Fluctuation Exchange Approximation Research Articles

Spin fluctuations and pairing symmetry in AxFe2−ySe2: dual effect of the itinerant and the localized nature of electrons

We investigate the spin fluctuations and the pairing symmetry in AxFe2−ySe2 by the fluctuation exchange approximation. Besides the on-site interactions, the next-nearest-neighbor antiferromagnetic coupling J2 is also included. We find that both the itinerant and the localized natures of electrons are important to describe recent experimental results on the spin fluctuations and the pairing symmetry. In particular, a small J2 coupling can change the pairing gap from the d-wave symmetry to the extended s-wave symmetry. We have also studied the real-space structures of the gap functions for different orbits in order to gain more insight into the nature of the pairing mechanism.

Validity of Fermi-Liquid Description of Low-Energy Magnetic Excitation in Electron-Doped Cuprate Superconductors

The spin-fluctuation spectrum of electron-doped cuprate superconductors is calculated using the single-band Hubbard model with realistic tight-binding parameters and the fluctuation–exchange approximation. No strong incommensurate wings are found in the superconducting state in agreement with experiments. Our results imply that the magnetic response of electron-doped cuprates can be explained with the conventional Fermi-liquid approach. We also give a detailed comparison with a previous work, where the spin-fluctuation spectrum calculated with the random phase approximation was found to be dominated by incommensurate wings and thereby the Fermi-liquid approach was seriously questioned.

Superconductivity assisted by interlayer pair hopping in multilayered cuprates

In order to explore why the multi-layered cuprates have such high Tc's, we have examined various inter-layer processes. Since the inter-layer one-electron hopping has little effects on the band structure, we turn to the inter-layer pair hopping. The superconductivity in a double-layer Hubbard model with and without the inter-layer pair hopping, as studied by solving the Eliashberg equation with the fluctuation exchange approximation, reveals that the inter-layer pair hopping acts to increase the pairing interaction and the self-energy simultaneously, but that the former effect supersedes the latter and enhances the superconductivity. The inter-layer pair hopping considered here is for off-site pairs, for which we discuss the effect of retaining SU(2) symmetry, along with how the the sign of the pair hopping determines the relative configuration of d-waves between the adjacent layers.

Understanding the reentrant superconducting phase diagram of the iron pnictide Ca4Al2O6Fe2(As1−xPx)2: First-principles calculations

Recently, a very rich phase diagram has been obtained for an iron-based superconductor Ca4Al2O6Fe2(As1-xPx)2. It has been revealed that nodeless (x=0) and nodal (x = 1) superconductivity are separated by an antiferromagnetic phase. Here we study the origin of this peculiar phase diagram using a five orbital model constructed from first principles band calculation, and applying the fluctuation exchange approximation assuming spin fluctuation mediated pairing. Based on the calculation results, we propose a scenario where the frustration in momentum space degrades superconductivity in the intermediate x regime, while antiferromangetism takes place due to a very good nesting. In order to see whether the present theoretical scenario is consistent with the actual nature of the competition between superconductivity and antiferromagnetism, we also perform hydrostatic pressure experiment for Ca4Al2O6Fe2(As1-xPx)2. In the intermediate x regime where antiferromagnetism occurs at ambient pressure, applying hydrostatic pressure smears out the antiferromagnetic transition, but superconductivity does not take place. This supports our scenario that superconductivity is suppressed by the momentum space frustration in the intermediate x regime, apart from the presence of the antiferromangnetism.

Polar charge fluctuation and superconductivity in organic conductors

Superconductivity and polar charge fluctuation are studied in an organic conductor with the dimer-molecule degree of freedom. The extended Hubbard models, where the intra-dimer electronic structure and the inter-dimer Coulomb interactions are taken into account, are analyzed by the random-phase approximation and the fluctuation-exchange approximation. Superconductivity appears in a vicinity of the charge-density wave (CDW) phase where the electronic charge distributions are polarized inside of dimers. The extended s-wave type paring is favored and its competitive relations with the superconductivity due to the spin fluctuation depends on the triangular lattice geometry. Comparison between two superconductivities realized near the polar and non-polar CDW phases are also presented.

Development of a two-particle self-consistent method for multiorbital systems and its application to unconventional superconductors

We extend the two-particle self-consistent method proposed by Vilk and Tremblay (J. Phys. I France 7, 1309-1368 (1997)) to study superconductivity in multi-orbital systems. Starting with the sum rules for the spin and charge susceptibilities, we derive self-consistent equations to determine the renormalized effective interactions. We apply this method to the two-orbital $d_{x^2-y^2}$-$d_{3z^2-r^2}$ model for La$_2$CuO$_4$ and the five-orbital $d$-model for LaFeAsO. Comparing the results with those of the random phase approximation or the fluctuation exchange approximation in which vertex corrections are ignored, we discuss how the vertex corrections affect the pairing instability of La$_2$CuO$_4$ and the dominant pairing symmetry of LaFeAsO.

Multiorbital analysis of the effects of uniaxial and hydrostatic pressure onTcin the single-layered cuprate superconductors

The origin of uniaxial and hydrostatic pressure effects on $T_c$ in the single-layered cuprate superconductors is theoretically explored. A two-orbital model, derived from first principles and analyzed with the fluctuation exchange approximation gives axial-dependent pressure coefficients, $\partial T_c/\partial P_a>0$, $\partial T_c/\partial P_c<0$, with a hydrostatic response $\partial T_c/\partial P>0$ for both La214 and Hg1201 cuprates, in qualitative agreement with experiments. Physically, this is shown to come from a unified picture in which higher $T_c$ is achieved with an "orbital distillation", namely, the less the $d_{x^2-y^2}$ main band is hybridized with the $d_{z^2}$ and $4s$ orbitals higher the $T_c$. Some implications for obtaining higher $T_c$ materials are discussed.

Coulomb Frustrated Phase Separation in Quasi-Two-Dimensional Organic Conductors on the Verge of Charge Ordering

On the basis of an analysis of a 3/4-filled two-dimensional (2D) extended Hubbard model under the fluctuation-exchange approximation, we find Coulomb frustrated phase separation (PS) in a region of nonzero temperature, where the quantum critical phenomenon of charge ordering (CO) dominates. In quasi-2D organic conductors on the verge of CO, this frustrated PS provides a mechanism for generating spatial inhomogeneity, which is characterized by an extremely slow relaxation and an intermediate length scale.

Non-Fermi-liquid transport phenomena and superconductivity driven by orbital fluctuations in iron pnictides: Analysis by fluctuation-exchange approximation

We study the five-orbital Hubbard model including the charge quadrupole interaction for iron pnictides. Using the fluctuation-exchange (FLEX) approximation, orbital fluctuations evolve inversely proportional to the temperature, and therefore the resistivity shows linear or convex T-dependence for wide range of temperatures. We also analyze the Eliashberg gap equation, and show that s-wave superconducting state without sign reversal (s++ -wave state) emerges when the orbital fluctuations dominate over the spin fluctuations. When both fluctuations are comparable, their competition gives rise to a nodal s-wave state. The present study offers us a unified explanation for both the normal and superconducting states.

Self-Consistent Approximations for Superconductivity beyond the Bardeen–Cooper–Schrieffer Theory

We develop a concise self-consistent perturbation expansion for superconductivity where all the pair processes are naturally incorporated without drawing "anomalous" Feynman diagrams. This simplification results from introducing an interaction vertex that is symmetric in the particle-hole indices besides the ordinary space-spin coordinates. The formalism automatically satisfies conservation laws, includes the Luttinger-Ward theory as the normal-state limit, and reproduces the Bardeen-Cooper-Schrieffer theory as the lowest-order approximation. It enables us to study the thermodynamic, single-particle, two-particle, and dynamical properties of superconductors with competing fluctuations based on a single functional $\Phi[\hat{G}]$ of Green's function $\hat{G}$ in the Nambu space. Specifically, we derive closed equations in the FLEX-S approximation, i.e., the fluctuation exchange approximation for superconductivity with all the pair processes, which contains extra terms besides those in the standard FLEX approximation.

Fermi Surface Deformation Near Charge-Ordering Transition

We study the deformation of a Fermi surface (FS) near charge-ordering (CO) transition. By applying a fluctuation-exchange approximation to the two-dimensional extended Hubbard model, we show that the FS is largely modified by strong charge fluctuations when the wave number of the CO pattern does not match the nesting vector of the FS in a noninteracting system. We also discuss the enhanced anisotropy in quasiparticle properties in the resultant metallic state.

Fluctuation-exchange approximation theory of the nonequilibrium singlet-triplet transition

As a continuation of a previous work [B. Horv\'ath et al., Phys. Rev. B {\bf 82}, 165129 (2010)], here we extend the so-called Fluctuation Exchange Approximation (FLEX) to study the non-equilibrium singlet-triplet transition. We show that, while being relatively fast and a conserving approximation, FLEX is able to recover all important features of the transition, including the evolution of the linear conductance throughout the transition, the two-stage Kondo effect on the triplet side, and the gradual opening of the singlet-triplet gap on the triplet side of the transition. A comparison with numerical renormalization group calculations also shows that FLEX captures rather well the width of the Kondo resonance. FLEX thus offers a viable route to describe correlated multi-level systems under non-equilibrium conditions, and, in its rather general form, as formulated here, it could find a broad application in molecular electronics calculations.

The Origin of Tc Enhancement in Heterostructure Cuprate Superconductors.

Recent experiments on heterostructures composed of two or more films of cuprate superconductors of different oxygen doping levels have shown a remarkable T enhancement (up to ) relative to single compound films. We provide a simple explanation of the enhancement which arises naturally from a collection of experimental works. We show that the enhancement could be caused by a structural change in the lattice, namely an increase in the distance of the apical oxygen from the copper-oxygen plane. This increase modifies the effective off-site interaction in the plane which in turn enhances the d-wave superconductivity order parameter. To illustrate this point we study the extended Hubbard model using the fluctuation exchange approximation.

Theory of the β-Type Organic Superconductivity under Uniaxial Compression

We study theoretically the shift of the superconducting transition temperature (Tc) under uniaxial compression in beta-type organic superconductors, beta-(BEDT-TTF)2I3 and beta-(BDA-TTP)2X[X=SbF6,AsF6], in order to clarify the electron correlation, the spin frustration and the effect of dimerization. The transfer integrals are calculated by the extended Huckel method assuming the uniaxial strain and the superconducting state mediated by the spin fluctuation is solved using Eliashberg's equation with the fluctuation-exchange approximation. The calculation is carried out on both the dimerized (one-band) and nondimerized (two-band) Hubbard models. We have found that (i) the behavior of Tc in beta-(BEDT-TTF)2I3 with a stronger dimerization is well reproduced by the dimer model, while that in weakly dimerized beta-BDA-TTP salts is rather well reproduced by the two-band model, and (ii) the competition between the spin frustration and the effect induced by the fluctuation is important in these materials, which causes nonmonotonic shift of Tc against uniaxial compression.

Study of non-Fermi-liquid-like state and pairing symmetry in iron pnictides based on the multiorbital Hubbard-Holstein model

We study the five-orbital Hubbard-Holstein model, taking account of the electron–phonon (e-ph) interaction due to the Fe-ion oscillation. In order to include the self-energy correction, we employ the fluctuation exchange (FLEX) approximation. It is revealed that the orbital fluctuations are enhanced by the e-ph interaction, which causes a strong attractive pairing interaction. The orbital fluctuations give rise to highly anisotropic quasiparticle lifetime (hot/cold spot structure) and non-Fermi-liquid-like transport phenomena. From the phase diagram obtained by the FLEX approximation, we find that (i) s-wave state without sign reversal is stable for the moderate e-ph coupling in the broad parameter region, which is consistent with the experimental non-magnetic impurity effect, (ii) the renormalization induced by the orbital fluctuation is not so strong, and (iii) superconducting (SC) state with node can appear in the broad parameter region in the presence of impurities.

Spin-fluctuation-mediated pairing symmetry on the metallic kagome lattice

We study the magnetic properties and the superconducting pairing mediated by spinfluctuations on the metallic kagome lattice by using the Hubbard model and the fluctuationexchange approximation. It is found that the spin susceptibility is caused by thenesting of the renormalized Fermi surface. We point out that superconductivity willbe favored in the spin-singlet channel and may be more easily realized around25% hole doping. We find an evolution of the pairing state from a d-wave-like symmetry, described by theE2g representation of thegroup D6h at low dopings,to that described by the A2g representation at heavy hole dopings.

D-wave pairing from spin fluctuations in theKxFe2−ySe2superconductors

Angle-resolved photoemission spectroscopy measurements on the recently discovered superconductors in the KFe${}_{2}$Se${}_{2}$ family with critical temperatures up to $~33$ K suggest that no Fermi pockets of hole character centered on the $\ensuremath{\Gamma}$ point of the Brillouin zone are present, in contrast to all other known ferropnictide and ferrochalcogenide superconductors. Using a fluctuation exchange approximation and a five-orbital tight-binding description of the band structure, we calculate the effective pairing interaction. We find that the pairing state in this system is most likely to have $d$-wave symmetry due to pair scattering between the remaining electron Fermi pockets at wave vector $\mathbf{q}~(\ensuremath{\pi},\ensuremath{\pi})$, but without any symmetry-imposed nodes for the given Fermi surface. We propose experimental tests of this result, including the form of the resonance spectrum probed by inelastic neutron scattering.

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.

Spectral analysis for the iron-based superconductors: Anisotropic spin fluctuations and fully gappeds±-wave superconductivity

Spin fluctuations are considered to be one of the candidates that drive a sign-reversed ${s}^{\ifmmode\pm\else\textpm\fi{}}$ superconducting state in the iron pnictides. In the magnetic scenario, whether the spin-fluctuation spectrum exhibits certain unique fine structures is an interesting aspect for theoretical study in order to understand experimental observations. We investigate the detailed momentum dependence of the short-range spin fluctuations using a two-orbital model in the self-consistent fluctuation exchange approximation and find that a common feature of those fluctuations that are capable of inducing a fully gapped ${s}^{\ifmmode\pm\else\textpm\fi{}}$ state is the momentum anisotropy with lengthened span along the direction transverse to the antiferromagnetic momentum transfer. Performing a qualitative analysis based on the orbital character and the deviation from perfect nesting of the electronic structure for the two-orbital and a more complete five-orbital model, we gain the insight that this type of anisotropic spin fluctuations favor superconductivity due to their enhancement of intraorbital, but interband, pair scattering processes. The momentum anisotropy leads to elliptically shaped magnetic responses which have been observed in inelastic neutron-scattering measurements. Meanwhile, our detailed study on the magnetic and the electronic spectrum shows that the dispersion of the magnetic resonance mode in the nearly isotropic ${s}^{\ifmmode\pm\else\textpm\fi{}}$ superconducting state exhibits anisotropic propagating behavior in an upward pattern and the coupling of the resonance mode to fermions leads to a dip feature in the spectral function.

Spin fluctuation spectrum of electron-doped high-Tc superconductors

The magnetic excitation spectrum of electron-doped copper oxide superconductors is calculated using the Hubbard model on a square lattice. First, the on-site repulsion is treated with the random phase approximation. The spectrum of electron-doped systems in the superconducting state is compared with that of hole-doped systems, and the relationship between the frequency at which a peak grows in the spectrum and the superconducting energy gap at a hot spot (an intersection of the Fermi surface and the magnetic Brillouin zone boundary) is investigated. As compared with the hole-doped systems, the resonance condition is difficult to be satisfied in the electron-doped systems because of the small density of states around the hot spot. Moreover, the correlation effect in the Hubbard model is treated by the fluctuation-exchange approximation (FLEX), and the spin fluctuation spectra in the superconducting state in a wide region of the wave vector and frequency are calculated. We have found that the intensity of the magnetic spectrum at incommensurate wave vectors obtained with the FLEX is considerably weaker than that obtained with the RPA. The validity of the Fermi-liquid approach is also discussed.