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arXiv:cond-mat/9812079 · Europhysics Letters (EPL)

Evidence for crossover from a Bose-Einstein condensate to a BCS-like superconductor with doping in YBa 2 Cu 3 O 7 − δ from quasiparticle relaxation dynamics experiments

Jure Demsar, Boštjan Podobnik, Jan E. Evetts, G. A Wagner, Dragan Mihailovic

Published Feb 1, 1999• 22 citations
arXivHTMLPDF

Abstract

Time-resolved measurements of quasiparticle (QP) relaxation dynamics on the femtosecond timescale are reported as a function of temperature and doping in YBa 2 Cu 3 O 7 − δ for (0.48 < δ < 0.1). In the underdoped state (δ > 0.15), there is no evidence for any changes in the low-energy gap structure at T c from either photoinduced QP absorption or QP relaxation time data. In combination with the sum rule, this implies the existence of pre-formed pairs up to a much higher temperature T *. Near δ = 0.1 a rapid cross-over is observed, to a state where the QP recombination time diverges and the photoinduced QP density falls to zero at T c , indicating the existence of a temperature-dependent superconducting gap which closes at T c .

DOI
10.1209/epl/i1999-00175-8

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Time-resolved measurements of quasiparticle (QP) relaxation dynamics on the femtosecond timescale are reported as a function of temperature and doping in YBa 2 Cu 3 O 7 − δ for (0.48 < δ < 0.1). In the underdoped state (δ > 0.15), there is no evidence for any changes in the low-energy gap structure at T c from either photoinduced QP absorption or QP relaxation time data. In combination with the sum rule, this implies the existence of pre-formed pairs up to a much higher temperature T *. Near δ = 0.1 a rapid cross-over is observed, to a state where the QP recombination time diverges and the photoinduced QP density falls to zero at T c , indicating the existence of a temperature-dependent superconducting gap which closes at T c .
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.
We perform time resolved photoelectron spectroscopy measurements of optimally doped $\tn{Bi}_2\tn{Sr}_2\tn{CaCu}_2\tn{O}_{8+δ}$ (Bi-2212) and $\tn{Bi}_2\tn{Sr}_{2-x}\tn{La}_{x}\tn{Cu}\tn{O}_{6+δ}$ (Bi-2201). The electrons dynamics show that inelastic scattering by nodal quasiparticles decreases when the temperature is lowered below the critical value of the superconducting phase transition. This drop of electronic dissipation is astonishingly robust and survives to photoexcitation densities much larger than the value sustained by long-range superconductivity. The unconventional behaviour of quasiparticle scattering is ascribed to superconducting correlations extending on a length scale comparable to the inelastic path. Our measurements indicate that strongly driven superconductors enter in a regime without phase coherence but finite pairing amplitude. The latter vanishes near to the critical temperature and has no evident link with the pseudogap observed by Angle Resolved Photoelectron Spectroscopy (ARPES).
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.
The low-temperature evolution from BCS to Bose-Einstein condensation (BEC) for a two-dimensional d-wave superconductor is discussed at the saddle point (mean field) level. A systematic study of the changes of low-temperature thermodynamic properties is presented as a function of the charge carrier density and fixed interaction. It has been found that when the interaction strength is large enough, there is a critical density below which the single quasiparticle excitation spectrum develops a gap. At higher density of carriers and lower interaction strength (towards the BCS regime) the superconductor has gapless quasiparticle excitations, while at lower densities and higher interactions (towards the BEC regime) quasiparticle excitations are fully gapped. The appearence of a full gap in the quasiparticle excitation spectrum has dramatic consequences to the compressibility, specific heat, and spin susceptibility at low temperatures, as the critical density nc{n}_{c}nc​ is crossed. The change in behavior of these quantities indicates a possible quantum phase transition between a d-wave gapless phase and a d-wave fully gapped phase, as nc{n}_{c}nc​ is crossed.
Abstract Fermi arcs observed in underdoped cuprates have sparked debate over whether they represent segments of a large Fermi surface or small Fermi pockets. This ambiguity has long hindered their classification as either the conventional Bardeen-Cooper-Schrieffer (BCS) regime or the strongly coupled Bose-Einstein condensation (BEC) crossover limit. Here, using angle-resolved photoemission spectroscopy and quantum oscillations, we demonstrate the coexistence of a small Fermi pocket and a large superconducting gap in the clean inner CuO 2 layers of the four-layer cuprate Ba 2 Ca 3 Cu 4 O 8 (F,O) 2 . This coexistence constitutes a hallmark of the BCS-BEC crossover and has remained elusive for decades. Despite the presence of antiferromagnetic (AF) order, the superconducting gap in the small pocket is remarkably large, yielding a gap-to-Fermi energy ratio (Δ pocket / ε F ~ 0.6) and a critical-to-Fermi temperature ratio ( T c / T F ~ 0.13) that reach the theoretical upper bound for two-dimensional superconductivity. Unexpectedly, this BCS-BEC crossover emerges not as the carrier density decreases but as it increases, abruptly within a narrow doping range of less than 1%. These results provide a long-sought microscopic foundation for the d -wave pairing mechanism in doped AF-Mott insulators.
Tuning across the BCS-BEC crossover in the multiband superconductor Fe1+y_{1+y}1+y​Sex_xx​Te1−x_{1-x}1−x​ : An angle-resolved photoemission study
The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal Fe1+y_{1+y}1+y​Sex_xx​Te1−x_{1-x}1−x​ by tuning the Fermi energy, εFε_FεF​, via chemical doping, which permits us to systematically change Δ/εFΔ/ ε_FΔ/εF​ from 0.16 to 0.5 were ΔΔΔ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic changes in the SC state electronic dispersion as the system evolves from a BCS to a BEC regime. Our results raise important questions about the crossover in multiband superconductors which go beyond those addressed in the context of cold atoms.