Properties of the multiorbital Hubbard models for the iron-based superconductors

Theoretical ideas and experimental results concerning high temperature superconductors are reviewed. Special emphasis is given to calculations carried out with the help of computers applied to models of strongly correlated electrons proposed to describe the two dimensional \({\rm Cu O_2}\) planes. The review also includes results using several analytical techniques. The one and three band Hubbard models, and the \({\rm t-J}\) model are discussed, and their behavior compared against experiments when available. Among the conclusions of the review, we found that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular abnormal features like the mid-infrared band of the optical conductivity \(\sigma(\omega)\), the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a \(\dx2y2\) superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others....(continues).

One way of making the transition between the quasi-long range order in a chain of S=1/2 spins coupled antiferromagnetically and the true long range order that occurs in a plane, is by assembling chains to make ladders of increasing width. Surprisingly this crossover between one and two dimensions is not at all smooth. Ladders with an even number of legs have purely short range magnetic order and a finite energy gap to all magnetic excitations. Predictions of this novel groundstate have now been verified experimentally. Holes doped into these ladders are predicted to pair, and possibly superconduct.