We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the $d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half-filling. We find a change in sign of the vertex contributions to $d_{xy}$ superconductivity from repulsive near half filling to attractive at large doping. $p$-wave superconductivity is not found at the parameters we study, and $s$-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase $T_c$.
The question of whether spatially inhomogeneous hopping in the two dimensional Hubbard model can lead to enhancement of superconductivity has been tackled by a number of authors in the context of the checkerboard Hubbard model (CHM). We address the effects of disorder on superconducting properties of the CHM by using exact diagonalization calculations for both potential and hopping disorder. We characterize the superconducting tendencies of the model by focusing on the pair binding energy, the spin gap, and d-wave pairing order parameter. We find that superconducting tendencies, particularly t…
We apply a renormalization group approach to the determination of the phase diagram of the t-t' Hubbard model at the Van Hove filling, as function of t'/t, for small values of U/t. The model presents ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.
Applying the recently developed variational approach to Kohn-Luttinger superconductivity to the t-t' Hubbard model in two dimensions, we have found, for sizeable next-nearest neighbor hopping, an electron density controlled quantum phase transition between a d-wave superconducting state close to half filling and an s-wave superconductor at lower electron density. The transition occurs via an intermediate time reversal breaking d+is superconducting phase, which is characterized by nonvanishing chirality and density-current correlation. Our results suggest the possibility of a bulk time reversal…
We demonstrate a robust frustration-driven charge-order to superconductivity transition in the half-filled negative-U extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.
We present many-body calculations of superconducting pair-pair correlations in the ground state of the half-filled band Hubbard model on large anisotropic triangular lattices. Our calculations cover nearly the complete range of anisotropies between the square and isotropic triangular lattice limits. We find that the superconducting pair-pair correlations decrease monotonically with increasing onsite Hubbard interaction U for inter-pair distances greater than nearest neighbor. For the large lattices of interest here the distance dependence of the correlations approaches that for noninteracting …
We propose theoretically how unconventional superconducting pairing in a repulsively interacting Hubbard ladder can be enhanced via the application of a Floquet driving. Initially the Hubbard ladder is prepared in its charge-density-wave dominated ground state. A periodic Floquet drive is applied which modulates oppositely the energy offset of the two chains and effectively reduces the tunneling along the rungs. This modulation of the energy offsets might be caused by the excitation of a suitable phononic mode in solids or a superlattice modulation in cold atomic gases. We use state-of-the-art…
For a class of generalized Hubbard models, we determine the maximal stability region for the superconducting eta-pairing ground state. We exploit the Optimized Ground State (OGS) approach and the Lanczos diagonalization procedure to derive a sequence of improved bounds. We show that some pieces of the stability boundary are asymptotic, namely independent on the OGS cluster size. In this way, necessary and sufficient conditions are obtained to realize superconductivity in terms of an eta-pairing ground state. The phenomenon is explained by studying the properties of certain exact eigenstates of…
The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients $ν\sb{ij}$ exist.
A trial wave function is proposed for studying the instability of the two-dimensional Hubbard model with respect to d-wave superconductivity. Double occupancy is reduced in a similar way as in previous variational studies, but in addition our wave function both enhances the delocalization of holes and induces a kinetic exchange between the electron spins. These refinements lead to a large energy gain, while the pairing appears to be weakly affected by the additional term in the variational wave function.
Using a dynamic cluster quantum Monte Carlo approximation, we study a two-dimensional Hubbard model with a small orthorhombic distortion in the nearest neighbor hopping integrals. We find a large nematic response in the low-frequency single-particle scattering rate which develops with decreasing temperature and doping as the pseudogap region is entered. At the same time, the d-wave superconducting gap function develops an s-wave component and its amplitude becomes anisotropic. The strength of the pairing correlations, however, is found to be unaffected by the strong anisotropy, indicating that…
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard model for particle densities close to the van Hove filling as a function of the next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around t'_c approx. -0.33t, suggesting a quantum critical point between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon increasing the particle density in the latter regime …
The CuO-planes of high-T_c superconductors were found to consist of geometric stripes with alternating superconducting and antiferromagnetic areas. Here we will investigate the repulsive Hubbard model of striped clusters as a possible microscopic description of the superconducting elements. The focus of our attention lies on the superconducting properties. We report in agreement with the square Hubbard model a signal in the d-wave channel and investigate its dependence on system size, cluster shape and interaction strength.
Recent scanning tunneling microscopy measurements on cuprate superconductors have revealed remarkable spatial inhomogeneities in the single-particle energy gap. Using cellular dynamical mean-field theory, we study the zero temperature superconducting properties of a single-band Hubbard model with a spatial modulation of the electron density. We find that the inhomogeneity in the electronic structure results in a substantial spatial variation in the superconducting order parameter and single-particle energy gap, reminiscent of the experimental results. In particular, we find that the order para…
We have applied the Fast Fourier transform (FFT), which allows to compute efficiently convolution sums, to solve the set of self-consistent T-matrix equations to get the Green function of the two dimensional attractive-U Hubbard modelbelow $T_c$, extending previous calculations of the same authors. Using a constant order parameter $Δ(T)$, we calculated $T_c$ as a function of electron density and interaction strength $U$. These global results deviate from the BCS behavior remarkably.
We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, $T_c$ may be enhanced through an increase in the d-wave pairing interaction ($V_d$) or the bare pairing susceptibility ($χ_{0d}$). At optimal doping, where $V_d$ is revealed to be featureless, we find a power-law behavior of $χ_{0d}(ω=0)$, replacing the BCS log, and strongly enhanced $T_c$. We suggest experiments to verify our predictions.
Recent excperiments (ARPES, Raman) suggest the presence of two distinct energy gaps in high-Tc superconductors (HTSC), exhibiting different doping dependences. Results of a variational cluster approach to the superconducting state of the two-dimensional Hubbard model are presented which show that this model qualitatively describes this gap dichotomy: One gap (antinodal) increases with less doping, a behavior long considered as reflecting the general gap behavior of the HTSC. On the other hand, the near-nodal gap does even slightly decrease with underdoping. An explanation of this unexpected be…
Superconductivity in the Hubbard model on a square lattice near half filling is studied using an optimization (or correlated) variational Monte Carlo method. Second-order processes of the strong-coupling expansion are considered in the wave functions beyond the Gutzwiller factor. Superconductivity of d_x^2-y^2-wave is widely stable, and exhibits a crossover around U=U_co\sim 12t from a BCS type to a new type. For U\gsim U_co (U\lsim U_co), the energy gain in the superconducting state is derived from the kinetic (potential) energy. Condensation energy is large and \propto exp(-t/J) [tiny] on th…
A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound st…
Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we st…
We review magnetic and superconducting instabilities in the t-t' Hubbard model on the two-dimensional square lattice as obtained with functional one-loop renormalization group techniques. Special emphasis is put on ferromagnetic and triplet superconducting tendencies that could be relevant to the triplet superconductor Sr2RuO4.
Doped Hubbard model is a simple model for the high-Tc cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidences that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction while the superexchange interaction enhances both. A…
The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba type spin-orbit coupling breaks inversion symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting stat…
We present an approach for determining susceptibilities and order parameters in multi-band Hubbard model within functional renormalization group method, and apply it to study various instabilities of the FeAs-based high temperature superconductor. First, we derive the formulae of susceptibilities and order parameters of superconducting parings, spin density waves and charge density waves with diverse wave vectors which could occur in multi-band Hubbard model. Second, we apply it to the FeAs-based high temperature superconductor and find an electronic-driven superconducting pairing instability …
An extended Hubbard model with phonons is considered. q-coherent states relative to the superconducting quantum symmetry of the model are constructed and their properties studied. It is shown that they can have energy expectation lower than eigenstates constructed via conventional processes and that they exhibit ODLRO.
We study the frequency-dependent structure of electronic self-energy in the pseudogap and superconducting states of the two-dimensional Hubbard model. We present the self-energy calculated with the cellular dynamical mean-field theory systematically in the space of temperature, electron density, and interaction strength. We show that the low-frequency part of the self-energy is well represented by a simple equation, which describes the transitions of an electron to and from a hidden fermionic state. By fitting the numerical data with this simple equation, we determine the parameters characteri…
We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model for the d-wave and extended s-wave pairing symmetries. The pairing structure factor shows a strong tendency to d-wave pairing and peaks at an interaction strength comparable to the bandwidth. The extend…
A Hubbard model at half-filling on an anisotropic triangular lattice has been proposed as the minimal model to describe conducting layers of $κ-(BEDT-TTF)_2X$ organic materials. The model interpolates between the square lattice and decoupled chains. The $κ-(BEDT-TTF)_2X$ materials present many similarities with cuprates, such as the presence of unconventional metallic properties and the close proximity of superconducting and antiferromagnetic phases. As in the cuprates, spin fluctuations are expected to play a crucial role in the onset of superconductivity. We perform a weak-coupling renormali…
The pseudogap phenomena in High-$T_{\rm c}$ cuprates are investigated on the basis of the Hubbard model which includes only the on-site repulsive interaction $U$. We consider the pairing scenario for the pseudogap. The pseudogap arises from the resonance scattering due to the strong superconducting fluctuations. First, the electronic state and the anti-ferromagnetic spin fluctuations are calculated by using the FLEX approximation. The T-matrix (the propagator of the superconducting fluctuations) is calculated by extending the $\acute{\rm E}$liashberg equation. The self-energy due to the superc…
The Roth's two-pole approximation has been used by the present authors to study the effects of the hybridization in the superconducting properties of a strongly correlated electron system. The model used is the extended Hubbard model which includes the $d-p$ hybridization, the $p$-band and a narrow $d$-band. The present work is an extension a previous reference [Intern. Journ. of Modern Phys. B, Vol. 18 No. 2 (2004) 241]. Nevertheless, some important correlation functions necessary to estimate the Roth's band shift, are included together with the temperature $T$ and the Coulomb interaction $U$…
We report exact calculations of magnetic and superconducting pair-pair correlations for the half-filled band Hubbard model on an anisotropic triangular lattice. Our results for the magnetic phases are similar to those obtained with other techniques. The superconducting pair-pair correlations at distances beyond nearest neighbor decrease monotonically with increasing Hubbard interaction U for all anisotropy, indicating the absence of frustration-driven superconductivity within the model.
We study the hole binding energy and pairing correlations in the three-band Hubbard model coupled to an apical oxygen phonon, by exact diagonalization and constrained-path Monte Carlo simulations. In the physically relevant charge-transfer regime, we find that the hole binding energy is strongly enhanced by the electron-phonon interaction, which is due to a novel potential-energy-driven pairing mechanism involving reduction of both electronic potential energy and phonon related energy. The enhancement of hole binding energy, in combination with a phonon-induced increase of quasiparticle weight…
The relationship between crystal structures and superconducting critical temperatures has attracted considerable attention as a clue to designing higher-$T_{\rm c}$ superconductors. In particular, the relationship between the number $n$ of CuO$_2$ layers in a unit cell of cuprate superconductors and the optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm opt}$ increases when $n$ is increased, up to $n=3$, and, then, decreases for larger $n$. However, the mechanism behind the $n$ dependence of $T_{\r…
We study spin-fluctuation-mediated superconductivity in the one-band Hubbard model. Higher order effective interactions in $U$ give rise to a superconducting instability which is very sensitive to changes in the Fermi surface topology arising as a function of doping and changes in the band structure. We show the superconducting phase diagram as a function of doping and next-nearest neighbor hopping in the limit of very small Coulomb interaction strength and discuss peculiarities arising at the phase boundaries separating different superconducting domains.
The competition between d-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quan…
The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U<0 and intersite repulsion W>0 in the presence of charge density waves, superconducting and $η$-superconducting order parameters. We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions. The other result of the paper is application of the exact solution of the Schrodinger equation for the two electron bound state, as an additional bound for the phase diagram of the model, resulting in th…
By a novel exact diagonalization technique we show that bound pairs propagate between repulsive Hubbard clusters in a superconducting fashion. The size of the matrices that must be handled depends on the number of fermion configurations {\em per spin}, which is of the order of the square root of the overall size of the Hilbert space. We use CuO$_{4}$ units connected by weak O-O links to model interplanar coupling and c-axis superconductivity in Cuprates. The numerical evidence on Cu$_{2}$O$_{8}$ and Cu$_{3}$O$_{12}$ prompts a new analytic scheme describing the propagation of bound pairs and al…
To understand the recently established unique magnetic and superconducting phase diagram of LaFeAsO$_{1-x}$H$_x$, we analyze the realistic multiorbital tight-binding model for $x=0 \sim 0.4$ beyond the rigid band approximation. Both the spin and orbital susceptibilities are calculated in the presence of the Coulomb and charge quadrupole interactions. It is found that both orbital and spin fluctuations strongly develop at both $x \sim 0$ and 0.4, due to the strong violation of the rigid band picture in LaFeAsO$_{1-x}$H$_x$. Based on this result, we discuss the experimental phase diagram, especi…
The interplay between magnetic and superconducting states on a square lattice is studied using the extended Hubbard model, which takes into account the attraction of electrons located at nearest neighbor sites. Ferro-, antiferro-, and spiral magnetic states with all possible sets of spiral wave vectors, as well as singlet superconducting states with s-wave and d-wave pairing order parameters, are considered. Formation of a state with the intermediate s+id-symmetry and phase separation between different phases are allowed. The results of the Hartree-Fock and slave boson approximations are compa…
Superconducting landscape of the strongly correlated bilayer Hubbard model
Graduate School of Engineering, Kyushu Institute of Technology（九州工业大学工学研究科）；Department of Material Science, University of Hyogo（兵库大学物质科学系）；Institute for Materials Research (IMR), Tohoku University（东北大学材料科学研究所）；International Quantum Materials Center (Q 2 ), Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究机构国际量子材料中心）；Physics Division, Sophia University（上智大学物理学部）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Department of Physics, The University of Tokyo（东京大学物理学系）
Bilayer Moiré structures are a highly tunable laboratory to investigate the physics of strongly correlated electron systems. Moiré transition metal dichalcogenides at low-energies, in particular, are believed to be described by a single narrow band Hubbard model on a triangular lattice with spin-orbit coupling. Motivated by recent experimental evidence for superconductivity in twisted bilayer materials, we investigate the possible superconducting pairings in a two-dimensional single band Rashba-Hubbard model. Using a random-phase approximation in the presence of nearest and next-nearest neighb…
Superconducting, magnetic, and charge correlation functions and dynamic spin correlation functions of the doped two-chain Hubbard model is studied with the projector Quantum Monte carlo method and Lanczos recursion method. Of the three correlation functions, the interchain singlet superconducting correlation function is the most long range. Our data is not consistent with the Luther-Emery picture.
The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the $d$-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($δ$) dependence of the Hubbard model in the ground states on a square lattice at strong coupling $U/t=10$, for the on-site interaction $U$ and the trans…
Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable $t'$ is necessary to obtain a sizable pairing gap.
We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a $d$-wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture $d$-wave pairing using only a single-site effecti…
Using a variational Monte Carlo method, we study competitions of strong electron-electron and electron-phonon interactions in the ground state of Holstein-Hubbard model on a square lattice. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched by antiferromagnetic and charge order (CO) insulating phases. By the carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS.
In this paper we determine the phase diagrams (for $T=0$ as well as $T>0$) of the Penson-Kolb-Hubbard model for two dimensional square lattice within Hartree-Fock mean-field theory focusing on investigation of superconducting phases and possibility of the occurrence of the phase separation. We obtain that the phase separation, which is a state of coexistence of two different superconducting phases (with $s$-wave and $η$-wave symmetries), occurs in define range of the electron concentration. In addition, increasing temperature can change the symmetry of the superconducting order parameter (from…
We observe the effect of non-zero magnetization m onto the superconducting ground state of the one dimensional repulsive Hubbard model with correlated hopping X. For t/2 < X < 2t/3, the system first manifests Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) oscillations in the pair-pair correlations. For m = m1 a kinetic energy driven macroscopic phase separation into low-density superconducting domains and high-density polarized walls takes place. For m > m2 the domains fully localize, and the system eventually becomes a ferrimagnetic insulator.
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulo…
The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature ($T_c$) curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in th…
Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the $s^{\pm}$-wave superconducting state appears in the small…
The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO$_2$ planes. Here, we use a dynamic cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring…
We employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Repulsive interactions usually lead to higher-angular momentum Cooper pairing. By considering not only longer-ranged hoppings, but also non-local electron-electron interactions, we are able to find superconducting solutions for all irreducible representations on the square and hexagonal lattices, including extended regions of chiral topological superconductivity. For the square, triangular and honey…
We review the explanation for resonant neutron scattering experiments in $YBa_2Cu_3O_{6+δ}$ and $Bi_2 Sr_2 Ca_2 O_{8+δ}$ materials from the point of view of triplet excitation in the particle-particle channel, the pi excitation. Relation of these resonances to the superconducting condensation energy and their role in stabilizing the superconducting state is discussed. Due to the superconducting fluctuations, the pi resonance may appear as a broad peak above Tc. Analogue problem to the pi excitation for the case of s-wave pairing, the eta excitation, is considered in the strong coupling limit w…
In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the $d_{x^2-y^2}$-wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppre…
The influence of a Zeeman magnetic field on the superconducting characteristics of the attractive Hubbard model was investigated. The ground state and temperature phase diagrams were obtained for a fixed number of particles. Two critical magnetic fields were found for the first order phase transition from the superconducting to the normal state for $n\neq 1$. For some range of parameters a reentrant transition was found and gapless superconductivity was obtained. The significance of the Hartree term was also analyzed.
