"Superfluid Density and Energy Scales of Unconventional Superconductors"
Soon after the discovery of high-Tc cuprate superconductors (HTSC) in 1986, condensed matter physicists started challenges to understand their mechanisms. We performed Muon Spin Relaxation (MuSR) measurements on HTSC and discovered a linear relationship between T c and the superfluid density (n s /m*) in 1989 [1], as one of the earliest signatures suggesting that their condensation mechanism is fundamentally different from BCS but possibly similar to Bose Einstein Condensation (BEC). It was in the midst of this study when I joined faculty of the Physics Department of Columbia in 1988. Subsequently we converted n s /m* to an effective Fermi Temperature T F , made a plot of T c versus T F in 1991 [2], compared with BEC-BCS crossover in 1994, included additional data on A 3 C 60 , BEDT, FeAs, and heavy-fermion superconductors, and developed energy-scale phenomenology which reveals impressive commonalities of these “unconventional superconductors (UCSC)”. Our findings [3] include: (A) Magnetic resonance mode in UCSC and rotons in superfluid 4 He represent a role of competing order which suppresses T c from the value expected for BEC in non-interacting Bose Gas; (B) Overcoming this suppression, Nernst effect (by Ong), photo-induced transient superconductivity (by Cavalleri) and the 400 cm -1 optical mode (by Bernhard) appear in the underdoped region well above T c where the local (yet not global) phase coherence develops among pre-formed pairs; (C) Overdoped / pressurized regions of UCSC, including the tri-layer magic angle twisted graphene, exhibit volume-wise disappearance of superconductivity accompanied by phase separation between condensed superfluid and uncondensed fermions; (D) Robustness of UCSC against disorder, reminiscent to superfluid 4 He and 4 He/ 3 He mixture films adsorbed on porous media; and (E) comparable spin and charge energy scales in the “optimum T c ” region which may lead to a novel resonant pairing mechanism.
