Low-lying excitations in super-conducting bilayer systems

The ground and first excited state of two superconducting layers in interaction are studied considering two different coupling terms, one represented by the standard Josephson interaction, and one new, which is a superexchange pairing force between bilayer pairs. It is shown that a moderate to strong Josephson interaction produces a low-lying collective state, pictured as an out-of-phase oscillation of the (Bardeen-Cooper-Schreiffer) gauge angles of the two layers. This antisymmetric angular oscillation might explain the 41 meV resonance observed in neutron-scattering experiments. The bilayer pairs are formed by electrons from different layers with an antiparallel orientation of the spins, being related to the antiferromagnetic arrangement. The pair operators within the layers together with the bilayer pairs generate by commutation an so(5) algebra. It is shown that the transition between the superconducting and antiferromagnetic phases can be explained assuming the dependence on concentration of the bilayer pairing strength, with maximum at half-filling.