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We derive an effective Hamiltonian for spin polarons forming in weakly dopedantiferromagnets and demonstrate that the system becomes superconducting atfinite doping. We argue that the driving mechanism which gives rise tosuperconductivity is lowering of the kinetic energy by formation of mobileantiferromagnetic spin bipolarons. That source of attraction between holes isby definition effective if the antiferromagnetic correlation length is longerthan the radius of forming polarons. Notwithstanding that the attraction isstrongest in the undoped system with long range order, the superconductingorder parameter vanishes when the doping parameter decreases which should beattributed to emptying the spin polaron band and approaching the Mott insulatorphase. Since the hypothetical normal phase of low density gas of fermions isunstable against formation of bound hole pairs the intensity of low energyexcitations is suppressed and the pseudogap forms in the underdoped region.Comment: 14 pages, 4 figure

Kinetic energy driven superconductivity and the pseudogap phase in weakly doped antiferromagnets