The year 2011 marks the 100th year anniversary of the discovery of superconductivity by Kammerlingh Onnes. Since then, superconductivity of simple metals, such as Al, Sn, and Hg, was explained by the BCS theory more than 50 years ago. The BCS theory has several key features: (a) pairing mediated by phonons; (b) energy scale of condensing charges, i.e., Fermi energy E_F, being much larger than that of mediating fluctuations hw_B (phonon frequency); (c) the transition temperature Tc scales with hw_B without directly depending on the carrier density. During recent 30 years, several new superconductors have been discovered: they include high- Tc cuprates, organic BEDT, alkali-doped A3C60, heavy-fermion, and FeAs superconductors which were discovered about three years ago. These systems are much different from BCS superconductors in: (a) pairing seems to be mediated by the spin fluctuations rather than lattice vibrations; (b) effective energy scales of superconducting charges are comparable with energy scales of spin fluctuations, indicating non-retarded interaction; and (c) the transition temperature scales with the superfluid density n_s/m* which represents the charge energy, suggesting relevance of Bose-Einstein condensation of pre-formed pairs. In this talk, I will demonstrate striking commonalities of these new unconventional superconductors by showing accumulated experimental results on energy scales and phase diagrams from muon spin relaxation (MuSR), neutron scattering, specific heat, and other measurements, and discuss their implications on pairing and condensation mechanisms. Especially, I will elucidate important roles of collective soft modes relevant to competing states in determining Tc, and advantage of possible resonance of the two key energy scales, E_F, for charges and hw_B for spins, in the process of crossover from Bose Einstein to BCS condensation for the pairing mediated by spin fluctuations. References: Y.J. Uemura, Nature Materials 8 (2009) 253-255. Y.J. Uemura, Physica B404 (2009) 3195-3201.
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