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

Mixed temperature-dependent order parameters in the extended Hubbard model

The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below T _c. Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.

Reentrants-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction

Spin-flip scattering from magnetic impurities has a strong pair-breaking effect ins-wave superconductors where increasing the concentration of impurities rapidly destroys superconductivity. For small Kondo temperatureTKthe destruction of superconductivity is preceded by the reentrant superconductivity at finite temperature rangeTc2 Collapse

Key Words

• Anderson lattice model
• dynamical mean field theory
• superconductivity

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Affiliation(s)

W V van Gerven Oei Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
D Tanasković Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

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Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters

We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.

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.

Hidden Fermionic Excitation Boosting High-Temperature Superconductivity in Cuprates

The dynamics of a microscopic cuprate model, namely, the two-dimensional Hubbard model, is studied with a cluster extension of the dynamical mean-field theory. We find a nontrivial structure of the frequency-dependent self-energies, which describes an unprecedented interplay between the pseudogap and superconductivity. We show that these properties are well described by quasiparticles hybridizing with (hidden) fermionic excitations, emergent from the strong electronic correlations. The hidden fermion enhances superconductivity via a mechanism distinct from a conventional boson-mediated pairing, and originates the normal-state pseudogap. Though the hidden fermion is elusive in experiments, it can solve many experimental puzzles.

Spatial correlations and the insulating phase of the high-T(c) cuprates: insights from a configuration-interaction-based solver for dynamical mean field theory

A recently proposed configuration-interaction-based impurity solver is used in combination with the single-site and four-site cluster dynamical mean field approximations to investigate the three-band copper oxide model believed to describe the electronic structure of high transition temperature copper-oxide superconductors. Use of the configuration interaction solver enables verification of the convergence of results with respect to the number of bath orbitals. The spatial correlations included in the cluster approximation substantially shift the metal-insulator phase boundary relative to the prediction of the single-site approximation and increase the predicted energy gap of the insulating phase by about 1 eV above the single-site result. Vertex corrections occurring in the four-site approximation act to dramatically increase the value of the optical conductivity near the gap edge, resulting in better agreement with the data. The calculations reveal two distinct correlated insulating states: the "magnetically correlated insulator," in which nontrivial intersite correlations play an essential role in stabilizing the insulating state, and the strongly correlated insulator, in which local physics suffices. Comparison of the calculations to the data places the cuprates in the magnetically correlated Mott insulator regime.

Photo-enhanced antinodal conductivity in the pseudogap state of high-Tc cuprates

A major challenge in understanding the cuprate superconductors is to clarify the nature of the fundamental electronic correlations that lead to the pseudogap phenomenon. Here we use ultrashort light pulses to prepare a non-thermal distribution of excitations and capture novel properties that are hidden at equilibrium. Using a broadband (0.5–2 eV) probe, we are able to track the dynamics of the dielectric function and unveil an anomalous decrease in the scattering rate of the charge carriers in a pseudogap-like region of the temperature (T) and hole-doping (p) phase diagram. In this region, delimited by a well-defined T*_neq(p) line, the photoexcitation process triggers the evolution of antinodal excitations from gapped (localized) to delocalized quasiparticles characterized by a longer lifetime. The novel concept of photo-enhanced antinodal conductivity is naturally explained within the single-band Hubbard model, in which the short-range Coulomb repulsion leads to a k-space differentiation between nodal quasiparticles and antinodal excitations.

The pseudogap phase exhibited by the cuprates is almost as enigmatic as superconductivity in these materials itself. A time-resolved study performed by Cilento et al. suggests that this state can be photoexcited into a transient non-equilibrium state that is more conductive than the equilibrium state.

Raman-scattering measurements and theory of the energy-momentum spectrum for underdoped Bi2Sr2CaCuO(8+δ) superconductors: evidence of an s-wave structure for the pseudogap

We reveal the full energy-momentum structure of the pseudogap of underdoped high-Tc cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B2g Raman response at finite energies in terms of a pseudogap appearing in the single-electron excitation spectra above the Fermi level in the nodal direction of momentum space. This result suggests an s-wave pseudogap (which never closes in the energy-momentum space), distinct from the d-wave superconducting gap. Recent tunneling and photoemission experiments on underdoped cuprates also find a natural explanation within the s-wave pseudogap scenario.

Superconductivity and the pseudogap in the two-dimensional Hubbard model

Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.

Two-particle response in cluster dynamical mean-field theory: formalism and application to the Raman response of high-temperature superconductors

A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman B(1g) and B(2g) scattering intensities of the two-dimensional Hubbard model in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the "two-magnon" peak characteristic of the Raman intensity of insulating parent compounds of high-T(c) copper oxide superconductors, and shows how it evolves to a quasiparticle response, as carriers are added. The method can be applied in any situation where a solution of equilibrium dynamical mean-field equations is feasible.

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang et al (2006 Phys. Rev. B 73 174501). This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons with experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.

Evolution of the dynamical pairing across the phase diagram of a strongly correlated high-temperature superconductor

We study the dynamics of the Cooper pairing across the T = 0 phase diagram of the two-dimensional Hubbard model, relevant for high-temperature superconductors, using a cluster extension of dynamical mean-field theory. We find that the superconducting pairing function evolves from an unconventional form in the overdoped region into a more conventional boson-mediated retarded form in the underdoped region of the phase diagram. The boson, however, promotes the rise of a pseudogap in the electron density of states rather than a superconducting gap as in the standard theory of superconductivity. We discuss our results in terms of Mott-related phenomena, and we show that they can be observed in tunneling experiments.

Valence bond glass theory of electronic disorder and the pseudogap state of high-temperature cuprate superconductors

We show that the low-energy fluctuations of the valence bond due to the superexchange are pinned by the electronic disorder from off-stoichiometric dopants, leading to a valence bond glass (VBG) pseudogap phase in underdoped high-T_{c} cuprates. The antinodal Fermi surface sections are gapped out, giving rise to a normal state Fermi arc whose length shrinks with underdoping. Below T_{c}, the superexchange interaction induces a d-wave superconducting gap that coexists with the VBG pseudogap. The evolution of the local and momentum-space spectroscopy with doping and temperature captures the salient properties of the pseudogap phenomena and the electronic disorder.

Coexistence of competing orders with two energy gaps in real and momentum space in the high temperature superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

Through a combined scanning tunneling microscopy and angle-resolved photoemission spectroscopy study, we report the observation of two distinct gaps (a small and a large gap) that coexist both in real space and in the antinodal region of momentum space, below the superconducting transition temperature (T_{c}) of Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}. We show that the small gap is associated with superconductivity. The large-gap persists above T_{c}, and seems linked to observed charge ordering. We find a strong correlation between the large and small gaps suggesting that they are affected by similar physical processes.

How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+delta

The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.

Effective masses in a strongly anisotropic fermi liquid

Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.