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To find out a primary determing factor of $T_{c}$ and a pairing mechanism inhigh-$T_{c}$ cuprates, we combine the muon spin relaxation results on$n_{s}/m^{*}$ (superconducting carrier density / effective mass), accumulatedover the last 15 years, with the results from neutron and Raman scattering,STM, specific heat, Nernst effect and ARPES measurements. We identify theneutron magnetic resonance mode as an analogue of roton minimum in thesuperfluid $^{4}$He, and argue that $n_{s}/m^{*}$ and the resonance mode energy$\hbar\omega_{res}$ play a primary role in determining $T_{c}$ in theunderdoped region. We propose a picture that roton-like excitations in thecuprates appear as a coupled mode, which has the resonance mode for spin andcharge responses at different momentum transfers but the same energy transfers,as detected respectively, by the neutron S=1 mode and the Raman S=0 A1$_{g}$mode. We shall call this as the ``hybrid spin/charge roton''. After discussingthe role of dimensionality in condensation, we propose a generic phase diagramof the cuprates with spatial phase separation in the overdoped region as aspecial case of the BE-BCS crossover conjecture where the superconductingcoupling is lost rapidly in the overdoped region. Using a microscopic model ofcharge motion resonating with antiferomagnetic spin fluctuations, we propose apossibility that the hybrid spin/charge roton and higher-energy spinfluctuations mediate the superconducting pairing. In this model, the resonancemodes can be viewed as a meson-analogue and the ``dome'' shape of the phasediagram can be understood as a natural consequence of departure from thecompeting Mott insulator ground state via carrier doping.Comment: 23 pages, 10 figures, to be published in Journal of Physics:  Condensed Matte

journal of physics. condensed matter

Condensation, excitation, pairing, and superfluid density in high-<i>T</i><sub>c</sub> superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing

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

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