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 ${T}_{c}$ counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the ``residual'' pseudogap below ${T}_{c},$ 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 $T<{T}_{c}$ and reproduces Leggett's results in the $T=0$ limit. We explore the resulting experimental implications.
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 counterpart? In this paper we characterize this unusual superconductor by investigating the nature of the ``residual'' pseudogap below 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<Tc and reproduces Leggett's results in the T=0 limit. We explore the resulting experimental implications.
We investigate the pseudogap onset temperature T∗, the superconducting transition temperature Tc and the general nature of the pseudogap phase using a diagrammatic BCS-Bose Einstein crossover theory. This decoupling scheme is based on the pairing approximation of Kadanoff and Martin, further extended by Patton (KMP). Our consideration of the KMP pairing approximation is driven by the objective to obtain BCS like behavior at weak coupling, (which does not necessarily follow for other diagrammatic schemes). The breakdown of the Fermi liquid state at T∗ is investigated within the lowest order theory and is associated with intermediate values of the coupling. The superconducting instability Tc is evaluated by introducing mode coupling effects, in which the long lived pairs are affected by the single particle pseudogap states and vice versa. Our Tc equations, which turn out to be rather simple as a result of the KMP scheme, reveal a rich structure as a function of g in which the pseudogap is found to compete with superconductivity. Our results are compared with alternate theories in the literature.
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.
The pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple s-wave picture.
Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-Tc cuprates and other systems
The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-Tc cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-Tc cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature Tc and then such bosons condenses into a Bose superfluid at Tc. The pair condensation of attracting bosons occurs at Tc and then their single particle condensation sets in at Tc∗ lower than Tc (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below Tc. By solving the mean field equations for high-Tc cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature Tv=Tc2D lower than T* but higher than Tc=Tc3D and two superconducting phases below Tc) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.
The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.
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.