Gossamer superconductivity, new paradigm?

We shall review our recent works on d-wave density wave (dDW) and gossamer superconductivity (i.e. d-wave superconductivity in the presence of dDW) in high-T_c cuprates and CeCoIn₅. a) We show that both the giant Nernst effect and the angle dependent magnetoresistance (ADMR) in the pseudogap phases of the cuprates and CeCoIn₅ are manifestations of dDW. b) The phase diagram of high-T_c cuprates is understood in terms of mean field theory, which includes two order parameters Δ₁ and Δ₂, where one order paremeter is from dDW and the other from d-wave superconductivity, c) In the optimally to the over-doped region we find the spatially periodic dDW, an analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, becomes more stable, d) In the underdoped region where Δ₂/Δ₁ ≪ 1 the Uemera relation is obtained within the present model. We speculate that the gossamer superconductivity is at the heart of high-T_c cuprate superconductors, the heavy-fermion superconductor CeCoIn₅ and the organic superconductors κ-(ET)₂Cu(NCS)₂ and (TMTSF)₂PF₆.