Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors

Abstract

Muon spin relaxation ($\mu$SR) studies of the "1111" and "122" FeAs systems have detected static magnetism with variably sized ordered moments in their parent compounds. The phase diagrams of FeAs, CuO, organic BEDT, A$_{3}$C$_{60}$ and heavy-fermion systems indicate competition between static magnetism and superconductivity, associated with first-order phase transitions at quantum phase boundaries. In both FeAs and CuO systems, the superfluid density $n_{s}/m^{*}$ at $T \to 0$ exhibits a nearly linear scaling with $T_{c}$. Analogous to the roton-minimum energy scaling with the lambda transition temperature in superfluid $^{4}$He, clear scaling with $T_{c}$ was also found for the energy of the magnetic resonance mode in cuprates, (Ba,K)Fe$_{2}$As$_{2}$, CeCoIn$_{5}$ and CeCu$_{2}$Si$_{2}$, as well as the energy of the superconducting coherence peak observed by angle resolved photo emission (ARPES) in the cuprates near ($\pi$,0). Both the superfluid density and the energy of these pair-non-breaking soft-mode excitations determine the superconducting $T_{c}$ via phase fluctuations of condensed bosons. Combining these observations and common dispersion relations of spin and charge collective excitations in the cuprates, we propose a resonant spin charge motion/coupling, "traffic-light resonance," expected when the charge energy scale $\epsilon_{F}$ becomes comparable to the spin fluctuation energy scale $\hbar\omega_{SF}\sim J$, as the process which leads to pair formation in these correlated electron superconductors.