Abstract

An energy scale of the superconducting condensate, which we call the effective Fermi temperature TF, can be derived from the magnetic field penetration depth λ determined by muon spin relaxation (μSR) measurements. We classify various superconductors in the crossover from Bose–Einstein (BE) to BCS condensation, based on the ratio Tc/TF. The phase diagram of high- Tc cuprate superconductors, as a function of carrier doping, can be understood in the context of this BE–BCS crossover, if we identify the ‘pseudo-gap’ as the signature of pair formation in the normal state. In particular, the universal linear relation between Tc and ns/m* (superconducting carrier density/effective mass), found in the underdoped region, comes from a general feature expected in the BE condensation of pre-formed pairs. The optimal Tc occurs around the doping concentration at which the condensate energy scale TF becomes comparable to the energy scale hωB of the pair-mediating interaction. A surprising decrease of ns/m* with increasing carrier doping was found in the overdoped Tl 2201 system. This behavior suggests that evolution to the BCS region does not occur in a simple way, but rather is associated with a possible microscopic separation between superconducting and residual normal metallic phases.

During the past several years, we have performed measurements of the magnetic field penetration depth λ of high- Tc cuprate and other superconducting systems using the muon spin relaxation (μSR) technique [1–5].