Generalization of BCS theory to short coherence length superconductors: A BCS--Bose-Einstein crossover scenario.

摘要

The microscopic theory of superconductivity by Bardeen, Cooper and Schrieffer (BCS) is considered one of the most successful theories in condensed matter physics. In ordinary metal superconductors the coherence length ξ is large, and a simple mean field approach, such as BCS, is thereby justified. This theory has two important features: (the amplitude of) the order parameter and excitation gap are identical, and the formation of pairs and their Bose condensation take place at the same temperature, T _c. However, BCS theory fails to explain the superconductivity in the underdoped copper oxide superconductors: the excitation gap Δ is finite at T_c and thus distinct from the order parameter Δ_sc.; In this thesis, we have extended BCS theory in a natural way to general short coherence length superconductors, based on a BCS-Bose-Einstein condensation (BEC) crossover scenario. We arrive at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, and lead to the distinction between Δ and Δ_sc. These finite momentum pairs are treated at a mean field level which addresses the pairs and the single particles on an equal footing. Within our picture, the superconducting transition from the fermionic perspective and Bose-Einstein condensation from the bosonic perspective are just two sides of the same coin.; In contrast to many other theoretical approaches, our theory is capable of making quantitative, testable predictions. The calculated cuprate phase diagram (with one free parameter) is in (semi-)quantitative agreement with experiment. The incoherent pair excitations lead to new low temperature power laws. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations have provided a natural explanation for the unexpected quasi-universal behavior of the normalized in-plane superfluid density as a function of reduced temperature. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat.