Condensation, excitation, pairing, and superfluid density in high-Tc superconductors:: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing

To find a primary factor determining T-c and a pairing mechanism in high-T-c cuprates, we combine the muon spin relaxation results on n(s)/m* (superconducting carrier density/effective mass), accumulated over the last 17 years, with the results from neutron and Raman scattering, scanning tunnelling microscopy, specific heat, Nernst effect, and angle-resolved photoemission spectroscopy measurements. We identify the neutron magnetic resonance mode as an analogue of the roton minimum in the superfluid He-4, and argue that n(s)/m* and the resonance mode energy (h) over bar omega(res) play a primary role in determining T-c in the underdoped region. We propose a picture wherein roton-like excitations in the cuprates appear as a coupled mode, which has resonance modes for spin and charge responses at different momentum transfers but the same energy transfer, as detected respectively by means of the neutron S = 1 mode and the Raman S = 0A1(g) mode. We shall call this the 'hybrid spin/charge roton'. After discussing the role of dimensionality in condensation, we propose a generic phase diagram for the cuprates with spatial phase separation in the overdoped region as a special case of the Bose-Einstein to Bardeen-Cooper-Schrieffer crossover conjecture where the superconducting coupling is lost rapidly in the overdoped region. Using a microscopic model of charge motion resonating with antiferromagnetic spin fluctuations, we propose the possibility that the hybrid spin/charge roton and higher-energy spin fluctuations mediate the superconducting pairing. In this model, the resonance modes can be viewed as a meson analogue and the 'dome' shape of the phase diagram can be understood as a natural consequence of departure from the competing Mott insulator ground state via carrier doping.