Competition between antiferromagnetism and superconductivity in high-Tc cuprates

Pseudogap in electron-doped cuprates: Strong correlation leading to band splitting

The pseudogap phenomena have been a long-standing mystery of the cuprate high-temperature superconductors. The pseudogap in the electron-doped cuprates has been attributed to band folding due to antiferromagnetic (AFM) long-range order or short-range correlation. We performed an angle-resolved photoemission spectroscopy study of the electron-doped cuprates Pr1.3-xLa0.7CexCuO4 showing spin-glass, disordered AFM behaviors, and superconductivity at low temperatures and, by measurements with fine momentum cuts, found that the gap opens on the unfolded Fermi surface rather than the AFM Brillouin zone boundary. The gap did not show a node, following the full symmetry of the Brillouin zone, and its magnitude decreased from the zone-diagonal to (π,0) directions, opposite to the hole-doped case. These observations were reproduced by cluster dynamical-mean-field-theory calculation, which took into account electron correlation precisely within a (CuO2)4 cluster. The present experimental and theoretical results are consistent with the mechanism that electron or hole doping into a Mott insulator creates an in-gap band that is separated from the upper or lower Hubbard band by the pseudogap.

Charge stripe manipulation of superconducting pairing symmetry transition

Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods ( P ) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period P , which is variable in different real material systems, could dictate the pairing symmetries-d wave for P ≥ 4 , s and d waves for P ≤ 3 . In the latter, tuning hole doping and charge-stripe amplitude can trigger a d-s wave transition and magnetic-correlation shift, where the d-wave state converts to a pairing-density wave state, competing with the s wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of P = 3 for the phase transition. In general, our findings offer important insights into the differences in the superconducting pairing mechanisms across many P -dependent superconducting systems, highlighting the decisive role of charge stripe.

Enhancedd-wave pairing in the two-dimensional Hubbard model with periodically modulated hopping amplitudes

Utilizing determinant quantum Monte Carlo algorithm, the evolution of thed-wave pairing in the Hubbard model on the square lattice tuned by the periodically modulated hopping amplitudes is studied. The hopping amplitudes are homogeneous in thexˆ-direction, while in theyˆ-direction the hopping amplitudes are modulated with periodP, wherety=t+dt,ty'=t-(P-1)dt, and the modulation periodPequals 2, 3 and 4 lattice spacings. The latter two modulation periods are motivated by the observation of period-3 and period-4 stripe order in cuprate superconductors. For all the periodsP, we find that the modulated hopping inhomogeneity enhances thed-wave pairing and an optimal inhomogeneity exists.

Ground-state phase diagram of the t-t'-J model

We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

Superconductivity in the three-band model of cuprates: nodal direction characteristics and influence of intersite interactions

The three-band Emery model is applied to study the selected principal features of thed-wavesuperconducting phase in the copper-based compounds. The electron-electron correlations are taken into account by the use of the diagrammatic expansion of the Guztwiller wave function (DE-GWF method). The nodal Fermi velocity, Fermi momentum, and effective mass are all determined in the paired state and show relatively good agreement with the available experimental data, as well as with the corresponding single-band calculations. Additionally, the influence of the next-nearest neighbor oxygen-oxygen hopping and intersite Coulomb repulsion terms on the superconducting phase is analyzed.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Correlation-Driven Charge Order in a Frustrated Two-Dimensional Atom Lattice

We thoroughly examine the ground state of the triangular lattice of Pb on Si(111) using scanning tunneling microscopy and spectroscopy. We detect electronic charge order, and disentangle this contribution from the atomic configuration which we find to be 1-down-2-up, contrary to previous predictions from density functional theory. Applying an extended variational cluster approach we map out the phase diagram as a function of local and nonlocal Coulomb interactions. Comparing the experimental data with the theoretical modeling leads us to conclude that electron correlations are the driving force of the charge-ordered state in Pb/Si(111). These results resolve the discussion about the origin of the well-known 3×3 reconstruction. By exploiting the tunability of correlation strength, hopping parameters, and band filling, this material class represents a promising platform to search for exotic states of matter, in particular, for chiral topological superconductivity.

Unconventional superconductivity in generalized Hubbard model: role of electron-hole symmetry breaking terms

We investigate the effect of the electron-hole (e-h) symmetry breaking on d-wave superconductivity induced by non-local effects of correlations in the generalized Hubbard model. The symmetry breaking is introduced in a two-fold manner: by the next-to-nearest neighbor hopping of electrons and by the charge-bond interaction-the off-diagonal term of the Coulomb potential. Both terms lead to a pronounced asymmetry of the superconducting order parameter. The next-to-nearest neighbor hopping enhances superconductivity for h-doping, while diminishes it for e-doping. The charge-bond interaction alone leads to the opposite effect and, additionally, to the kinetic-energy gain upon condensation in the underdoped regime. With both terms included, with similar amplitudes, the height of the superconducting dome and the critical doping remain in favor of h-doping. The influence of the charge-bond interaction on deviations from [Formula: see text] symmetry of the shape of the gap at the Fermi surface in the momentum space is briefly discussed.

An organizing principle for two-dimensional strongly correlated superconductivity

Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature , the maximum of the condensation energy as a function of doping, the correlation between maximum and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

Orbital nematic order and interplay with magnetism in the two-orbital Hubbard model

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturing symmetry broken magnetic and orbitally ordered phases. Both approaches show that the electron and hole doping affect the two orders differently. While hole doping tends to suppress both magnetism and orbital ordering, the electron doping suppresses magnetism faster. Crucially, we find a realistic parameter regime for moderate electron doping that stabilizes orbital nematicity in the absence of long-range antiferromagnetic order. This is reminiscent of the non-magnetic orbital nematic phase observed recently in FeSe and a number of iron pnictide materials and raises the possibility that at least in some cases, the observed electronic nematicity may be primarily due to orbital rather than magnetic fluctuations.

Nodeless superconducting phase arising from a strong (π, π) antiferromagnetic phase in the infinite-layer electron-doped Sr(1-x)La(x)CuO2 compound

The asymmetry between electron and hole doping remains one of the central issues in high-temperature cuprate superconductivity, but our understanding of the electron-doped cuprates has been hampered by apparent discrepancies between the only two known families: Re(2-x)Ce(x)CuO4 and A(1-x)La(x)CuO2. Here we report in situ angle-resolved photoemission spectroscopy measurements of epitaxially stabilized Sr(1-x)La(x)CuO2 thin films synthesized by oxide molecular-beam epitaxy. Our results reveal a strong coupling between electrons and (π, π) antiferromagnetism that induces a Fermi surface reconstruction which pushes the nodal states below the Fermi level. This removes the hole pocket near (π/2, π/2), realizing nodeless superconductivity without requiring a change in the symmetry of the order parameter and providing a universal understanding of all electron-doped cuprates.

Strong coupling superconductivity, pseudogap, and Mott transition

An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

Considerations on the mechanisms and transition temperatures of superconductivity induced by electronic fluctuations

An overview of the momentum and frequency dependence of effective electron-electron interactions which favor electronic instability to a superconducting state in the angular-momentum channel ℓ and the properties of the interactions which determine the magnitude of the temperature T(c) of the instability is provided. Interactions induced through exchange of electronic fluctuations of spin density, charge density or current density are considered. Special attention is paid to the role of quantum-critical fluctuations (QCFs) including pairing due to their virtual exchange as well as de-pairing due to inelastic scattering. Additional insight is gained by reviewing empirical data and theory specific to superfluidity in liquid He(3), superconductivity in some of the heavy-fermion compounds, in cuprates, in pncitides and the valence skipping compound. The physical basis for the following observation is provided: the ratio of the maximum T(c) to the typical phonon frequency in phonon induced s-wave superconductivity is O(10(-1)); the ratio of p-wave T(c) to the renormalized Fermi energy in liquid He(3), a very strongly correlated Fermi liquid near its melting pressure, is only O(10(-3)); in the cuprates and the heavy fermions where d-wave superconductivity occurs in a region governed by QCFs, this ratio rises to O(10(-2)). These discussions also suggest factors important for obtaining higher T(c). Experiments and theoretical investigations are suggested to clarify the many unresolved issues.

Correlation-induced Suppression of Bilayer Splitting in High-Tc Cuprates: A Variational Cluster Approach

We carry out a theoretical study of the bilayer single-band Hubbard model in the undoped and in the superconducting phases by means of the variational cluster approach. In particular, we focus on the splitting between the "bonding" and "antibonding" bands induced by the interlayer hopping, as well as its interplay with strong correlation effects. We find that the splitting is considerably suppressed in both the normal and superconducting phases, in qualitative agreement with experiments on Bi2Sr2CaCu2O8+δ . In addition, in the superconducting phase, the shape of the splitting in k space is modified by correlations.

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping, h. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is 2/h. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolve into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.

Mott physics and topological phase transition in correlated dirac fermions

We investigate the interplay between the strong correlation and the spin-orbit coupling in the Kane-Mele-Hubbard model and obtain the qualitative phase diagram via the variational cluster approach. We identify, through an increase of the Hubbard U, the transition from the topological band insulator to either the spin liquid phase or the easy-plane antiferromagnetic insulating phase, depending on the strength of the spin-orbit coupling. A nontrivial evolution of the bulk bands in the topological quantum phase transition is also demonstrated.

Evaluation of the two-particle propagator for the Hubbard model with the help of the Hubbard-I approximation

The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for the Hubbard model on a two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada (2007 J. Phys. Soc. Japan 76 113708) in the limit of strong electron-electron interaction. The Hubbard-I predictions are in good qualitative agreement with the Monte Carlo results. In particular, d-wave correlations decay as cr( - 3) ('free-electron' behaviour) if the separation r exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates the coefficient c by a factor of about 3. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of r.

From underdoped to overdoped cuprates: two quantum phase transitions

Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T(c) cuprates' phase diagram. There are at least two distinct proposals on the critical concentration and its physical origin. The first one is associated with the pseudogap formation for p < p, with p≈0.2. The other relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p(opt)≈0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.

Coexistence of the antiferromagnetic and superconducting order and its effect on spin dynamics in electron-doped high-T(c) cuprates

In the framework of the slave-boson approach to the t-t'-t''-J model, it is found that for electron-doped high- T(c) cuprates, the staggered antiferromagnetic (AF) order coexists with the superconducting (SC) order in a wide doping level ranged from underdoped to nearly optimally doped at the mean-field level. In the coexisting phase, it is revealed that the spin response is commensurate in a substantial frequency range below a crossover frequency ω(c) for all dopings considered, and it switches to the incommensurate structure when the frequency is higher than ω(c). This result is in agreement with the experimental measurements. Comparison of the spin response between the coexisting phase and the pure SC phase with a d(x(2)-y(2))-wave pairing plus a higher harmonics term (DP+HH) suggests that the inclusion of the two-band effect is important to consistently account for both the dispersion of the spin response and the non-monotonic gap behavior in the electron-doped cuprates.

Strong antiferromagnetic correlation effects on the momentum distribution function of the Hubbard model

Strong antiferromagnetic correlations can radically change the behavior of an otherwise paramagnetic system, inducing anomalous effects in the single particle properties and driving the behavior of spin-spin response functions. In order to investigate such physics, we have studied the momentum distribution function of the two-dimensional Hubbard model at low doping, low temperatures and high values of the on-site Coulomb repulsion. The interpretation of the results has greatly benefited from the parallel analysis of the filling, temperature and interaction dependences of the spin-spin correlation function, the antiferromagnetic correlation length and the pole of the spin-spin propagator. On reducing doping or temperature and on increasing the interaction strength, the correlations become stronger and stronger and the Fermi surface develops hole and electron pockets and shows a dual nature (small-large).

Competition between antiferromagnetic and superconducting states, electron-hole doping asymmetry, and fermi-surface topology in high temperature superconductors

We investigate the asymmetry between electron and hole doping in a 2D Mott insulator and the resulting competition between antiferromagnetism (AFM) and d-wave superconductivity (SC), using variational Monte Carlo calculations for projected wave functions. We find that key features of the T=0 phase diagram, such as critical doping for SC-AFM coexistence and the maximum value of the SC order parameter, are determined by a single parameter eta which characterizes the topology of the "Fermi surface" at half filling defined by the bare tight-binding parameters. Our results give insight into why AFM wins for electron doping, while SC is dominant on the hole-doped side. We also suggest using band structure engineering to control the eta parameter for enhancing SC.

Hubbard model on the triangular lattice: spiral order and spin liquid

We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion U (or equivalently increasing pressure) we go from a phase with long-range, three-sublattice, spiral magnetic order, to a nonmagnetic Mott insulating phase--a spin liquid--and then, for U less or similar to 6.7t, to a metallic phase. Clusters of sizes 3, 6, and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at U = 8t, but to a spiral order at U greater or similar to 12.

Nodal-antinodal dichotomy and the two gaps of a superconducting doped Mott insulator

We study the superconducting state of the hole-doped two-dimensional Hubbard model using cellular dynamical mean-field theory, with the Lanczos method as impurity solver. In the underdoped regime, we find a natural decomposition of the one-particle (photoemission) energy gap into two components. The gap in the nodal regions, stemming from the anomalous self-energy, decreases with decreasing doping. The antinodal gap has an additional contribution from the normal component of the self-energy, inherited from the normal-state pseudogap, and it increases as the Mott insulating phase is approached.

Superconducting gap in the hubbard model and the two-gap energy scales of high-T{c} cuprate superconductors

Recent experiments (angle-resolved photoemission spectroscopy and Raman) suggest the presence of two distinct energy gaps in high-temperature superconductors (HTSC), exhibiting different doping dependences. The 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. The antinodal gap 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 behavior is given which emphasizes the crucial role of spin fluctuations in the pairing mechanism.

Antiferromagnetism and superconductivity in layered organic conductors: Variational cluster approach

The kappa-(ET)2X layered conductors (where ET stands for BEDT-TTF) are studied within the dimer model as a function of the diagonal hopping t' and Hubbard repulsion U. Antiferromagnetism and d-wave superconductivity are investigated at zero temperature using variational cluster perturbation theory (VCPT). For large U, Néel antiferromagnetism exists for t' < t(c2)', with t(c2)' approximately 0.9. For fixed t', as U is decreased (or pressure increased), a d(x2-y2) superconducting phase appears. When U is decreased further, then a d(xy) order takes over. There is a critical value of t(c1)' approximately 0.8 of t' beyond which the AF and dSC phases are separated by the Mott disordered phase.

Fluctuation-exchange study of antiferromagnetism in disordered electron-doped cuprate superconductors

On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of the antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can consistently account for the experimental measurements.

Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors

We study the Mott transition, antiferromagnetism, and superconductivity in layered organic conductors using the cellular dynamical mean-field theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for t'/t=0.3-0.7 or between a nonmagnetic Mott insulator (spin liquid) and a metal for t'/t>or=0.8, in agreement with experiments on layered organic conductors including kappa-(ET)2Cu2(CN)3. These phases are separated by a strong first-order transition. The phase diagram gives much insight into the mechanism for -wave superconductivity. Two predictions are made.

Structure of the pairing interaction in the two-dimensional Hubbard model

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.

Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model

The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the dynamical cluster approximation and quantum Monte Carlo simulations as a cluster solver. Because of the nonlocality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.