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 demonstrate that many 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 from half filling to the overdoped system. In the normal state, the spectral function reveals four subbands: two widely split incoherent bands representing the remnant of the two 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 resulting coherent subbands closely resemble our earlier mean-field results. Here we present an overview of the combined results of our mean-field calculations and the newer extensions into the intermediate coupling regime.
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.
Angle-dependent studies of the gap function provide evidence for the coexistence of two distinct gaps in hole doped cuprates, where the gap near the nodal direction scales with the superconducting transition temperature $T_c$, while that in the antin
odal direction scales with the pseudogap temperature. We present model calculations which show that most of the characteristic features observed in the recent angle-resolved photoemission spectroscopy (ARPES) as well as scanning tunneling microscopy (STM) two-gap studies are consistent with a scenario in which the pseudogap has a non-superconducting origin in a competing phase. Our analysis indicates that, near optimal doping, superconductivity can quench the competing order at low temperatures, and that some of the key differences observed between the STM and ARPES results can give insight into the superlattice symmetry of the competing order.
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.
