We discuss a reduction of superconducting transition temperature by the intersite Coulomb repulsion for the d-wave pairing in cuprates. We compare the results found for the spin-fermion model and the extended Hubbard model. We argue that in both the models the d-wave superconducting transition temperature is reduced by the Coulomb repulsion of holes in different unit cells. We also show that in the strong correlation limit the s-wave superconductivity cannot occur due to the kinematic restriction of no double occupancy in the Hubbard subbands.
Quantum Monte Carlo is used to calculate various pairing correlations of the 2D Hubbard model possessing band features experimentally observed in the cuprates. In the hole-doped case, where the Fermi level lies close to the van Hove singularities around $(0,π)$, the d$_{x^2-y^2}$ pairing correlation is selectively enhanced, while in the electron-doped case, where the singularities are far below the Fermi level and the Fermi surface runs through $(\pm π/2,\pm π/2)$, both d$_{x^2-y^2}$ and d$_{xy}$ correlations are enhanced with the latter having a $\sqrt{2}\times \sqrt{2}$ structure. The two pa…
One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase(PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra(ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parame…
In this Letter, we develop a microscopic theory to describe the close proximity between the insulating antiferromagnetic (AF) order and the d-wave superconducting (dSC) order in cuprates. We show that the cuprate ground states form a configuration of coherent pairing states consisting of extended singlet Cooper pairs and triplet $π$ pairs, which can simultaneously describe AF and dSC orders.
There is a clear discrepancy among the energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram for hole-doped cuprates we show that tunneling measurements performed on 90 K cuprates, simply, detect two different energy gaps: the pairing gap and the coherent gap, which are identical in conventional superconductors. We find that there are two reasons why tunneling measurements show in one cuprate exclusively the coherent gap while, in another cuprate, they show the pairing gap: (i) the number of CuO2 planes per unit cell in the cuprate, and…
The symmetries of the order parameter (OP) responsible for pairing and the OP responsible for phase coherence in hole-doped cuprates are discussed. We analyze angle-resolved tunneling, ARPES, Raman scattering and torque measurements performed on hole-doped cuprates. We conclude that, most likely, the OP responsible for phase coherence has the d-wave symmetry whereas the OP responsible for pairing has an anisotropic s-wave symmetry.
An emergence of magnetic boson of instantonic nature, that provides a Cooper-'pairing glue', is considered in the repulsive 'nested' Hubbard model of superconducting cuprates. It is demonstrated, that antiferromagnetic instantons of a spin density wave type may have negative energy due to coupling with Cooper pair condensate. A set of Eliashberg-like equations is derived and solved self-consistently, proving the above suggestion. An instantonic propagator plays the role of Green function of pairing 'glue' boson. Simultaneously, the instantons defy condensation of the mean-field SDW order. We h…
The symmetries and origins of the order parameters (OPs) for pairing and long-range phase coherence in hole-doped cuprates are discussed. By analyzing tunneling, inelastic neutron scattering and torque measurements we conclude that the Cooper pairs in cuprates consist of spinons, and the pairing OP has an anisotropic s-wave symmetry, whereas the OP for long-range phase coherence has the magnetic origin due to spin fluctuations and, has the d-wave symmetry. All conclusions are based exclusively on experimental facts.
Pairing Correlations are studied numerically in the hole-doped spin-fermion model for cuprates. Simulations performed on up to 12x12 clusters provide robust indications of D-wave superconductivity away from half-filling. The pairing correlations are the strongest in the direction perpendicular to the dynamic stripe-like inhomogeneities that appear in the ground state at some densities. An optimal doping, where the correlations reach a maximum value, was observed at about 25% doping, in qualitative agreement with hight T_{c} cuprates' experiments. On the other hand, pairing correlations are sup…
Kinematic constraint arising in the case of superconducting pairing with large momentum results in a cutoff of the screened Coulomb potential excluding large momentum transfers. This leads to a pairing potential oscillating in the real space that ensures a rise of bound singlet pairs. In multilayer cuprates, there is strong Coulomb interaction between particles composing the pair not only in the same cuprate layer but in the neighboring layers as well. In the framework of such a scenario, we explain a universal dependence of the superconducting transition temperature on the number of layers in…
We compare the one-loop functional renormalization group results for the cuprates and the iron pnictides. Interestingly a coherent picture suggesting that antiferromagnetic correlation causes pairing for both materials emerges.
We propose a microscopic theory of superconductivity for systems with strong electron correlations such as cuprates in the framework of the extended Hubbard model where the intersite Coulomb repulsion and electron-phonon interaction are taken into account. The Dyson equation for the normal and pair Green functions for the Hubbard operators (HOs) is derived. Due to the unconventional commutation relations for the HOs, a specific kinematical interaction of electrons with spin and charge fluctuations with a large coupling constant of the order of the kinetic energy of electrons $W$ emerges that r…
Tunneling and inelastic neutron scattering (INS) measurements in cuprates are discussed. There is a clear discrepancy among energy-gap values for different 90 K cuprates, inferred from tunneling measurements. By using the phase diagram of hole-doped cuprates we interpret tunneling measurements in 90 K cuprates and INS data in YBCO.
Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism -- based on local screening effects -- by which the oxygen dopants do modify the electronic parameters within the CuO_2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.
We report a scaling relation between $ρ_s(0)$ and the product of the pseudogap temperature $T^{*}$, $σ_{\rm DC}$ and $T_c$, with $T^{*}$ rescaled by the maximum transition temperature $T_c^{\max}$, which holds universally in the entire doping range for the hole-doped cuprates.
The phase diagram of order parameters for pairing and phase coherence in hole-doped cuprates is discussed. By examining carefully some recent inelastic neutron scattering data obtained on hole-doped cuprates and heavy fermion compound UPd2Al3 in which the superconductivity is mediated by spin fluctuations, we conclude that the coherent gap in hole-doped cuprates has most likely the magnetic origin and scales with Tc, on average, as 2Dc/kBTc = 5.4. We discuss a model of the superconductivity in hole-doped cuprates and the symmetries of two order parameters.
The real-space localized hole pair is constructed in the Cu-O plane of the hole-doped cuprate superconductors. We prove analytically and numerically that two electrons, due to the nearest-neighbor Coulomb repulsive confinement effect, can be in pairing inside a single plaquette with the d-wave symmetry. The scenario supports the `no glue' pairing picture for the cuprates. Based on the scenarios, the physical origin of the Fermi pocket (or Fermi arc) and the two pseudogap behavior are provided. Our framework leads directly to a unified linear relationship between the pseudogap temperature T* an…
Giant and nil proximity effects and unconventional symmetry of cuprate superconductors are explained as a result of the strong Froehlich interaction of holes with c-axis polarised optical phonons acting together with an anisotropic nonlocal deformation potential.
A comparison of pairing properties in cuprates and nuclear matter is briefly discussed. Quartet (alpha-particle) condensation is a very important aspect of nuclear physics. The physics of the Hoyle state in 12 C will be outlined and its crucial role for the existence of life on earth explained.
Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.
We have computed alpha^2F's for the hole-doped cuprates within the framework of the one-band Hubbard model, where the full magnetic response of the system is treated properly. The d-wave pairing weight alpha^2F_d is found to contain not only a low energy peak due to excitations near (pi,pi) expected from neutron scattering data, but to also display substantial spectral weight at higher energies due to contributions from other parts of the Brillouin zone as well as pairbreaking ferromagnetic excitations at low energies. The resulting solutions of the Eliashberg equations yield transition temper…
We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the hole-doped cuprates and mixed quantum mechanically with pairs of them (Cooper pairs). Superconductivity occurring at the transition temperature T_c is the long-range, d-wave symmetry phase coherence of these Cooper pairs. Fluctuations necessarily associated with incipient long-range superconducting order have a generic large distance behaviour near T_c. We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that features observed in Angle Resolved…
Superconductivity originates from the coupling between charge carriers and bosonic excitations of either phononic or electronic origin. Identifying the most relevant pairing glue is a key step towards a clear understanding of the unconventional superconductivity. Here, by applying the ultrafast optical spectroscopy on the electron-doped cuprates La$_{1.9}$Ce$_{0.1}$CuO$_{4\pmδ}$, we discern a bosonic mode of electronic origin that has the strongest coupling with the charge carriers near $T_c$. We argue that this mode is associated with the two-dimensional antiferromagnetic spin fluctuations, a…
It is found that the carriers of the high-T_c cuprates are polaron-like "stripons" carrying charge and located in stripe-like inhomogeneities, "quasi-electrons" carrying charge and spin, and "svivons" carrying spin and lattice distortion. This is shown to result in the observed anomalous spectroscopic properties of the cuprates. The AF/stripe-like inhomogeneities result from the Bose condensation of the svivon field, and the speed of their dynamics is determined by the width of the double-svivon neutron-resonance peak. Pairing results from transitions between pair states of stripons and quasi-…
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 study optimally doped Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+δ}$ (Bi2212) using angle-resolved two-photon photoemission spectroscopy. Three spectral features are resolved near 1.5, 2.7, and 3.6 eV above the Fermi level. By tuning the photon energy, we determine that the 2.7-eV feature arises predominantly from unoccupied states. The 1.5- and 3.6-eV features reflect unoccupied states whose spectral intensities are strongly modulated by the corresponding occupied states. These unoccupied states are consistent with the prediction from a cluster perturbation theory based on the sing…
Evidence for strong electron-phonon coupling in high-Tc cuprates is reviewed, with emphasis on the electron and phonon spectral functions. Effects due to the interplay between the Coulomb and electron-phonon interactions are studied. For weakly doped cuprates, the phonon self-energy is strongly reduced due to correlation effects, while there is no corresponding strong reduction for the electron self-energy. Polaron formation is studied, focusing on effects of Coulomb interaction and antiferromagnetic correlations. It is argued that experimental indications of polaron formation in undoped cupra…
Superconducting transition temperature is calculated for differently doped bilayer cuprates. Superexchange is assumed to be the dominating mechanism of high-temperature superconductivity, but the contribution from the phonon potential is not negligible, which qualitatively explains the observed weak isotopic effect. The calculated value 2$Δ_{max}/k_B T_C \simeq 4.5$ is close to the experiment in the case of optimum doping.
A more extended low density region of coexisting uniform antiferromagnetism and d-wave superconductivity has been reported in multilayer cuprates, when compared to single or bilayer cuprates. This coexistence could be due to the enhanced screening of random potential modulations in inner layers or to the interlayer Heisenberg and Josephson couplings. A theoretical analysis using a renormalized mean field theory, favors the former explanation. The potential for an improved determination of the antiferromagnetic and superconducting order parameters in an ideal single layer from zero field NMR an…
The normal and pairing self-energies are the microscopic quantities which reflect and characterize the underlying interaction in superconductors. The momentum and frequency dependence of the self-energies, therefore, provides the experimental criteria which can single out the long sought-after pairing interaction among many proposed ideas. This line of research to pin down the pairing interaction for the cuprate superconductors has been carried out with some success by analyzing the momentum distribution curves of laser angle-resolved photo-emission spectroscopy (ARPES) data. Some progress and…
A grand challenge in many-body quantum physics is to explain the apparent connection between quantum criticality and high-temperature superconductivity in the cuprates and similar systems, such as the iron pnictides and chalcogenides. Here we argue that the quantum-critical regime plays an essential role in activating a strong-pairing mechanism: although pairing bosons create a symmetry-breaking instability which suppresses pairing, the combination of these broken-symmetry states within the critical regime can restore this symmetry for the paired quasiparticles. This condition is shown to be m…
We re-analyzed the issue whether the resonance peak observed in neutron scattering experiments on the cuprates is an exciton, a π-resonance, or a magnetic plasmon. We considered a toy model with on-cite Hubbard U and nearest-neighbor interactions in both charge and spin channels. We found that the resonance is predominantly an exciton, even if magnetic interaction is absent and d-wave pairing originates from attractive density-density interaction. Our results indicate that one cannot distinguish between spin and charge-mediated pairing interactions by just looking at the resonance peak in the …
A strategy to enhance d-wave superconducting correlations is proposed based on our numerical study for correlated electron models for high-Tc cuprates. We observe that the pairing is enhanced when the single-electron level around (pi,0) is close to the Fermi level E_F, while the d-wave pairing interaction itself contains elements to disfavor the pairing due to shift of the (pi,0)-level. Angle-resolved photoemission results in the cuprates are consistently explained in the presence of the d-wave pairing interaction. Our proposal is the tuning of the (pi,0)-level under the many-body effects to E…
We consider the evolution of d-wave pairing, mediated by nearly critical spin fluctuations, with the coupling strength. We show that the onset temperature for pairing, T*, smoothly evolves between weak and strong coupling, passing through a broad maximum at intermediate coupling. At strong coupling, T* is of order the magnetic exchange energy J. We argue that for all couplings, pairing is confined to the vicinity of the Fermi surface. We also find that thermal spin fluctuations only modestly reduce T*, even at criticality, but they substantially smooth the gap anisotropy. The latter evolves wi…
There is a multiplicity of charge ordered, pairing-based or pair density wave theories of the cuprate pseudogap, albeit arising from different microscopic mechanisms. For mean field schemes (of which there are many) we demonstrate here that they have precise implications for two body physics in the same way that they are able to address the one body physics of photoemission spectroscopy. This follows because the full vertex can be obtained exactly from the Ward-Takahashi identity. As an illustration, we present the spin response functions, finding that a recently proposed pair density wave (Am…
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing correlations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Green's function in the particle-particle channel to determine the transit…
We apply the spin-fermion model to study the normal state and pairing instability in electron-doped cuprates near the antiferromagnetic QCP. Peculiar frequency dependencies of the normal state properties are shown to emerge from the self-consistent equations on the fermionic and bosonic self-energies, and are in agreement with experimentally observed ones. We argue that the pairing instability is in the $d_{x^{2}-y^{2}}$ channel, as in hole-doped cuprates, but theoretical $T_{c}$ is much lower than in the hole-doped case. For the same hopping integrals and the interaction strength as in hole-d…
The issues of single particle coherence and its interplay with singlet pairing are studied within the slave boson gauge theory of a doped Mott insulator. Prior work by one of us (T. Senthil, arXiv:0804.1555) showed that the coherence scale below which Landau quasiparticles emerge is parametrically lower than that identified in the slave boson mean field theory. Here we study the resulting new non-fermi liquid intermediate temperature regime characterized by a single particle scattering rate that is linear in temperature ($T$). In the presence of a d-wave pair amplitude this leads to a pseudoga…
A microscopic theory of superconductivity is formulated within an effective $p$-$d$ Hubbard model for a CuO2 plane. By applying the Mori-type projection technique, the Dyson equation is derived for the Green functions in terms of Hubbard operators. The antiferromagnetic exchange caused by interband hopping results in pairing of all carries in the conduction subband and high Tc proportional to the Fermi energy. Kinematic interaction in intraband hopping is responsible for the conventional spin-fluctuation pairing. Numerical solution of the gap equation proves the d-wave gap symmetry and defines…
We develop Ginzburg-Landau approach to the problem of superconducting pairing with large momentum under screened Coulomb repulsion (eta_K-pairing). Two-component order parameter arising in this scheme can be associated with charge and orbital current degrees of freedom of the relative motion of eta_K-pair corresponding to superconducting and orbital antiferromagnetic ordered states, respectively. All basic features of the phase diagram of cuprate superconductors result directly from the eta_K-pairing concept.
We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some $T$ range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermio…
The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation between linear resistivity and Tc is found in organic superconductors, for which pairing is known to come from fluctuations of a nearby antiferromagnetic phase, and in pnictide superconductors, for which an antiferromagnetic scenario is also likely.…
The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and three-dimensional media, and the Umklapp processes are shown to be crucial in determining the spectrum of the density fluctuations (especially for the two-dimensional systems). This and other standard sum rules can be used in conjunction with experimental spectroscopies (electron-energy loss spectroscopy, optical ellipsometry, etc.) to analyse changes of the electron-…
A system of self-consistent integral equations for the superconducting gap is formulated and solved taking account of the instability of the normal phase of bilayered cuprates against charge-density waves. The critical parameters are calculated as a function of the wave vector, temperature, and doping index. It is found that the region in which superconductivity coexists with d-type charge-density waves depends strongly on the doping index. The effective energy-gap parameter, determined as the interval between the peaks of the density of states, can have a local minimum at temperatures T$<$T$_…
Fermionic atoms in 2D optical lattices and electrons in HTc cuprates may both be described by the Hubbard model. However, if Coulomb frustration is responsible for the striped phases in 2D cuprates the phase diagrams will differ markedly. Two representative scenarios are described by a simple stripe model without phase separation and a mean field model with phase separation in the absence of Coulomb frustration. When Coulomb frustrated both models display antiferromagnetism (AF) and stripe phases with d-wave superfluidity, whereas neutral atoms in optical lattices will only do so in the stripe…
Recently, machine learning was applied to extract both the normal and the anomalous components of the self-energy from photoemission data at the antinodal points in Bi-based cuprate high-temperature superconductors [Y. Yamaji {\it et al.}, arXiv:1903.08060]. It was argued that both components do show prominent peaks near 50 meV, which hold information about the pairing glue, but the peaks are hidden in the actual data, which measure only the total self-energy. We analyze the self-energy within an effective fermion-boson theory. We show that soft thermal fluctuations give rise to peaks in both …
In the underdoped high temperature superconductors, instead of a complete Fermi surface above Tc, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near E_F behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is hard to reconcile with a competing order parameter, but is consistent with pairing without condensation.
Using the t-J Hamiltonian of U(1) slave-boson symmetry, bose condensation is discussed by showing the occurrence of symmetry breaking in the hole doped high $T_c$ cuprates. The symmetry breaking is shown to take place with the d-wave hole pairing, but not with the s-wave hole pairing. Based on a derived supersymmetry Hamiltonian we find that there exists a possibility of supersymmetry conditions in association with the pairing order parameters of both spinon and holon.
We analyze optical spectra of high temperature superconductors using a minimal model of electrons coupled to bosons. We consider the marginal Fermi liquid theory and the spin fluctuation theory, as well as a histogram representation of the bosonic spectral density. We find that the two theories can both be used to describe the experimental data provided that we allow for an additional scattering channel with an energy of 55 meV.
We study the effect of Coulomb repulsion between oxygen holes on the London penetration depth $λ$ based on the concept of spin-polaron nature of Fermi quasiparticles in cuprates superconductors. It is shown that for the generally accepted values of the parameters of the spin-fermion model, taking into account the Coulomb interaction, both the one-site Hubbard $U_p$ and interaction between the holes on next-nearest-neighbor oxygen ions $V_2$, allows one to achieve a much better agreement of the calculated temperature dependencies of the value $λ^{-2}$ with the experimental data in La$_{2-x}$Sr$…
We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level.
We analyze the superconducting state and the c-axis charge dynamics of cuprates using a charged ordered bilayer superlattice model in which pairing is supported by inter-layer Coulomb energy gain. The superlattice nature of high temperature superconductivity is experimentally suggested by the smallness of the coherent length ξ= 10 to 30 A which is comparable with a width of a 4X4 to 8X8 square supercell lattice layer. The temperature induced 2D-3D quantum phase transition of the hole-content is also studied. Pair condensation leads to the sharp decrease of the normal state c-axis anisotropy of…
The extended $t-J$ model is theoretically studied, in the context of hole underdoped cuprates. Based on results obtained by recent numerical studies, we identify the mean field state having both the antiferromagnetic and staggered flux resonating valence bond orders. The random-phase approximation is employed to analyze all the possible collective modes in this mean field state. In the static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime, we obtain the effective superconducting interaction between the doped holes at the small pockets located around $\bm{k}= (\pm π/2, …
We propose a microscopical theory of superconductivity in CuO$_2$ layer within the effective two-band Hubbard model in the strong correlation limit. By applying a projection technique for the matrix Green function in terms of the Hubbard operators, the Dyson equation is derived. It is proved that in the mean-field approximation d-wave superconducting pairing mediated by the conventional exchange interaction occurs. Allowing for the self-energy corrections due to kinematic interaction, a spin-fluctuation d-wave pairing is also obtained. $T\sb{c}$ dependence on the hole concentration and $\bf k$…
We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order paramete…
In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional copper-oxide chain Ba$_{2-x}$Sr$_x$CuO$_{3+δ}$. Yet, it is unclear how this strong near-neighbor attraction $V$ influences the superconductivity pairing in the compound. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion $U>0$ and attra…
