Pseudogaps in strongly correlated metals: A generalized dynamical mean-field theory approach

We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale xi via a momentum dependent external self-energy Sigma(k). This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave-like antiferromagnetic spin (or the charge density wave-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized DMFT+Sigma(k) approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized DMFT+Sigma(k) is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth W less than or similar to U (U-value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the DMFT+Sigma(k) show a pseudogap formation near the Fermi level of the quasiparticle band.