Bound states of two holes in the two chains of d and pi electrons

I have studied the effect of the antiferromagnet ic (AF) exchange interacti on between the pi-electron spins along the chain, J, on the bound state of holes in the two chains composed of d electrons with localized spin 1/2 and itinerant pi electrons. I have computed the binding energy of two holes do ped away from half-filling. I have used a mean-field approximation and peri odic boundary conditions. As J increases, the binding energy of two holes d ecreases and is negative for J greater than or equal to J(c)(,) where J(c) is the critical value of J. As a result, the holes on the rungs form a boun d state and the bound state is stabilized as J increases for J greater than or equal to J(c). The spin of two holes is singlet. (C) 2000 Elsevier Scie nce B.V. All rights reserved.