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Acta Physica Polonica A

Evolution from the BCS to the Bose-Einstein Limit in a d-Wave Superconductor at T=0

Lech S. Borkowski, C. A. R. Sá de Melo

Published Jun 1, 2001• 3 citations
Publisher

Abstract

W e study the evolution from BC S to Bose limit in a two-dimensional d -w ave superconductor at zero temp erature and low density of charge carriers w ithin the mean-Ùeld theory .W e examine single quasipa rticl e prop erties w hen particle density and attraction strength are v aried.F or su£ciently high interaction strength there is a critical density b elow w hich the system has a gap.T he spectral and thermo dynami c prop erties of the system do not evolve smo othly from the BC S-like to the Bose-like regime.

DOI
10.12693/aphyspola.99.691

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arXiv:cond-mat/9903399•Physical review. B, Condensed matter•Nov 1, 1999•74 citations
W e study the evolution from BC S to Bose limit in a two-dimensional d -w ave superconductor at zero temp erature and low density of charge carriers w ithin the mean-Ùeld theory .W e examine single quasipa rticl e prop erties w hen particle density and attraction strength are v aried.F or su£ciently high interaction strength there is a critical density b elow w hich the system has a gap.T he spectral and thermo dynami c prop erties of the system do not evolve smo othly from the BC S-like to the Bose-like regime.
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.
The evolution from BCS to BEC superconductivity in the s-wave and d-wave channels is analyzed at zero temperature for a two-dimensional superconductor. Spectroscopic quantities for s-wave and d-wave systems present fundamental differences when particle density and attraction strength are varied. A detailed analysis of single quasiparticle properties (excitation spectrum, momentum distribution, spectral function and density of states) indicates that the evolution of these spectroscopic quantities in the d-wave case is not smooth, unlike the situation encountered for the s-wave system.
I nst i tut e o f P hysi cs, A dam Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Pozna¥ ( Recei ved Jul y 2, 2001)T w o-dim ension al ( d = 2 ) Penson À K olb mo del , i .e. t he ti ght-bindin g mo del with the pai r-hopp in g (intersite charge exchange ) interaction, is considered and the e˜ects of phase Ûuctuation s on the s -wave sup erconducti vi t y of this system are discussed w ithin the K osterlit z{T houl ess scenario.T he London penetration depth Ñ at T = 0 ; the K osterlitz-T houle ss critical temp erature T c , and the H artree{ Fock approximation critical temp erature T p are determined as a function of particle concentration and interaction.T he U emura typ e plots ( T c vs: Ñ À 2 ( 0) ) are derived.Beyond w eak coupli ng and for low concentrations they show the existence of universal scaling : T c ¿ 1=Ñ 2 ( 0) , as it w as previousl y found for the attractive H ubbard mo del and for the mo dels with intersite electron pairing.PAC S numb ers: 74.20.{z, 71.28.+ d, 74.25.H
Abstract We discuss the evolution from Bardeen-Cooper-Schrieffer (BCS) to Bose superconductivity vs . carrier density n in two-dimensional (2D) gated superconductors and address the fundamental role that the interaction range plays in the Berezinskii-Kosterlitz-Thouless transition. We investigate the density dependence of the critical temperature ( T c ), superfluid density, order parameter modulus, chemical potential and pair size. Our most important finding is that it is absolutely essential to include classical and quantum phase fluctuations, as well as finite-ranged interactions to explain the non-monotonic behavior of T c vs . n and to guarantee that the upper bound on T c is not exceeded in 2D superconductors, as experimentally observed in (Nakagawa Y. et al. , Science , 372 (2021) 190), a lithium-intercalated layered nitride, and in magic-angle twisted trilayer graphene (Park J. M. et al. , Nature , 590 (2021) 249). Furthermore, we show that we can extract, from measurements of T c and the order parameter modulus, the effective mass of charge carriers and their interaction strength and range.
The work by Soares et al. [Phys. Rev. B 65, 174506 (2002)] investigates the BCS to Bose-Einstein crossover for d-wave pairing in the two-dimensional attractive Hubbard model. Contrary to their claims, we found that a nonpairing region does not exist in the density vs coupling phase diagram. The gap parameter at T=0,T=0,T=0, as obtained by solving analytically as well as numerically the BCS equations, is in fact finite for any nonzero density and coupling, even in the weak-coupling regime.
We investigate the zero-temperature BCS to Bose-Einstein crossover at the mean-field level, by driving it with the attractive potential and the particle density. We emphasize specifically the role played by the particle density in this crossover. Three different interparticle potentials are considered for the continuum model in three spatial dimensions, while both s- and d-wave solutions are analyzed for the attractive (extended) Hubbard model on a two-dimensional square lattice. For this model the peculiar behavior of the crossover for the d-wave solution is discussed. In particular, in the strong-coupling limit when approaching half-filling we evidence the occurrence of strong correlations among antiparallel-spin fermions belonging to different composite bosons, which give rise to a quasi-long-range antiferromagnetic order in this limit.