～ 7), demonstrating the strong-coupling superconductivity. The observed similarity of low-energy electronic excitations between iron-chalcogenides and iron-arsenides strongly suggests that common interactions which involve Q～(π,π) scattering are responsible for the SC pairing.     

Mirror nesting: A superconducting pairing of carriers with a large momentum

The coincidence of Fermi contour portions with isolines of zero kinetic energy of the relative pair motion (the pair Fermi contour) is a necessary condition for superconducting pairing of carriers with a large total pair momentum. In high?T _c cuprates, this situation can occur either due to the formation of a stripe structure or in the absence of the stripe structure when the Fermi contour satisfies the mirror nesting condition. A gradual deviation from this condition leads to a decrease in the superconducting energy gap to zero.     

Quasiparticles in a strongly correlated liquid with the fermion condensate: applications to high-temperature superconductors

A model of a strongly correlated electron liquid based on fermion condensation (FC) is extended to high-temperature superconductors. Within our model, the appearance of FC presents a boundary separating the region of a strongly interacting electron liquid from the region of a strongly correlated electron liquid. We study the superconductivity of a strongly correlated liquid and show that, under certain conditions, the superconductivity vanishes at temperatures T > T _c ≈ T _node, with the superconducting gap being smoothly transformed into a pseudogap. As a result, the pseudogap occupies only a part of the Fermi surface. The gapped area shrinks with increasing the temperature and vanishes at T = _T*. The single-particle excitation width is also studied. The quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by the effective masses and, intersecting near the binding energy that is on the order of the superconducting gap. It is argued that this strong change of the quasiparticle dispersion upon binding can be enhanced in underdoped samples because of strengthening the FC influence. The FC phase transition in the presence of the superconductivity is examined, and it is shown that this phase transition can be considered as driven by the kinetic energy.     

Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

It has been shown that the strong coupling model taking into account a rise in the spin antiferromagnetic insulating state explains the doping dependence of the topology and shape of the Fermi contour of superconducting cuprates. Hole pockets with shadow bands in the second Brillouin zone form the Fermi contour with perfect ordinary and mirror nesting, which ensures the coexistence of orbital antiferromagnetism and superconductivity with a large pair momentum for T < T_C. The weak pseudogap region (T_* < T < T*) corresponds to the orbital antiferromagnetic ordering, which coexists with the incoherent state of superconducting pairs with large momenta in the strong pseudogap region (T_C < T < T_*).     

Anisotropic superconductivity in UPt3

A consistent picture of conventional superconductivity in UPt₃ is presented which explains qualitatively the gap anisotropy, the dependence of T_c on crystal perfection, the low value of the specific heat discontinuity at T_c and the induced magnetic form factor. The model obtained is based on results of a local density band calculation for UPt₃ which are in excellent agreement with photoemission experiments and on estimates of the strength and anisotropy of the electron-phonon interaction. The key feature is anisotropy of the superconducting energy gap which arises from the variation of the electronic mass on the Fermi surface.     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

Superconductivity in the t-J model in the large-N limit

Using a 1/N expansion for X-operators the leading contributions to the linearized equation for the superconducting gap of the t-J model are derived and the gap equation solved numerically on a square lattice. We find a strong instability towards superconductivity only in the d-wave (T ₃) channel with T _c/│t│ ～ 0:01 where T _c is the transition temperature and t the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term with the band width, and a retarded term due to charge and spin fluctuations with ～ J, as energy scale.     

Robustness of <Emphasis Type="Italic">s</Emphasis>-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 A _1g s-wave. Robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high-T _c superconducting mechanisms: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-T _c 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-T _c 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-T _c superconductivity.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

Inelastic neutron scattering studies of the spin and lattice dynamics in iron arsenide compounds

Although neutrons do not couple directly to the superconducting order parameter, they have nevertheless played an important role in advancing our understanding of the pairing mechanism and the symmetry of the superconducting energy gap in the iron arsenide compounds. Measurements of the spin and lattice dynamics have been performed on non-superconducting ‘parent’ compounds based on the LaFeAsO (‘1111’) and BaFe₂As₂ (‘122’) crystal structures, and on electron and hole-doped superconducting compounds, using both polycrystalline and single crystal samples. Neutron measurements of the phonon density-of-state, subsequently supported by single crystal inelastic X-ray scattering, are in good agreement with ab initio calculations, provided the magnetism of the iron atoms is taken into account. However, when combined with estimates of the electron–phonon coupling, the predicted superconducting transition temperatures are less than 1 K, making a conventional phononic mechanism for superconductivity highly unlikely. Measurements of the spin dynamics within the spin density wave phase of the parent compounds show evidence of strongly dispersive spin waves with exchange interactions consistent with the observed magnetic order and a large anisotropy gap. Antiferromagnetic fluctuations persist in the normal phase of the superconducting compounds, but they are more diffuse. Below T_c, there is evidence in three ‘122’ compounds that these fluctuations condense into a resonant spin excitation at the antiferromagnetic wavevector with an energy that scales with T_c. Such resonances have been observed in the high-T_c copper oxides and a number of heavy fermion superconductors, where they are considered to be evidence of d-wave symmetry. In the iron arsenides, they also provide evidence of unconventional superconductivity, but a comparison with ARPES and other measurements, which indicate that the gaps are isotropic, suggests that the symmetry is more likely to be extended-s_± wave in character.