  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.
