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arXiv:cond-mat/0211561 · Acta Physica Polonica A

On the Crossover from BCS Superconductivity to Bose Condensation

R. Micnas

Published Dec 1, 2001• 9 citations
arXivHTMLPDF

Abstract

ct iv it y to B ose C on d en sation R .M ic na s In st i tute of P hysi cs, A. Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Po zna¥, Pol an d ( Recei ved December 17, 2001)W e out li ne a mi cro scopic approac h to the sup ercon ducti ng Ûuctuation s and pairing correlations in the attracti ve H ubbard mo del ab ove T c , using the functional integral metho d.A crosso ver from BC S sup erconducti vit y to Bose condensatio n of pref ormed pairs is studied by constructing the appropriate Gin zburg { La ndau functional s.T he di ˜erences bet ween the lattice and the continuum mo dels are discussed.T he case of quasi -tw o-dimensional sup erconductors as w ell as the mo del with non-local pairin g interaction are also examined.T he e˜ects of Gaussian Ûuctuation s of the order parameter are analyzed in the T -matrix approach, the self-consistent H artree approach and Ùnally w ithin the Ginzburg{Lan dau theory .Similari tie s with a paramagnon theory of itineran t-electron magnetism are p ointed out.

DOI
10.12693/aphyspola.100.177

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ct iv it y to B ose C on d en sation R .M ic na s In st i tute of P hysi cs, A. Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Po zna¥, Pol an d ( Recei ved December 17, 2001)W e out li ne a mi cro scopic approac h to the sup ercon ducti ng Ûuctuation s and pairing correlations in the attracti ve H ubbard mo del ab ove T c , using the functional integral metho d.A crosso ver from BC S sup erconducti vit y to Bose condensatio n of pref ormed pairs is studied by constructing the appropriate Gin zburg { La ndau functional s.T he di ˜erences bet ween the lattice and the continuum mo dels are discussed.T he case of quasi -tw o-dimensional sup erconductors as w ell as the mo del with non-local pairin g interaction are also examined.T he e˜ects of Gaussian Ûuctuation s of the order parameter are analyzed in the T -matrix approach, the self-consistent H artree approach and Ùnally w ithin the Ginzburg{Lan dau theory .Similari tie s with a paramagnon theory of itineran t-electron magnetism are p ointed out.
We generalize the standard attractive Hubbard, having an on-site pair creation operator Qi = ai|ai|, to one with n components Qiα = aiα|aiα|, a = 1, 2, ... , n.In the limit n -> co we obtain the Ginzburg-Landau functional.On this basis we explore the crossover from weak (BCS) to strong coupling (Bose-Einstein condensation) superconductivity.The associated self-consistent equations for the Ginzburg-Landau parameters are similar to those of the T-matrix approach.The evolution of the band structure with increasing interaction strength is studied and correlated with the behavior of the pair propagator and the transition temperature.We find that the pairing interaction creates a new band which moves downwards in energy as the interaction strength increases and separates into a lower Hubbard band when the interaction strength becomes comparable to the band width.In the strong coupling regime, a third band with small spectral weight is also found in between the lower and upper Hubbard bands.
We use a functional integral formulation to study the crossover from cooperative Cooper pairing to the formation and condensation of tightly bound pairs in a 3D continuum model of fermions with attractive interactions. The inadequacy of a saddle point approximation with increasing coupling is pointed out, and the importance of temporal (quantum) fluctuations for normal state properties at intermediate and strong coupling is emphasized. In addition to recovering the Nozieres-Schmitt-Pink interpolation scheme for T{sub c}, and the Leggett variational results for T = 0, we also present results for evolution of the time-dependent Ginzburg-Landau equation and collective mode spectrum as a function of the coupling.
of Col or ado and Na ti onal Insti t ute of Standa rds and T echno lo gy Bo ul der, Col ora do 80 309-0440, U. S.A. and M. Chi of al o Scuol a No r mal e Superi ore, Pi azza dei Caval i eri 7, 56126 Pi sa, Ita l y W e consi der t he sup erÛuid ph ase transition that arises when a F eshbach resonance pairin g occurs in a dilute F ermi gas.T his is related to the phenomenon of sup ercondu cti v it y describ ed by the seminal Bardeen { Coop er{ Schrie ˜er theory .In supercondu ctivi ty , the phase transition is caused by a couplin g betw een pairs of electrons w ithin the medium.T his coupli ng is perturbative and leads to a critical temp erature T c w hich is small compared to the Fermi temp erature T F .Even high-T c sup erconductors typically ha ve a critical temp erature which is two orders of magnitude below T F .H ere w e describ e a resonance pairing mechanism in a quantum degenerate gas of potassium ( 4 0 K ) atoms w hich leads to sup erÛui di ty in a no vel regime | a regime that promises the unique opp ortunity to exp erimentally study the cross-over from the Bardeen À C oop er{Schrie˜er phase of w eakly-coupled fermions to the Bose{Einstei n condensate of strongly-boun d comp osite bosons.W e Ùnd that the transitio n to a superÛuid phase is possible at the high critical temp erature of about 0 :5 T F .I t should b e straightf orw ard to verif y this prediction, since these temp eratures can already be achieved exp erimentally .
[[abstract]]The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U < 0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n not equal 1 as \U \ increases. (C) 2001 Elsevier Science B.V. All rights reserved.
[[abstract]]one- and two-dimensional attractive Hubbard models in the presence of magnetic field h are studied in a wide range of on-site interaction strength U, temperature T and electron concentration n by means of the generalized self-consistent field (GSCF) approach with renormalized chemical potential. Pairing, the smooth crossover from the BCS regime into the Bose condensation state and the inhomogeneous superconductivity with the non-uniform order parameter are investigated. The excitation spectrum, the momentum distribution function and thermodynamic properties, including the concentration of double occupied sites, the kinetic energy, and the chemical potential, are calculated. The numerical calculations are found in a good agreement with the Bethe-ansatz results and quantum Monte-Carlo calculations in a wide range of system parameters U, n and h. The GSCF theory correctly displays the separation of the energy gap from the order parameter (crossover) as n or \U\ decrease. The concentration of double occupied sites and the bound electron pairs n(pair) are calculated and we found a simple relationship between the order parameter and n(pair), valid for the arbitrary U and ail n in any dimension. The developed GSCF approach in magnetic field suggests a smooth transition into the inhomogeneous superconducting state.
Abstract Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg‐Landau theory describing the crossover from BCS‐superconductivity to Bose‐condensation. We find a smooth crossover from the standard BCS‐limit to a Gross‐Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ0/Tc ≈ 5 which are characteristic for high Tc superconductors.