Twin spin/charge roton mode and superfluid density: Primary determining factors of Tc in high-Tc superconductors observed by neutron, ARPES, and μSR

In the quest for primary factors which determine the transition temperature Tc of high-Tc cuprate superconductors (HTSC), we develop a phenomenological picture combining experimental results from muon spin relaxation (μSR), neutron and Raman scattering, and angle-resolved photoemission (ARPES) measurements, guided by an analogy with superfluid 4He. The 41meV neutron resonance mode and the ARPES superconducting coherence peak (SCP) can be viewed as direct observations of spin and charge soft modes, respectively, appearing near (π,π) and the center of the Brillouin zone, having identical energy transfers and dispersion relations. We present a conjecture that the mode energy of this twin spin/charge collective excitation, as a roton analogue in HTSC, plays a primary role in determining Tc, together with the superfluid density ns/m* at T->0. We further propose a microscopic model for pairing based on a resonant spin-charge motion, which explains the extremely strong spin-charge coupling, relevant energy scales, disappearance of pairing in the overdoped region, and the contrasting spin-sensitivities of nodal and antinodal charges in HTSC systems. Comparing collective vs. single-particle excitations, pair formation vs. condensation, and local vs. long-range phase coherence, we argue that many fundamental features of HTSC systems, including the region of the Nernst effect, can be understood in terms of condensation and fluctuation phenomena of bosonic correlations formed above Tc