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 wea
k or the strong coupling limits. A robust, `beyond LDA 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 (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), 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.
We have computed alpha^2Fs for the hole-doped cuprates within the framework of the one-band Hubbard model, where the full magnetic response of the system is treated properly. The d-wave pairing weight alpha^2F_d is found to contain not only a low ene
rgy peak due to excitations near (pi,pi) expected from neutron scattering data, but to also display substantial spectral weight at higher energies due to contributions from other parts of the Brillouin zone as well as pairbreaking ferromagnetic excitations at low energies. The resulting solutions of the Eliashberg equations yield transition temperatures and gaps comparable to the experimentally observed values, suggesting that magnetic excitations of both high and low energies play an important role in providing the pairing glue in the cuprates.
We demonstrate that most features ascribed to strong correlation effects in various spectroscopies of the cuprates are captured by a calculation of the self-energy incorporating effects of spin and charge fluctuations. The self energy is calculated o
ver the full doping range of electron-doped cuprates from half filling to the overdoped system. The spectral function reveals four subbands, two widely split incoherent bands representing the remnant of the split Hubbard bands, and two additional coherent, spin- and charge-dressed in-gap bands split by a spin-density wave, which collapses in the overdoped regime. The incoherent features persist to high doping, producing a remnant Mott gap in the optical spectra, while transitions between the in-gap states lead to pseudogap features in the mid-infrared.
We discuss evolution of the Fermi surface (FS) topology with doping in electron doped cuprates within the framework of a one-band Hubbard Hamiltonian, where antiferromagnetism and superconductivity are assumed to coexist in a uniform phase. In the li
ghtly doped insulator, the FS consists of electron pockets around the $(pi,0)$ points. The first change in the FS topology occurs in the optimally doped region when an additional hole pocket appears at the nodal point. The second change in topology takes place in the overdoped regime ($sim18%$) where antiferromagnetism disappears and a large $(pi,pi)$-centered metallic FS is formed. Evidence for these two topological transitions is found in recent Hall effect and penetration depth experiments on Pr$_{2-x}$Ce$_{x}$CuO$_{4-delta}$ (PCCO) and with a number of spectroscopic measurements on Nd$_{2-x}$Ce$_{x}$CuO$_{4-delta}$ (NCCO).
We have investigated the doping dependence of the penetration depth vs. temperature in electron doped Pr$_{2-x}$Ce$_x$CuO$_{4-delta}$ using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despit
e the presence of a $d_{x^2-y^2}$ pairing gap in the underlying spectrum, we find nodeless behavior of the low-$T$ penetration depth in underdoped case, in accord with experimental results. As doping increases, a linear-in-$T$ behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.
