In a two-dimensional $t\text{\ensuremath{-}}J$ model that includes anisotropy in the hopping frequency of the charge carriers, the crossover scenario from a BCS superconductor to a condensate of tightly bound bosonic pairs is studied. The important length scales, such as the mean pair radius and penetration depth, are obtained as a function of the anisotropy parameter that distinguishes hopping in one direction with respect to the other. The results indicate a smooth evolution from a picture of highly overlapping Cooper pairs to a condensate of short-range bosonic pairs with increasing anisotropy. The claim for the crossover phenomena is supported by calculating the renormalized chemical potential which slips below the band minimum in the extreme anisotropy limit, implying the onset of a Bose phase.
In a two-dimensional t\ensuremath-J model that includes anisotropy in the hopping frequency of the charge carriers, the crossover scenario from a BCS superconductor to a condensate of tightly bound bosonic pairs is studied. The important length scales, such as the mean pair radius and penetration depth, are obtained as a function of the anisotropy parameter that distinguishes hopping in one direction with respect to the other. The results indicate a smooth evolution from a picture of highly overlapping Cooper pairs to a condensate of short-range bosonic pairs with increasing anisotropy. The claim for the crossover phenomena is supported by calculating the renormalized chemical potential which slips below the band minimum in the extreme anisotropy limit, implying the onset of a Bose phase.
The BCS superconductivity to Bose condensation crossover problem is studied in two dimensions in S, P, and D waves, for a simple anisotropic pairing, with a finite-range separable potential at zero temperature. The gap parameter and the chemical potential as a function of Cooper-pair binding Bc exhibit universal scaling. In the BCS limit the results for coherence length \ensuremath{\xi} and the critical temperature Tc are appropriate for high-Tc cuprate superconductors and also exhibit universal scaling as a function of Bc.
The role of random onsite and hopping disorder in inducing a Bardeen–Cooper–Schrieffer superconductor to Bose–Einstein condensate (BCS–BEC) crossover is investigated using the Bogoliubov–de Gennes (BdG) method on a negative- U Hubbard model in two dimensions. In the strong disorder limit, the BdG state becomes highly inhomogeneous with the formation of superconducting ' droplets ' which are characterized by large pairing amplitudes. The different physical properties calculated for the inhomogeneous state differ significantly from the pure system at all values of electron densities, while we show that a crossover to a BEC state, if at all, is possible at low electron densities. The random onsite disorder supports such a crossover scenario, which is confirmed by observing the chemical potential to slip below the noninteracting band (Leggett criterion). The hopping disorder, however, renders a delocalized phase which allows for overlapping between the pairs, thus preventing the formation of a 'local pair' phase. Also the increase in bandwidth induced by hopping disorder always accommodates the chemical potential inside the band, and hence rules out a crossover phenomenon. However, another variant of the off-diagonal inhomogeneity, i.e. an anisotropic hopping, offers a pro-crossover scenario in the large anisotropy limit.
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.
Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The extension of the crossover regime increases when the pairing strength and/or the characteristic energy of the interaction get larger. Our results indicate the coexistence of large and small Cooper pairs in the crossover regime, leading to the optimal parameter configuration for high transition temperature superconductivity.
We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.
Physical properties of two-dimensional (2D) superconductors is an active area of long time researches in which many, even principle, questions are still open. One of them is a possibility of a smooth crossover of the system from the standard Bardeen–Cooper–Schrieffer (BCS) regime of strongly overlapping Cooper pairs to the regime of Bose–Einstein condensation (BEC) of almost non-overlapping local pairs. The adequate to the real process description of this transition which can happen either by changing the doping or temperature would lead to a better understanding of the superconducting properties of materials. Though the crossover is not observed in one of the most important layered systems—namely, cuprate superconductors—we demonstrate that in systems with stronger electron-electron attraction it is possible. In particular, in the d-wave channel at sufficiently high doping the crossover can take place with growth of temperature two times, i.e., as BEC→BCS, and followed by reverse BCS→BEC condensation. The physical mechanisms of such transitions and possibility to detect them experimentally in real systems are discussed.