Using variational wave functions the construction of which is based on the ''string'' or ''spin bag'' picture, we calculate the energies of two-hole states classified according to the momentum and the different irreducible representations of the C 4v point group. We study different ratios J/t, interesting from the experimental viewpoint, and compare our results to exact diagonalization. The energetically most favorable pair symmetries are d x 2 Ϫy 2 and p like. The mechanism of hole binding is the caterpillar-type motion of two holes connected by a string of spin defects, whereas the well-known ''broken bond'' mechanism does not produce binding for t/JϾ0/4. ͓S0163-1829͑98͒05442-3͔

We derive an effective Hamiltonian for spin polarons forming in weakly doped antiferromagnets and demonstrate that the system becomes superconducting at finite doping. We argue that the driving mechanism which gives rise to superconductivity is lowering of the kinetic energy by formation of mobile antiferromagnetic spin bipolarons. That source of attraction between holes is by definition effective if the antiferromagnetic correlation length is longer than the radius of forming polarons. Notwithstanding that the attraction is strongest in the undoped system with long range order, the superconducting order parameter vanishes when the doping parameter decreases which should be attributed to emptying the spin polaron band and approaching the Mott insulator phase. Since the hypothetical normal phase of low density gas of fermions is unstable against formation of bound hole pairs the intensity of low energy excitations is suppressed and the pseudogap forms in the underdoped region.

We establish a novel mechanism of stripe formation in doped systems with alternating t(2g) orbital order--the stripe takes the form of a ferro-orbitally ordered domain wall separating domains with staggered order and allowing for deconfined motion of holes along the stripe. At a finite level of hole concentration this gives rise to the stability of this solitonic type of stripes, while we show that the phase change of the staggered order by π plays a minor role in orbitally ordered systems. These results shed new light on the physics of doped materials in which orbital degeneracy is present.

Motivated by recent Raman and resonant inelastic X-ray scattering experiments performed for Mott insulators, which suggest formation of excitons in these systems, we present a theory of exciton formation in the upper Hubbard band. The analysis based on the spin polaron approach is performed in the framework of an effective t-J model for the subspace of states with one doubly occupied site. Our results confirm the existence of excitons and bear qualitative resemblance to experimental data despite some simplifications in our approach. They prove that the basic underlying mechanismof exciton formation is the same as that which gives rise to binding of holes in weakly doped antiferromagnets.Comment: 4 pages, 1 figur