Mott gap excitations and resonant inelastic x-ray scattering in doped cuprates

Predictions are made for the momentum- and carrier-dependent degradation of the Mott gap upon doping in high-T(c) cuprates as would be observed in Cu K-edge resonant inelastic x-ray scattering (RIXS). The two-dimensional Hubbard model with second- and third-nearest-neighbor hopping terms has been studied by numerical exact diagonalization. Special emphasis is placed on the particle-hole asymmetry of the Mott gap excitations. We argue that the Mott gap excitations observed by RIXS are significantly influenced by the interaction between charge carriers and antiferromagnetic correlations.     

Theory of RIXS in strongly correlated electron systems: Mott gap excitations in cuprates

We theoretically examine the momentum dependence of resonant inelastic X-ray scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates based on the single-band Hubbard model with realistic parameter values. The spectrum is calculated by using the numerical diagonalization technique for finite-size clusters. We focus on excitations across the Mott gap and clarify spectral features coming from the excitations as well as the physics behind them. Good agreement between the theoretical and existing experimental results clearly demonstrates that the RIXS is a potential tool to study the momentum-dependent charge excitations in strongly correlated electron systems.     

Competing phases in the cuprates: Charge vs spin order

We have investigated magnetic and charge instabilities of the cuprates within the Gutzwiller approximation RPA (GA+RPA). Interestingly, in GA the dressed Hubbard U is not a single parameter, but has different forms in the spin and charge responses, with distinct doping dependencies. While there are a number of competing magnetic instabilities for hole-doped cuprates, we fail to find any purely electronic charge density waves. The dominant magnetic instabilities are associated with ‘double nesting’, and the phase diagrams are material dependent, with LSCO differing from other cuprates.     

Electronic excitations in hole-doped La1−xSrxMnO3 studied by resonant inelastic X-ray scattering

We report a resonant inelastic X-ray scattering (RIXS) study on perovskite manganese oxides La_1−xSr_xMnO₃ (x=0, 0.2, and 0.4) at Mn K-absorption edge. Hole-doping effect on the electronic excitations in the strongly correlated electron systems is elucidated by comparing with undoped LaMnO₃. The scattering spectra of metallic La_0.6Sr_0.4MnO₃ show that a salient peak appears in low energies indicating the persistence of the Mott gap. At the same time, the energy gap is partly filled by doping holes and the spectral weight shifts toward lower energies. Though the peak position of the excitations shows weak dispersion in momentum dependence, RIXS intensity changes as a function of the scattering angle (2θ), which is related to the anisotropy. Furthermore, anisotropic temperature dependence is observed in La_0.8Sr_0.2MnO₃ which shows a metal-insulator transition associated with a ferromagnetic transition. We consider that the anisotropy in the RIXS spectra is possibly attributed to the correlation of the orbital degrees of freedom. The anisotropy is large in LaMnO₃ with long-range orbital order, while it is small but finite in hole-doped La_1−xSr_xMnO₃ which indicates persistence of short-range orbital correlation.     

Evidence for two types of low-energy charge transfer excitations in Sr2CuO3

A comparative analysis of electron energy-loss spectroscopy (EELS) spectra for the 1D insulating cuprate Sr2CuO3 with transferred momentum q--> axially and radially to the chain axis allows one to elucidate the structure of the charge transfer gap in in-chain response. It is determined by the superposition of two types of excitations with different magnitudes of dispersion. The low-energy response with q--> radially to the chain direction, but yet within the plane of CuO4 plaquettes, exhibits also a dispersionless peak near 2 eV. The theoretical simulation of the EELS data using exact diagonalizations of an appropriate extended Hubbard Hamiltonian for relevant clusters requires the explicit consideration of low-lying oxygen 2p pi states within the CuO4 plaquette plane beyond the standard pd sigma extended Hubbard model widely used for cuprates with corner-shared CuO4 plaquettes.     

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.     

Operator projection theory for electron differentiation in underdoped cuprate superconductors

Metals approaching the Mott insulator generate a new hierarchy in the electronic structure accompanied by an electron differentiation with emergence of strongly momentum dependent structure, beyond the Mott-Hubbard, Brinkman-Rice and Slater pictures of the Mott transition. To consider such nonlinear phenomenon, we develop an analytic nonperturbative theory based on operator projections combined with a self-consistent treatment of the low-energy excitations. This reproduces the Hubbard bands, Mott gap, spin fluctuations, mass divergence, diverging charge compressibility, and strongly renormalized flat and damped dispersion similar to angle-resolved photoemission data in high-T_c cuprates. Electronic spectra show a remarkable similarity to numerical results.     

Strongly correlated s-wave superconductivity in the N-type infinite-layer cuprate

Quasiparticle tunneling spectra of the electron-doped ( n-type) infinite-layer cuprate Sr0.9La0.1CuO2 reveal characteristics that counter a number of common phenomena in the hole-doped ( p-type) cuprates. The optimally doped Sr0.9La0.1CuO2 with T(c) = 43 K exhibits a momentum-independent superconducting gap Delta = 13.0+/-1.0 meV that substantially exceeds the BCS value, and the spectral characteristics indicate insignificant quasiparticle damping by spin fluctuations and the absence of pseudogap. The response to quantum impurities in the Cu sites also differs fundamentally from that of the p-type cuprates with d(x(2)-y(2))-wave pairing symmetry.     

Pseudogaps in the three-band Hubbard model

Using the strong coupling diagram technique, the energy spectrum of the three-bandHubbard model is investigated. In these calculations, the series in powers of thecopper-oxygen hybridization for the irreducible part is approximated by two lowest-orderterms. For parameters of hole-doped cuprates the calculated energy spectrum consists oflower and upper Hubbard subbands of predominantly copper nature, oxygen bands with someadmixture of copper states and the Zhang-Rice states of mixed nature. The spectrumcontains two pseudogaps, the lower of which separates the Hubbard subband from Zhang-Riceand oxygen bands. The pseudogaps arise due to multiple reabsorption of carriers in stateswith double occupancy of sites by holes or electrons.     

Single-particle spectral function of the Hubbard chain: frustration induced

The one-electron spectral function of a frustrated Hubbard chain is computed by making use of the cluster perturbation theory. The spectral weight we found turns out to be strongly dependent on the frustrating next-nearest-neighbor hopping t'. A frustration induced pseudogap arises when the system evolves from a gapful Mott insulator to a gapless conductor for an intermediate value of the frustration parameter |t'|. Furthermore, the opening of a pseudogap in the density of states already in the metallic side leads to a continuous opening of the true gap in the insulator. For the hole-doped case, the pseudogap is pinned at the Fermi energy, while the Mott gap is shifted in energy with increasing Hubbard interaction U. The separation of the pseudogap and Mott gap in the hole-doped system demonstrates the validity of the existence of a pseudogap.     

Stripe formation in electron-doped cuprates

We investigate the formation of charge domain walls in an electron-doped extended Hubbard model for the superconducting cuprates. Within an unrestricted Hartree-Fock approach, extended by slave bosons to obtain a better treatment of strong correlations, we demonstrate the occurrence of stripes in the (1,1) and (1,-1) directions having one doped electron per stripe site. The different filling, direction, and width of these electron-doped stripes with respect to those obtained in the hole-doped systems have interesting observable consequences.     

Temperature and doping dependence of the high-energy kink in cuprates

It is shown that spectral functions within the extended t-J model, evaluated using the finite-temperature diagonalization of small clusters, exhibit the high-energy kink in single-particle dispersion consistent with recent angle-resolved photoemission results on hole-doped cuprates. The kink and waterfall-like features persist up to large doping and to temperatures beyond J; hence, the origin can be generally attributed to strong correlations and incoherent hole propagation at large binding energies. In contrast, our analysis predicts that electron-doped cuprates do not exhibit these phenomena in photoemission.     

Two-step evolution of doping dependent antiferromagnetism and charge imbalance in multilayered cuprates

The properties of the charge imbalance and magnetism are investigated in the multilayered cuprates. The effective Hubbard constants are much reduced and show clear electron-hole asymmetry due to the screening effect. Phase diagrams are obtained, which may give the clue to search for the self-doped cuprates. An unexpected increase of the charge density upon doping in the layer with minority charge is predicted. The antiferromagnetism follows a two-step evolution with respective origin in the layer with minority charge, in contrast to the conventional doping dependence in the layer with major charge.     

Marginal fermi liquid theory in the Hubbard model

We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.     

Low energy electronic excitations in the layered cuprates studied by copper L3 resonant inelastic x-ray scattering

We have measured the resonant inelastic x-ray scattering (RIXS) spectra at the Cu L3 edge in a variety of cuprates. Exploiting a considerably improved energy resolution (0.8 eV) we recorded significant dependencies on the sample composition and orientation, on the scattering geometry, and on the incident photon polarization. The RIXS final states correspond to two families of electronic excitations, having local (dd excitations) and nonlocal (charge-transfer) character. The dd energy splitting can be estimated with a simple crystal field model. The RIXS at the L3 edge demonstrates here a great potential, thanks to the resonance strength and to the large 2p spin-orbit splitting.     

Nodal superconductivity and antinodal pseudogap in cuprate superconductors

According to recent experimental findings the leading pairing resides in the nodal (FS arcs) momentum region of hole doped cuprates. The pseudogap is an antinodal feature. A corresponding multiband model of the electronic background evolving with doping serves the usually presented phase diagram. The pairing is due by the pair-transfer between overlapping nodal defect (polaron) band and the itinerant band. A bare gap vanishing with extended doping between the antinodal defect subband and the itinerant band top leads to the formation of the pseudogap as a perturbative band-structure effect. The calculated behaviour of two superconducting gaps and of the pseudogap on the whole doping scale is in qualitative agreement with the observations. Arguments to include cuprates into the class of multiband-multigap superconductors are given by these results.     

Spin fluctuation spectrum of electron-doped high-Tc superconductors

The magnetic excitation spectrum of electron-doped copper oxide superconductors is calculated using the Hubbard model on a square lattice. First, the on-site repulsion is treated with the random phase approximation. The spectrum of electron-doped systems in the superconducting state is compared with that of hole-doped systems, and the relationship between the frequency at which a peak grows in the spectrum and the superconducting energy gap at a hot spot (an intersection of the Fermi surface and the magnetic Brillouin zone boundary) is investigated. As compared with the hole-doped systems, the resonance condition is difficult to be satisfied in the electron-doped systems because of the small density of states around the hot spot. Moreover, the correlation effect in the Hubbard model is treated by the fluctuation-exchange approximation (FLEX), and the spin fluctuation spectra in the superconducting state in a wide region of the wave vector and frequency are calculated. We have found that the intensity of the magnetic spectrum at incommensurate wave vectors obtained with the FLEX is considerably weaker than that obtained with the RPA. The validity of the Fermi-liquid approach is also discussed.     

Phase diagram of superconductivity and antiferromagnetism in high-Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential (μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap (z), AFM gap (h) and chemical potential (μ) are solved self consistently for different dopant concentrations (x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (?39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.     

d Orbital doping into pi charge-ordered molecular insulator

A quasi-one-dimensional pi-electron charge-ordered insulator, (DI-DCNQI)2Ag, is metallized by Cu doping into the Ag sites. It is found that with doping the charge gap is diminished and then disorder-induced insulating nature comes up, eventually followed by transition or crossover to a pi-d networked metal. The profile of the charge-gap collapse is consistent with the prediction of the theory highlighting the interplay between electron correlation and disorder. The present doping method is regarded as doping of d orbital, which is different from the conventional charge and/or spin doping developed in cuprates and manganites.     

Momentum dependence of charge excitations in the electron-doped superconductor Nd1.85 Ce0.15 CuO4: a resonant inelastic x-ray scattering study

We report a resonant inelastic x-ray scattering (RIXS) study of charge excitations in the electron-doped high-T(c) superconductor Nd1.85 Ce0.15 CuO4. The intraband and interband excitations across the Fermi energy are separated for the first time by tuning the experimental conditions properly to measure charge excitations at low energy. A dispersion relation with q-dependent width emerges clearly in the intraband excitation, while the intensity of the interband excitation is concentrated around 2 eV near the zone center. The experimental results are consistent with theoretical calculation of the RIXS spectra based on the Hubbard model.