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Recently, we have solved the long-standing problem of connecting the physics of the Mott insulator to the underdoped regime of the t-J model [PRB 82, 014504, 2010]. We have derived a renormalized Hamiltonian valid for small doping (x) which is characterized by a spin gap, and sublattice preserving hopping by a hole, and by a pair of holes, both accompanied by a spin-singlet backflow. The phase diagram obtained by continuing the spin states from half filling reproduces the phases of the cuprates. Remarkably, confinement of metallic conduction to 2d emerges from the theory (i.e., it is not assumed). Here we show that the Hamiltonian naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet which (2d) condenses below T*. The charge part is a real-space holon pair formed at Tp < T*, which undergoes a (3d) Bose-Einstein condensation at Tc < Tp. While neither is observable separately, the combination is, as a well-defined excitation of momentum q, and energy w(q). The mechanism is consistent with the small superfluid density, the decline of Tc at small doping, and the existence of pairs above Tc in cuprates, as indicated by the observation of diamagnetism and Nernst effect.

Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulators