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arXiv:cond-mat/9908362 · Physical Review Letters

Unusual Thermodynamical and Transport Signatures of the BCS to Bose-Einstein Crossover Scenario below Tc

Qijin Chen, Ioan Kosztin, Kathryn Levin

Published Sep 1, 2000• 46 citations
arXivHTMLPDF

Abstract

In this paper we present predictions for thermodynamic and transport properties of a BCS to Bose-Einstein crossover theory, below T(c), which satisfies the reasonable constraints that it yields (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures T. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high T(c) systems, are presented, which provide some support for the present picture.

DOI
10.1103/physrevlett.85.2801

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The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length $ξ$ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small $ξ$ materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short $ξ$ superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.

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•Jan 1, 2006•84 citations
In this paper we present predictions for thermodynamic and transport properties of a BCS to Bose-Einstein crossover theory, below T(c), which satisfies the reasonable constraints that it yields (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures T. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high T(c) systems, are presented, which provide some support for the present picture.
The (mean field based) BCS theory is considered one of the most successful theories in condensed matter physics. It is justified in ordinary metal superconductors the coherence length ξξξ is large, with two important features: the order parameter (OP) and excitation gap (EG) are identical, and the pair formation and their Bose condensation take place at the same temperature Tc. It fails to explain the underdoped cuprate superconductivity: EG is finite at Tc and thus distinct from OP. Since these superconductors belong to a large class of small ξξξ materials, this failure has the potential for widespread impact. Here we have extended BCS theory in a natural way to short ξξξ superconductors, based on a BCS--BEC crossover scenario, and arrived at a simple physical picture in which incoherent, finite momentum pairs become progressively more important as the pairing interaction becomes stronger, leading to the distinction between EG and OP. The superconductivity from the fermionic perspective and BEC from the bosonic perspective are just two sides of the same coin. Our theory is capable of making verifiable quantitative predictions. We obtain a cuprate phase diagram (with one free parameter) , in (semi-)quantitative agreement with experiment. The mutually compensating contributions from fermionic quasiparticles and bosonic pair excitations provides a natural explanation for the quasi-universal behavior of the in-plane superfluid density versus T. Our bosonic pair excitations also provide an intrinsic mechanism for the long mysterious linear T terms in the specific heat. Incoherent pair contributions lead to new low T power laws, consistent with existing experiments. Finally, we demonstrated that the onset of superconducting long range order leads to sharp features in the specific heat at Tc, consistent with experiment.
This review is written at the time of the twentieth anniversary of the discovery of high-temperature superconductors, which nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We show how these two subjects have much in common. Both have been addressed from the perspective of the BCS—Bose–Einstein condensation (BEC) crossover scenario, which is designed to treat short coherence length superfluids with transition temperatures which are “high” with respect to the Fermi energy. A generalized mean field treatment of BCS–BEC crossover at general temperatures T, based on the BCS–Leggett ground state, has met with remarkable success in the fermionic atomic systems. Here we summarize this success in the context of four different cold atom experiments, all of which provide indications, direct or indirect, for the existence of a pseudogap. This scenario also provides a physical picture of the pseudogap phase in the underdoped cuprates which is a central focus of high Tc research. We summarize successful applications of BCS–BEC crossover to key experiments in high Tc systems, including the phase diagram, specific heat, and vortex core STM data, along with the Nernst effect, and exciting recent data on the superfluid density in very underdoped samples.
Abstract The superfluid density ns(T)n_{s}(T)ns​(T) n s ( T ) of a superconductor is calculated based on the generalized Bose–Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus two-electron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%–0% (i.e., with no condensed 2hCPs) and (ii) 0%–100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen–Cooper–Schrieffer (BCS) and Bose–Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime ns(0)n_{s}(0)ns​(0) n s ( 0 ) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature TcT_{c}Tc​ T c vs ns(0)n_{s}(0)ns​(0) n s ( 0 ) obtained here is just as Božović et al. (2016) found. However, in 2D with a linear relation accounting for 0%–100%, ns(T)/ns(0)n_{s}(T)/n_{s}(0)ns​(T)/ns​(0) n s ( T ) / n s ( 0 ) compares well with some high- TcT_{c}Tc​ T c -cuprate SC data between the two coupling regimes.
In this paper we study the BCS Bose-Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosoniclike excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T, BCS-BEC approaches introduce an important parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}={\ensuremath{\Delta}}^{2}\ensuremath{-}{\ensuremath{\Delta}}_{\mathrm{sc}}^{2}$ into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects that are significant for sufficiently large g. In the fermionic regime, ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}$ represents the difference between the square of the excitation gap ${\ensuremath{\Delta}}^{2}$ and that of the superconducting order parameter ${\ensuremath{\Delta}}_{\mathrm{sc}}^{2}.$ The parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2},$ which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines ${\ensuremath{\Delta}}_{\mathrm{pg}})$ and the widely discussed phase fluctuation scenario in which the plasma frequency is the tuning parameter. Finally, we emphasize that in the strong coupling limit, there are important differences between the composite bosons that arise in crossover theories and the usual bosons of the (interacting) Bose liquid. Because of constraints imposed on the fermionic excitation gap and chemical potential, in crossover theories, the fermionic degrees of freedom can never be fully removed from consideration.
The existence of a normal-state spectral gap in underdoped cuprates raises important questions about the associated superconducting phase. For example, how does this pseudogap evolve into its below Tc{T}_{c}Tc​ counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the ``residual'' pseudogap below Tc,{T}_{c},Tc​, and find that it leads to an important distinction between the superconducting excitation gap and order parameter. Our approach is based on a conserving diagrammatic BCS Bose-Einstein crossover theory which yields the precise BCS result in weak coupling at any T<TcT<{T}_{c}T<Tc​ and reproduces Leggett's results in the T=0T=0T=0 limit. We explore the resulting experimental implications.
PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning