  In the generalized-tJ model the effect of the large local Coulomb repulsion
is accounted for by restricting the Hilbert space to states with at most one
electron per site. In this case the electronic system can be viewed in terms of
holes hopping in a lattice of correlated spins, where holes are the carriers
doped into the half-filled Mott insulator. To explicitly capture the interplay
between the hole dynamics and local spin correlations we derive a new
formulation of the generalized-tJ model where doped carrier operators are used
instead of the original electron operators. This ``doped carrier'' formulation
provides a new starting point to address doped spin systems and we use it to
develop a new, fully fermionic, mean-field description of doped Mott insulators
This mean-field approach reveals a new mechanism for superconductivity, namely
spinon-dopon mixing, and we apply it to the tt't''J model as of interest to
high-temperature superconductors. In particular, we use model parameters
borrowed from band calculations and from fitting ARPES data to obtain a
mean-field phase diagram that reproduces semi-quantitatively that of hole and
electron doped cuprates. The mean-field approach hereby presented accounts for
the local antiferromagnetic and d-wave superconducting correlations which, we
show, provide a rational for the role of t' and t'' in strengthening
superconductivity as expected by experiments and other theoretical approaches.
As we discuss how t, t' and t'' affect the phase diagram, we also comment on
possible scenarios to understand the differences between as-grown and oxygen
reduced electron doped samples.
