Projected SO(5) Hamiltonian for cuprates and its applications

The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and superconducting fluctuations of underdoped cuprates in terms of four bosons moving on a coarse grained lattice. A simple mean field approximation can explain some key features of the experimental phase diagram: (i) The Mott transition between antiferromagnet and superconductor, (ii) the increase of T-c and superfluid stiffness with hole concentration x and (iii) the increase of antiferromagnetic resonance energy as rootx-x(c) in the superconducting phase. We apply this theory to explain the "two gaps" problem in underdoped cuprate SNS junctions. In particular we explain the sharp subgap Andreev peaks of the differential resistance, as signatures of the antiferromagnetic resonance (the magnon mass gap). A critical test of this theory is proposed. The tunneling charge, as measured by shot noise, should change by increments of DeltaQ = 2e at the Andreev peaks, rather than by DeltaQ = e as in conventional superconductors.