Antiferromagnetic spin fluctuations in a two-dimensional metal, such as doped high-T, superconductors, lead to a pseudogap in the electronic spectrum. In the spectral function weight is shifted from the single quasiparticle peak of the Fermi-liquid regime to the incoherent particle and hole backgrounds, which evolve into the upper and lower Mott-Hubbard bands of the antiferromagnetic insulator. Precursors of these split bands show up as "shadow bands" in angle-resolved photoemission spectra.

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We use a combination of numeric and analytic techniques to determine the groun d state phase diagram of the Bose--Hubbard Hamiltonian with longer range repulsi ve interactions. At half filling one finds superfluidity and an insulating solid phase. Depending on the relative sizes of near--neighbor and next near--neighbor interactions, this solid either follows a checkerboard or a striped pattern. In neither case is there a coexistence with superfluidity. However upon doping ``supersolid'' phases appear with simultaneous diagonal and off--diagonal long range order.Comment: 11 pages, Revtex 3.0, 6 figures (upon request

Analysis of the structural, transport, and superconducting properties of Nd-doped La2 "Sr Cu04 reveals a critical tilt angle of the Cu06 octahedra for the disappearance of superconductivity in the low temperature tetragonal phase. Our results indicate a strong inAuence of the tilt of the Cu06 octahedra on the electronic properties, suggesting the importance of spin-orbit coupling for the destruction of superconductivity and for the stabilization of a magnetic state.

It is shown that antiferromagnetic spin fluctuations in a two-dimensional metal, such as heavily doped cuprate superconductors, lead to a pseudogap in the electronic spectrum. The spectral function evolves from one peak in the Fermi-liquid regime to two peaks, one for particles and one for holes. The self-energy of spin bags and their pairing interaction are calculated. These results are consistent with the corresponding results in the weakly doped ordered antiferromagnet.