Fluctuation Exchange Approximation Research Articles

Material-Dependent Screening of Coulomb Interaction in Single-Layer Cuprates

To explore the material dependence of cuprate superconductors, we evaluate effective Coulomb interactions for Hg1201 and Tl1201, where Tl1201 has nearly half value of Tc as that of Hg1201 even at the optimal oxygen concentration. Although the structures of these superconductors are similar, there is an apparent difference in the occupied levels below EF. The characteristic difference in the band structure is correlated with the oxygen content in the buffer layer. By using a constrained random phase approximation, effective screened Coulomb interactions are estimated for HgBa2CuO4 and TlBa2CuO5. The results show that the screened on-site Coulomb interaction in Hg1201 is nearly twice as large as that in Tl1201. In addition, the eigenvalues of the linearized Eliashberg equation of the single-band Hubbard model within the fluctuation exchange approximation can explain the apparent difference in Tc. When we assume that the screened on-site Coulomb interaction is twice as large for Hg as for Tl, the material-dependent Tc can be explained.

Self-energy driven resonancelike inelastic neutron spectrum in the s++ -wave state in Fe-based superconductors

To elucidate the pairing states in Fe-based superconductors, we perform careful calculation of the dynamical spin susceptibility $\chi^S(q, \omega)$ at very low temperatures ($T \sim 1$ meV). The feedback effect on both the self-energy and $\chi^S(q, \omega)$ from the superconducting gap are self-consistently analyzed based on the fluctuation-exchange (FLEX) approximation. In the $s_{+-}$-wave state, which has sign-reversal in the gap function, $\chi^S(q, \omega)$ at the nesting momentum $q = Q$ shows a resonance peak even when the system is away from the magnetic quantum-critical-point (QCP). In the $s_{++}$-wave state that has no sign-reversal, $\chi^S(q, \omega)$ shows a large hump structure when the system is close to the magnetic QCP. This result confirms the validity of self-energy driven resonance-like peak in $s_{++}$-wave state proposed in our previous semi-microscopic study: The enhancement in $\chi^S(q, \omega)$ due to self-energy effect exceeds the suppression due to coherence factor effect near magnetic QCP. We stress that the hump structure in the $s_{++}$-wave state given by the FLEX method smoothly changes to resonance-like sharp peak structure as the system approaches magnetic QCP, which was not reported in our previous studies. The obtained $\omega$- and $T$-dependences of $\chi^S(q, \omega)$ in the $s_{++}$-wave state resemble to the resonance-like feature in inelastic neutron scattering spectra recently observed in Na(Fe,Co)As and FeSe

Edge-induced Strongly Correlated Electronic States in Two-dimensional Hubbard Model: Enhancement of Magnetic Correlations and Self-energy Effects

To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the RPA+FLEX approximation. For the charge response, RPA+FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that RPA+FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

Wide applicability of high- Tc pairing originating from coexisting wide and incipient narrow bands in quasi-one-dimensional systems

We study superconductivity in the Hubbard model on various quasi-one-dimensional lattices with coexisting wide and narrow bands originating from multiple sites within a unit cell, where each site corresponds to a single orbital. The systems studied are the 2-leg and 3-leg ladders, the diamond chain, and the criss-cross ladder. These one-dimensional lattices are weakly coupled to form two-dimensional (quasi-one-dimensional) ones, and the fluctuation exchange approximation is adopted to study spin-fluctuation-mediated superconductivity. When one of the bands is perfectly flat, and the Fermi level, intersecting the wide band, is placed in the vicinity of the flat band, superconductivity arising from the interband scattering processes is found to be strongly enhanced owing to the combination of the light electron mass of the wide band and the strong pairing interaction due to the large density of states of the flat band. Even when the narrow band has finite band width, the pairing mechanism still works since the edge of the narrow band, due to its large density of states, plays the role of the flat band. The results indicate the generality of the high $T_c$ pairing mechanism due to coexisting wide and "incipient" narrow bands in quasi-one-dimensional systems.

Origin of the quasiparticle peak in the spectral density of Cr(001) surfaces

In the spectral density of Cr(001) surfaces a sharp resonance close to the Fermi level is observed in both experiment and theory. For the physical origin of this peak two mechanisms were proposed. A single particle dz2 surface state renormalised by electron-phonon coupling and an orbital Kondo effect due to the degenerate dxz/dyz states. Despite several experimental and theoretical investigations, the origin is still under debate. In this work we address this problem by two different approaches of the dynamical mean-field theory. First, by the spin-polarized T-matrix fluctuation exchange approximation suitable for weakly and moderately correlated systems. Second, by the non-crossing approximation derived in the limit of weak hybridization (i.e. for strongly correlated systems) capturing Kondo-like processes. By using recent continuous-time quantum Monte Carlo calculations as a benchmark, we find that the high-energy features, everything except the resonance, of the spectrum is captured within the spin-polarized T-matrix fluctuation exchange approximation. More precisely the particle-particle processes provide the main contribution. For the non-crossing approximation it appears that spin-polarized calculations suffer from spurious behavior at the Fermi level. Then, we turned to non spin-polarized calculations to avoid this unphysical behavior. By employing two plausible starting hybridization functions, it is observed that the characteristics of the resonance are crucially dependent on the starting point. It appears that only one of these starting hybridizations could result in an orbital Kondo resonance in the presence of a strong magnetic field like in the Cr(001) surface. It is for a future investigation to first resolve the unphysical behavior within the spin-polarized non-crossing approximation and then check for an orbital Kondo resonance.

An effective Hamiltonian and its phase diagram for T’-structure cuprates

We study the superconducting transition near the half-filling of electron-doped cuprates with the so-called T’-structure based on an effective two-band model using fluctuation-exchange approximation and solving the linearized Eliashberg equation. We find d-wave superconductivity even at the half-filling of this model when the energy difference between the upper Hubbard level of Cu orbitals and O 2p levels is less than about 1.5eV, which is plausible for the T’-type cuprates.

Finite-energy spin fluctuations as a pairing glue in systems with coexisting electron and hole bands

We study, within the fluctuation-exchange approximation, the spin-fluctuation-mediated superconductivity in Hubbard-type models possessing electron and hole bands, and compare them with a model on a square lattice with a large Fermi surface. In the large Fermi surface model, superconductivity is more enhanced for better nesting for a fixed band filling. By contrast, in the models with electron and hole bands, superconductivity is optimized when the Fermi surface nesting is degraded to some extent, where finite-energy spin fluctuations around the nesting vector develop. The difference lies in the robustness of the nesting vector, namely, in models with electron and hole bands, the wave vector at which the spin susceptibility is maximized is fixed even when the nesting is degraded, whereas when the Fermi surface is large, the nesting vector varies with the deformation of the Fermi surface. We also discuss the possibility of realizing in actual materials the bilayer Hubbard model, which is a simple model with electron and hole bands, and is expected to have a very high ${T}_{c}$.

Spectral function method for Hall conductivity of incoherent metals

Using a model spectral function of the electron, the Hall conductivity in the normal metallic state of the Pr[Formula: see text]CexCuO4 (PCCO) superconductor is calculated neglecting the current vertex-correction. The result is qualitatively consistent with the experiment. Consequently, the reason becomes clear why the Fermi-liquid theory fails to explain the anomaly of the Hall conductivity. The inconsistency of the fluctuation-exchange approximation also becomes clear.

Interplay of Pomeranchuk instability and superconductivity in the two-dimensional repulsive Hubbard model

Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the four-fold symmetric Fermi surface becomes unstable against a spontaneous distortion into two-fold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk distorted Fermi surface is modified from the d-wave pairing to (d+s)-wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature $T_{\rm c}^{\rm PI}$ of Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting $T_{\rm c}^{\rm SC}$. This implies that the filling region for strong Pomeranchuk instability and that for strong superconducting fluctuations can be separated, and Pomeranchuk instability can appear even if the peak of $T_c^{\rm PI}$ is lower than the peak of $T_c^{\rm SC}$. An interesting observation is that the Fermi surface distortion can enhance the superconducting $T_{\rm c}^{\rm SC}$ in the overdoped regime, which is explained with a perturbation picture for small distortions.

Weak-coupling analysis of quasiparticle excitations in Sr2RuO4 along the Γ−M cut

We examine normal-state quasiparticle excitations along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ cut in momentum space for the putative $p$-wave superconductor ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ on the basis of fluctuation exchange approximation calculations. We take as input first-principles derived parameters for the band structure and spin-orbit and electron-electron interactions. The numerical results are in excellent agreement with data from photoemission experiments and provide insight into the underlying quasiparticle properties. We find that, despite the correlation-induced effective mass increase near the Fermi surface, the full $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ bandwidths are, if anything, increased by correlations. Furthermore, for the $\ensuremath{\gamma}$ band we find anomalous lifetime broadening and a significant temperature of variation of unoccupied state quasiparticle energies for temperatures between 25 and 100 K, both of which are accounted for by the momentum dependence of the electron self-energy. In addition to aiding our understanding of experimental data, these results point to the challenge of assigning appropriate Fermi-liquid parameters or momentum-independent self-energies for schemes that require such approximations in order to model ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$.

Microscopic theory on charge transports of a correlated multiorbital system

Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, $\rho_{ab}$, and the Hall coefficient in the weak-field limit, $R_{\textrm{H}}$, in addition to the magnetic properties and the electronic structure, for a $t_{2g}$-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy ($\Sigma$), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the Aslamasov-Larkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the $\Sigma$ CVC and the MT CVC. Second, $\rho_{ab}$ and $R_{\textrm{H}}$ near the AF QCP have high-temperature region, governed mainly by the $\Sigma$ CVC, and low-temperature region, governed mainly by the $\Sigma$ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only $R_{\textrm{H}}$ at low temperatures, although $R_{\textrm{H}}$ at high temperatures and $\rho_{ab}$ at all temperatures considered are sufficiently described by including only the $\Sigma$ CVC. I also achieved the qualitative agreement with several experiments of Sr$_{2}$RuO$_{4}$ or Sr$_{2}$Ru$_{0.975}$Ti$_{0.025}$O$_{4}$. Moreover, I showed several better points of this theory than other theories.

Renormalization group flow of the Luttinger-Ward functional: Conserving approximations and application to the Anderson impurity model

We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle irreducible vertex functions, given a cut-off in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to non-conserving approximations introduced in an earlier publication ctuation exchange approximation as well as to nonconserving approximations introducen [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015)]. We apply the different approximate flow equations to the single impurity Anderson model in thermal equilibrium at vanishing temperature. Numerical results for the effective mass, the spin susceptibility, the charge susceptibility, and the linear conductance reflect the similarity of the methods to the fluctuation exchange approximation. We find the majority of the approximations to deviate stronger from the exact results than one-particle irreducible functional renormalization group schemes. However, we identify a simple static two-particle irreducible flow scheme which performs remarkably well and produces an exponential Kondo-like scale in the renormalized level position.

Electronic structure of palladium in the presence of many-body effects

Including on-site electronic interactions described by the multi-orbital Hubbard model we study the correlation effects in the electronic structure of bulk palladium. We use a combined density functional and dynamical mean field theory, LDA+DMFT, based on the fluctuation exchange approximation. The agreement between the experimentally determined and the theoretical lattice constant and bulk modulus is improved when correlation effects are included. It is found that correlations modify the Fermi surface around the neck at the $L$-point while the Fermi surface tube structures show little correlation effects. At the same time we discuss the possibility of satellite formation in the high energy binding region. Spectral functions obtained within the LDA+DMFT and $GW$ methods are compared to discuss non-local correlation effects. For relatively weak interaction strength of the local Coulomb and exchange parameters spectra from LDA+DMFT shows no major difference in comparison to $GW$.

Spin fluctuations and superconductivity in layeredf-electron superlattices

We investigate magnetic and superconducting properties of layered $f$-electron superlattices within the fluctuation exchange approximation (FLEX). We show that spin fluctuations, which are characterized by the maximum value of the spin susceptibility in the three-dimensional (3D) Brillouin zone, are strongly suppressed in $f$-electron superlattices. However, effective 2D spin fluctuations can be increased due to the spatial confinement of the $f$ electrons. Therefore the tendency towards ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity, mediated by these spin fluctuations, can be strongly increased in $f$-electron superlattices. This is in sharp contrast to superlattices composed of conventional $s$-wave superconductors, where superconductivity is generally suppressed.

Many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid theory

I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki–Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr 2 RuO 4 and Sr 2 Ru 0.075 Ti 0.025 O 4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW+DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second order diagram. FLEX+DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

Orbital-cooperative spin fluctuation and orbital-dependent transport in ruthenates

Unusual transport properties deviating from the Fermi liquid are observed in ruthenates near a magnetic quantum-critical point (QCP). To understand the electronic properties of the ruthenates near and away from an antiferromagnetic (AF) QCP, I study the electronic structure and magnetic and transport properties for the $t_{2g}$-orbital Hubbard model on a square lattice in fluctuation-exchange approximation including Maki-Thompson (MT) current vertex correction (CVC). The results away from the AF QCP reproduce several experimental results of Sr$_{2}$RuO$_{4}$ qualitatively and provide new mechanisms about the enhancement of spin fluctuation at $Q_{\textrm{IC-AF}}\approx (0.66\pi,0.66\pi)$, larger mass enhancement of the $d_{xy}$ orbital than that of the $d_{xz/yz}$ orbital, and nonmonotonic temperature dependence of the Hall coefficient. Also, the results near the AF QCP explain the $T$-linear inplane resistivity in Sr$_{2}$Ru$_{0.075}$Ti$_{0.025}$O$_{4}$ and give an experimental test on the obtained temperature dependence of the Hall coefficient. I reveal spatial correlation including the self-energy of electrons beyond mean-field approximations is essential to determine the electronic properties of the ruthenates. I also show several ubiquitous transport properties near an AF QCP and characteristic transport properties of a multiorbital system by comparison with results of a single-orbital system near an AF QCP.

Spin fluctuations and unconventional pairing on the Lieb lattice

Abstract The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the ( π , π ) and ( 0.4 π , 0 ) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate d x 2 − y 2 - and g x y ( x 2 − y 2 ) -wave pairing states. After further doped, the d x y -wave state is favored via the intra-sublattice spin fluctuations with a wave vector ( π , 0 ). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.

Strong-Coupling Approach to Antiferromagnetic Ordering Driven by Paramagnetic Pair-Breaking in d-Wave Superconducting Phase

The field-induced antiferromagnetic (AFM) ordering in the $d_{x^2-y^2}$-paired superconducting phase, which has been recently found in the weak-coupling approach as a basic mechanism due to the Pauli paramagnetic pair-breaking (PPB) in relation to the high-field behaviors in CeCoIn_5, is studied in the strong-coupling approach taking account of the electron correlation. Applying the fluctuation-exchange (FLEX) approximation to the two-dimensional Hubbard model including the Zeeman term, it is shown that the PPB-induced AFM ordering in the superconducting (SC) phase and the first order SC transition on H_{c2}(T) are realized in the strong-coupling approach as well as those in the weak-coupling model, and that the AFM ordering is affected by the quasiparticle renormalization and the amplitude of the SC order parameter. This AFM ordering may appear in a wide range of materials close to an AFM quantum critical point (QCP).