We review the intermediate coupling model for treating electronic correlations in the cuprates. Spectral signatures of the intermediate coupling scenario are identified and used to adduce that the cuprates fall in the intermediate rather than the weak or the strong coupling limits. A robust, ‘beyond local-density approximation’ framework for obtaining wide-ranging properties of the cuprates via a GW-approximation based self-consistent self-energy correction for incorporating correlation effects is delineated. In this way, doping- and temperature-dependent spectra, from the undoped insulator to the overdoped metal, in the normal as well as the superconducting state, with features of both weak and strong coupling can be modeled in a material-specific manner with very few parameters. Efficacy of the model is shown by considering available spectroscopic data on electron- and hole-doped cuprates from angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, neutron scattering, inelastic light scattering, optical and other experiments. Generalizations to treat systems with multiple correlated bands such as the heavy-fermions, the ruthenates and the actinides are discussed.
The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function
n(k), the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime
(U=8) at low temperatures
(T=0.01−−0.02). At high doping
(n=0.7), the system resembles an ordinary weakly interacting metal. At low doping
(n=0.92), a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-
Tc cuprates superconductors.
A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple post-Gaussian approximation valid for the intermediate couplings
U/t=1.5−−4 in relevant temperatures
T>100K. In the doping range
p=0.1−−0.3, the value of
U is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coupling is large compared to the effective tight binding scale and a different method is required. This scenario provides an alternative to the paradigm that the coupling should be strong, say
U/t>6, in order to describe the strange metal. We argue that, to obtain phenomenologically acceptable underdoped normal state characteristics like
T∗, pseudogap values, and spectral weight distribution, a large value of
U is detrimental. Surprisingly the resistivity in the above temperature range is linear, $\ensuremath{\rho}={\ensuremath{\rho}}_{0}+\ensuremath{\alpha}\frac{{m}^{*}}{{e}^{2}n\ensuremath{\hbar}}T$, with the ``Planckian'' coefficient $\ensuremath{\alpha}$ of order 1.
The discovery of high-Tc superconductivity in cuprates in 1986 moved strongly correlated systems from exotic worlds interesting only for pure theorists to the focus of solid-state research. In recent decades, the majority of hot topics in condensed matter physics (high-Tc superconductivity, colossal magnetoresistance, multiferroicity, ferromagnetism in diluted magnetic semiconductors, etc.) have been related to strongly correlated transition metal compounds. The highly successful electronic structure calculations based on density functional theory lose their predictive power when applied to such compounds. It is necessary to go beyond the mean field approximation and use the many-body theory. The methods and models that were developed for the description of strongly correlated systems are reviewed together with the examples of response function calculations that are needed for the interpretation of experimental information (inelastic neutron scattering, optical conductivity, resonant inelastic X-ray scattering, electron energy loss spectroscopy, angle-resolved photoemission, electron spin resonance, and magnetic and magnetoelectric properties). The peculiarities of (quasi-) 0-, 1-, 2-, and 3- dimensional systems are discussed.
In recent years there has been significant work aimed at understanding what effect the variation of electronic doping has on material properties. In the high transition-temperature (high-T
c) cuprate superconductors hole doping has an impact on the superconducting transition temperature. In the underdoped regime, the cuprates exhibit anomalous properties due to a pseudogap which forms and is thought to be related to Mott insulating physics. While there is no general consensus as to the mechanism underlying high temperature superconductivity, the resonating valence bond (RVB) theory proposed by Anderson in 1987 with a Gutzwiller projected d-wave BCS wave function could give a first picture of the high-T
c cuprates. We have calculated properties of the cuprates using the assumption that the pseudogap state acts as a normal state to an otherwise standard BCS mean field theory. We find that the phenomenological RVB spin liquid model proposed by Yang, Rice and Zhang (YRZ) is highly successful at describing the doping dependent features of the cuprates. Through application of the YRZ model and the tools of many-body theory we present results on anomalous properties observed in: electronic specific heat; Raman and angle-resolved photoemission spectroscopy (ARPES) data; effective mass renormalization; and thermal broadening seen in ARPES. We verify that the YRZ ansatz qualitatively describes these anomalies along with their doping dependent variations. We conclude from this work that the physics underlying the pseudogap, while distinct in origin from superconductivity, is likely to arise from an RVB wavefunction that is closely related to the BCS state. In graphene, variation in doping modifies the polarization function which describes a screened electron-electron interaction. This leads to additional features in the spectral function which are due to electron-plasmon coupling. In this work, we calculated the electronic density of states including this interaction along with its doping dependence with and without an electron-phonon interaction. We find clear features of electron-electron interactions in the density of states. These features are related to the energies of plasmaron bands in the spectral function and can be modified through doping so as to be distinct from the phonon energy scales.
We have analyzed experimental evidence for an anomalous transfer of spectral weight from high- to low-energy scales in both electron- and hole-doped cuprates as a function of doping. X-ray scattering, optical, and photoemission spectra are all found to show that the high-energy spectral weight decreases with increasing doping at a rate much faster than predictions of the large
U-limit calculations. The observed doping evolution is however well described by an intermediate coupling scenario where the effective Hubbard
U is comparable to the bandwidth. The experimental spectra across various spectroscopies are inconsistent with fixed-
U exact diagonalization or quantum Monte Carlo calculations, and suggest a significant doping dependence of the effective
U in the cuprates.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.