We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature $T_c$ of the superfluid transition, is often interpreted in terms of preformed, uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood in terms of local excitations which lead to a splitting of the quasiparticle peak for sufficiently large interaction. This effect becomes prominent at intermediate and high temperatures when the quantum mechanical hopping is incoherent. We clarify the existence of a conjectured temperature below which pseudogap physics is expected to occur. Our results are based on approximating the physics of the three-dimensional Hubbard model by dynamical mean field theory calculations and a momentum independent self-energy. Our predictions can be tested with ultracold atoms in optical lattices with currently available temperatures and spectroscopic techniques.
We compute unbiased spectral functions of the two-dimensional Hubbard model by extrapolating Green functions, obtained from determinantal quantum Monte Carlo simulations, to the thermodynamic and continuous time limits. Our results clearly resolve the pseudogap at weak to intermediate coupling, originating from a momentum selective opening of the charge gap. A characteristic pseudogap temperature T*, determined consistently from the spectra and from the momentum dependence of the imaginary-time Green functions, is found to match the dynamical mean-field critical temperature, below which antife…
We study the pseudogaps in the spectra of the half-filled 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. A charge pseudogap, accompanied by non-Fermi liquid behavior in the self energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling.
It is shown that in the two-dimensional attractive Hubbard model, the mean-field phase transition is replaced by a renormalized classical regime of fluctuations where a pseudogap opens up in the single-particle spectral weight. It is argued that this pseudogap and precursors of the ordered state quasiparticles can occur only in strongly anisotropic quasi two-dimensional materials. This precursor phenomenon differs from preformed local pairs. Furthermore, while critical antiferromagnetic fluctuations would also lead to a pseudogap in the repulsive model, there are some important differences bet…
The opening of a critical-fluctuation induced pseudogap (or precursor pseudogap) in the one-particle spectral weight of the half-filled two-dimensional Hubbard model is discussed. This pseudogap, appearing in our Monte Carlo simulations, may be obtained from many-body techniques that use Green functions and vertex corrections that are at the same level of approximation. Self-consistent theories of the Eliashberg type (such as the Fluctuation Exchange Approximation) use renormalized Green functions and bare vertices in a context where there is no Migdal theorem. They do not find the pseudogap, …
The condensation energy and the specific heat jump of a two-dimensional Hubbard model, suitable to discuss high-$T_c$ superconductors, is studied. In this work, the Hubbard model is investigated by the Green's function method within a $n$-pole approximation, which allows to consider superconductivity with $d_{x^2-y^2}$-wave pairing. In the present scenario, the pseudogap regime emerges when the antiferromagnetic (AF) correlations become sufficiently strong to move to lower energies the region around of the nodal point $(π,π)$ on the renormalized bands. It is observed that above a given total o…
In this work the specific heat of a two-dimensional Hubbard model, suitable to discuss high-$T_c$ superconductors (HTSC), is studied taking into account hopping to first ($t$) and second ($t_2$) nearest neighbors. Experimental results for the specific heat of HTSC's, for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green's function method within a $n$-pole approximation. The specific heat is calculated on the pseudogap and on the superconducting regions. In the present scenario, …
Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are considered. The strong correlation between excitations on parallel neighboring bonds suggests bond singlet dime…
The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classic…
We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo Néel or spiral magnetic order below a density dependent transition temperature $T^*$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are applicable for a weak or moderate H…
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…
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…
One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak coupling regime using the non-selfconsistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real frequency axis. For temperatures sufficiently close to the superconducting transition temperature a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.
Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Notre Dame（圣母大学）
We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the Cellular Dynamical Mean Field Theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism th…
We show that antiferromagnetic spin-density wave order in the two-dimensional Hubbard model yields a drop of the charge carrier density as observed in recent transport measurements for cuprate superconductors in high magnetic fields upon entering the pseudogap regime. The amplitude and the (generally incommensurate) wave vector of the spin-density wave is obtained from dynamical mean-field theory (DMFT). An extrapolation of the finite temperature results to zero temperature yields an approximately linear doping dependence of the magnetic gap $Δ(p) \propto p^*-p$ in a broad doping range below t…
In the half-filled one-orbital Hubbard model on a square lattice, we find pseduogap features in the form of two-peak structures associated with the momentum-resolved spectral function, which exists within the temperature window $T_N \lesssim T \lesssim T^*$. $T^*$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window $T_N \lesssim T \lesssim T^*$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function rises on moving away from the point ($π/2, π/2$) along the normal state Fermi surface towards $(π, 0)$…
We describe a quantum simulator for the Hubbard--Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing, and Berezinskii--Kosterlitz--Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed: (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon i…
In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of functional derivative approaches to many-body theories. The first step of the approximation is based on a local field type ansatz. All physical quantities can be expressed as a function of double-occupancy (in addition to temperature and filling). Double-occupancy is determined without adjustable parameter by imposing the Pauli principle and a crucial sum-rule, mak…
We use microscopic Bogoliubov-de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.
A new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial sum-rules. More specifically, spin and charge susceptibilities are expressed, in a conserving approximation, as a function of two constant irreducible vertices whose values are found self-consistently. The Mermin-Wagner theorem in two dimensions is automatically satisfied. The effect of collective modes on single-particle properties is then obtained by a paramagnon-like formula that is consistent with …
We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster DMFT method, and focusing in particular on the role of non-local quantum fluctuations. We show that non-local quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.
Deviations from Fermi liquid behavior are well documented in the normal state of the cuprate superconductors, and some of these differences seem to be related to pre-transitional features appearing at temperatures above T$_c$. The observation of a pseudogap, e.g. in ARPES experiments, is a familiar example of this physics. One potential explanation for this behaviour involves preformed pairs with finite lifetimes existing in the normal state above T$_c$. In this way two characteristic temperatures can be established. A higher one T$^*$ at which pairs begin to form and the actual T$_c$ at which…
The influence of the Zeeman magnetic field ($h$) on the ground state evolution of superfluid properties from the weak coupling (BCS like) to the strong coupling limit of tightly bound local pairs (LP) with increasing attraction has been studied. The analysis was carried out within the spin-polarized attractive Hubbard model, for a fixed number of particles and a $d=3$ simple cubic lattice. The broken symmetry Hartree approximation was used. For strong attraction and in the dilute limit, the homogeneous magnetized superconducting phase (SC$_M$) was found in the $(h-|U|)$ and ($P-|U|$) diagrams.
High-Tc superconducting materials (HTSC) have anomalous properties such as the pseudo-gap or spin-gap etc., in Hall coefficient, 1/T1T and the density of states etc. First including effects of strong on-site repulsion between d-electrons at Cu-sites, we obtain quasi-particles with super-exchange interaction Js, whose band width tends to zero, i.e., the system goes to insulator, as the hole-doping rate tends to zero. The quasi-particles correspond to Zhang-Rice singlet states. Js larger than the band width combined with the 2-dimensional character of the system induces strong antiferro-magnetic…
We investigate the microscopic origin of the pseudogap in the weakly doped 2D Hubbard model using Quantum Monte Carlo within the dynamical cluster approximation. We compare our results with proposed scenarios for the pseudogap. All our numerical evidence is in favor of spin-charge separation as described in the resonating valence bond picture as the cause of the pseudogap behavior. Scenarios of "preformed pairs", the coupling of quasiparticles to antiferromagnetic spin-fluctuations and stripes are inconsistent with our results.
This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observe…
Extending the U(1) slave-rotor representation\cite{FG_SRR} of the repulsive Hubbard model, we propose an SU(2) slave-rotor decomposition for the attractive Hubbard model, where the SU(2) slave-rotor variables represent order parameter fluctuations associated with superconductivity and charge density wave. This decomposition method allows us to modify the standard Hartree-Fock mean field theory by incorporating order parameter fluctuations on an equal footing. Deriving an effective SU(2) slave-rotor action from the attractive Hubbard model, and analyzing it at the mean field level, we demonstra…
The topology of the Fermi surface of an extended $d-p$ Hubbard model is investigated using the Green's function technique in a n-pole approximation. The effects of the $d-p$ hybridization on the Fermi surface are the main focus in the present work. Nevertheless, the effects of doping, Coulomb interaction and hopping to second-nearest-neighbors on the Fermi surface, are also studied. Particularly, it is shown that the crossover from hole-like to electron-like Fermi surface (Lifshitz transition) is deeply affected by the $d-p$ hybridization. Moreover, the pseudogap present in the low doping regi…
We study the percolative superconducting transition as the density of randomly placed attractive centers grows in a host metal. Employing the Hubbard-Stratanovich transformation for the interaction and allowing for spatial, thermal fluctuations of the pairing field, we obtain real-space features of the transition from weak to strong coupling. Spectral and transport properties are studied in detail. BCS-BEC crossover is discussed in the context of site dilution of attractive centers.
The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. We use the Two-Particle Self-Consistent approach that satisfies crucial constraints such as the Mermin-Wagner theorem, the Pauli principle and sum rules in order to reach non-perturbative regimes. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The …
The origin of the pseudogap (PG) phase and superconducting behaviors in high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls formation, that carry Cooper/local-pair condensates inside their volumes. Unlike the baryonic Q-balls in supersymmetric standard model, the Euclidean Q-balls describe spin-/charge densities, that oscillate in Matsubara time, and are found in the 'nested' repulsive Hubbard model of high-Tc superconductors. Euclidean Q-balls arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of spin-/charge fl…
We present reliable many-body calculations for the t-t'-t''-U Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering and for the phase diagram.
Using the negative U Hubbard model we analyze normal state properties of a superconductor. In this model there exists a characteristic pairing temperature T_P above a superconducting critical temperature. Below T_P electrons start to form incoherent pairs. The fluctuations in charge and phase are precursors of charge density wave and superconductivity phases depending on band filling. They lead naturally to pseudogap opening in the density of states.
Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices, allow the study of an attractive Hubbard model for which the strength of the on site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of nu…
We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite latti…
The superfluid properties of the attractive Hubbard model in a Zeeman magnetic field, and in the weak coupling regime have been investigated. The temperature and magnetic field dependencies of the order parameter have been analyzed. Furthermore, the temperature vs. magnetic field and temperature vs. spin polarization phase diagrams for the 2D and 3D lattices have been obtained. For some parameters a reentrant transition has been found.
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.
The phase diagram of the attractive Hubbard model with spatially inhomogeneous interactions is obtained using a single site dynamical mean field theory like approach. The model is characterized by three parameters: the interaction strength, the active fraction (fraction of sites with the attractive interaction), and electron filling. The calculations indicate that in a parameter regime with intermediate values of interaction strength (compared to the bare bandwidth of the electrons), and intermediate values of the active fraction, "non-BCS" superconductivity is obtained. The results of this wo…
We propose a fully microscopic theory of the anomalous normal state of the attractive Hubbard model in the low-density limit that accounts for propagator renormalization. Our analytical conclusions, which focus on the thermodynamic instabilities contained in the self-consistent equations associated with our formulation, have been verified by our comprehensive numerical study of the same equations. The resulting theory is found to contain no transitions at non-zero temperatures for all finite lattices, and we have confirmed, using our numerical studies, that this behaviour persists in the therm…
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.
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff} can be mapped onto two XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422 and U<-4, singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in BaKBiO.
We have made a variational analysis on an evolution of superconductivity from weak to strong coupling regime. In contrast to a crossover without thermodynamic anomaly found in a dilute system, we show the existence of a quantum phase transition near half filling. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined and the quantum phase transition is an attractive version of the Mott transition.
We determine the magnetic field dependence of the pseudogap closing temperature T* within a precursor superconductivity scenario. Detailed calculations with an anisotropic attractive Hubbard model account for a recently determined experimental relation in BSCCO between the pseudogap closing field and the pseudogap temperature at zero field, as well as for the weak initial dependence of T* at low fields. Our results indicate that the available experimental data are fully compatible with a superconducting origin of the pseudogap in cuprate superconductors.
This short paper summarizes a calculational method for obtaining the dynamical properties of many-body theories formulated in terms of (unrenormalized) bare propagators (and more generally, in terms of meromorphic functions, or convolutions over meromorphic functions) to a very high accuracy. We demonstrate the method by applying it to a T-matrix theory of the attractive Hubbard model in two dimensions. We expand the pair propagator using a partial fraction decomposition, and then solve for the residues and pole locations of such a decomposition using a computer algebra system to an arbitraril…
The critical temperature for the attractive Hubbard model on a square lattice is determined from the analysis of two independent quantities, the helicity modulus, $ρ_s$, and the pairing correlation function, $P_s$. These quantities have been calculated through Quantum Monte Carlo simulations for lattices up to $18\times 18$, and for several densities, in the intermediate-coupling regime. Imposing the universal-jump condition for an accurately calculated $ρ_s$, together with thorough finite-size scaling analyses (in the spirit of the phenomenological renormalization group) of $P_s$, suggests th…
The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly wi…
Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping $δ^*$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite temperature critical endpoint of a first-order transition between a pseudogap phase with dominant singlet correlations and a…
We apply a wilsonian renormalization group approach to the continuum limit of the attractive $t-t'$ Hubbard model, taken when the Fermi level is at the Van Hove singularity of the density of states. The model has well-defined scaling properties and the effective couplings display an unbounded flow in the infrared. We determine the leading instabilities by computing the different response functions up to $t' = 0.5 t$. The phase diagram shows a large boundary between superconducting and charge-density-wave phases, that merge in a triple point with a phase separation instability. The latter is re…
A Dynamical Mean Field Theory analysis of the attractive Hubbard model is carried out. We focus on the normal state upon restricting to solutions where superconducting order is not allowed. Nevertheless a clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half-filling. The transition occurs between a Fermi liquid, stable for $U < U_c$, and an insulating bound pairs phase for $U > U_c$. The spectral function in the Fermi liquid phase is constituted by a low energy structure around the Fermi level (similar to the Kondo resonance of…
Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the Dynamical Mean Field Theory solution of a twofold-orbital degenerate Hubbard model with inverted Hund's rules on-site exchange, which favors local spin-singlet configurations. Close to the Mott insulator, which is a local version of a valence bond insulator, a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of the cuprates. The strongly correlated superconducting state has a larger Drude weight than the corresponding…
We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. …
The BCS-BEC crossover within the two-dimensional attractive Hubbard model is studied by using the Cellular Dynamical Mean-Field Theory both in the normal and superconducting ground states. Short-range spatial correlations incorporated in this theory remove the normal-state quasiparticle peak and the first-order transition found in the Dynamical Mean-Field Theory, rendering the normal state crossover smooth. For $U$ smaller than the bandwidth, pairing is driven by the potential energy, while in the opposite case it is driven by the kinetic energy, resembling a recent optical conductivity experi…
To understand the interplay of d-wave superconductivity and antiferromagnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homogeneous (coexisting superconducting and antiferromagnetic) state calculated a s a function of the band filling shows a region of of phase separation. The phase separation caused by the intersite attractive force leads to novel insights into salient features of the pseudogap phase diagram. In particular, the upper crossover curve can be identified with the phase separation boundar…
After providing a brief genealogy of our recently proposed model for High-Tc cuprates, we investigate the details of the microscopic mechanism that produces an attractive interaction between neighboring holes. We show that a peculiar arrangement of the $p_x$ and $p_y$ oxygen orbitals makes the mutual magnetic interaction of the holes with the localized copper ions to produce a net attractive interaction between themselves, which is responsible for the emergence of a superconducting phase. We also study the connection existing between the proposed pseudogap order parameter and the spectral dens…
We show that the extended attractive Hubbard model on a square lattice hosts a variety of superconducting phases, including exotic mixed-symmetry phases with $d_{x^2-y^2} + {\rm i} [s + d_{x^2+y^2}]$ and $ d_{x^2-y^2} + p_{x}$ symmetries, and a novel $p_x + {\rm i} p_y$ state. The calculations are performed within the mean-field Bogoliubov-deGennes (BdG) framework. The ground states of the BdG Hamiltonian are obtained via a minimization scheme that does not impose symmetry constraints on the superconducting solutions, hence allowing a mixing of $s$-, $p$- and $d$-wave order parameters. Our res…
In a recent preprint [arXiv:1803.04118v2] Chern and Barros report numerical simulations of the mean-field interaction quench dynamics, $U_i\to U_f$, of the attractive Hubbard model that confirm our earlier prediction [Europhys. Lett. 85, 20004 (2008), arXiv:0805.2798] of spontaneous eruption of spatial inhomogeneities in the post-quench state with periodically oscillating superconducting order. Chern and Barros attribute this instability with respect to spatial fluctuations to the large magnitude of the final Hubbard coupling $U_f$. We point out that this interpretation is inaccurate and discu…
