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 t ransition between antiferromagnet and superconductor, (ii) the increase of T-c and superfluid stiffness with hole concentration x and (iii) the increa se of antiferromagnetic resonance energy as rootx-x(c) in the superconducti ng phase. We apply this theory to explain the "two gaps" problem in underdo ped cuprate SNS junctions. In particular we explain the sharp subgap Andree v peaks of the differential resistance, as signatures of the antiferromagne tic resonance (the magnon mass gap). A critical test of this theory is prop osed. The tunneling charge, as measured by shot noise, should change by inc rements of DeltaQ = 2e at the Andreev peaks, rather than by DeltaQ = e as i n conventional superconductors.