Hole { polaron formation in the 2 D Holstein { t { J model :

Polaronic features of dopant{induced charge carriers are manifest in recent experiments on La 2?x Sr x CuO 4+y and La 2?x Ni x CuO 4+y. To study the formation of hole (bi)polarons in such systems exhibiting strong Coulomb interactions, the Holstein{t{J model is examined by means of a variational diagonalization technique for a wide range of phonon frequencies and electron-phonon (EP) couplings on nite square lattices, up to 18 eeective sites in size. Including static displacement eld, polaron and squeezing eeects, our approach allows for the description of`nearly free' polarons in the weak{coupling limit as well as foràdiabatic' Holstein polarons and`nonadiabatic' Lang{Firsov polarons in the case of strong EP interaction. At low doping level and low phonon frequencies we demonstrate that antiferromagnetic spin correlations and EP interaction reinforce each other to the eeect of lowering the threshold for po-laronic self{localisation in a strongly distorted lattice. This is contrasted with the nonadiabatic regime, where we observe the formation of Lang{Firsov po-larons with moderate polaronic mass enhancement in a nearly undistorted lattice. In the case of two doped holes the hole binding energy is analyzed in detail and we nd that hole binding is enhanced as a dynamical (static) eeect of a rather weak (extremely strong) EP interaction for delocalized (self{ trapped) polarons. At quarter lling we notice, in the adiabatic regime, a sequence of transitions as the EP coupling increases from nearly free mobile polarons to a polaronic superlattice and nally to a charge separated state. The ordering of polarons disappears at higher phonon frequencies.