In this work we use functional integral techniques to examine the nearest-neighbor attractive Hubbard model on a quasi-two-dimensional lattice. It is a simple phenomenological model for the high- ${T}_{c}$ cuprates that allows both extended (nonlocal) s- and d-wave singlet superconductivity as well as mixed symmetry states. The Hartree-Gor'kov mean-field theory of the model has a finite-temperature phase diagram which shows a transition from pure s-wave to pure d-wave superconductivity, via a mixed symmetry $s+id$ state, as a function of doping. Including Gaussian fluctuations we examine the crossover from weak-coupling BCS superconductivity to the strong-coupling Bose-Einstein condensation of composite s- or d-wave bosons and comment on the origin and symmetry of the pseudogap.In this work we use functional integral techniques to examine the nearest-neighbor attractive Hubbard model on a quasi-two-dimensional lattice. It is a simple phenomenological model for the high-${T}_{c}$ cuprates that allows both extended (nonlocal) s- and d-wave singlet superconductivity as well as mixed symmetry states. The Hartree-Gor'kov mean-field theory of the model has a finite-temperature phase diagram which shows a transition from pure s-wave to pure d-wave superconductivity, via a mixed symmetry $s+id$ state, as a function of doping. Including Gaussian fluctuations we examine the crossover from weak-coupling BCS superconductivity to the strong-coupling Bose-Einstein condensation of composite s- or d-wave bosons and comment on the origin and symmetry of the pseudogap.

arXiv:cond-mat/9909043Physical review. B, Condensed matterJan 1, 200026 citations

Crossover from BCS to Bose superconductivity: A functional integral approach

Mohit Randeria, Sa de Melo, C. A. R., Jan R. Engelbrecht

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.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.

Apr 1, 19930 citations

BCS to Bose crossover: Broken-symmetry state

Jan R. Engelbrecht, Mohit Randeria, C.A.R. Sáde Melo

A functional integral formulation, used previously to calculate ${\mathrm{T}}_{\mathrm{c}}$ and describe normal state properties of the BCS-Bose crossover, is extended to T ${\mathrm{T}}_{\mathrm{c}}$ . The saddle point approximation is shown to be qualitatively correct for T\ensuremath{\ll} ${\mathrm{T}}_{\mathrm{c}}$ for all couplings, in contrast to the situation above ${\mathrm{T}}_{\mathrm{c}}$ . Several features of the crossover are described. The difference between the T=0 ``pair size'' and the (prefactor of the T dependent) Ginzburg-Landau coherence length is pointed out: the two quantities are the same only in the BCS limit. The evolution of the collective modes from the BCS to the Bose regime is discussed together with the mixing of the amplitude and phase in the absence of a particle-hole symmetry.A functional integral formulation, used previously to calculate ${\mathrm{T}}_{\mathrm{c}}$ and describe normal state properties of the BCS-Bose crossover, is extended to T${\mathrm{T}}_{\mathrm{c}}$. The saddle point approximation is shown to be qualitatively correct for T\ensuremath{\ll}${\mathrm{T}}_{\mathrm{c}}$ for all couplings, in contrast to the situation above ${\mathrm{T}}_{\mathrm{c}}$. Several features of the crossover are described. The difference between the T=0 ``pair size'' and the (prefactor of the T dependent) Ginzburg-Landau coherence length is pointed out: the two quantities are the same only in the BCS limit. The evolution of the collective modes from the BCS to the Bose regime is discussed together with the mixing of the amplitude and phase in the absence of a particle-hole symmetry.

Physical review. B, Condensed matterJun 1, 1997400 citations

In this work we use functional integral techniques to examine the nearest-neighbor attractive Hubbard model on a quasi-two-dimensional lattice. It is a simple phenomenological model for the high-

{T}_{c}

cuprates that allows both extended (nonlocal) s- and d-wave singlet superconductivity as well as mixed symmetry states. The Hartree-Gor'kov mean-field theory of the model has a finite-temperature phase diagram which shows a transition from pure s-wave to pure d-wave superconductivity, via a mixed symmetry

s+id

state, as a function of doping. Including Gaussian fluctuations we examine the crossover from weak-coupling BCS superconductivity to the strong-coupling Bose-Einstein condensation of composite s- or d-wave bosons and comment on the origin and symmetry of the pseudogap.

A functional integral formulation, used previously to calculate

{\mathrm{T}}_{\mathrm{c}}

and describe normal state properties of the BCS-Bose crossover, is extended to T

{\mathrm{T}}_{\mathrm{c}}

. The saddle point approximation is shown to be qualitatively correct for T\ensuremath{\ll}

{\mathrm{T}}_{\mathrm{c}}

for all couplings, in contrast to the situation above

{\mathrm{T}}_{\mathrm{c}}

. Several features of the crossover are described. The difference between the T=0 ``pair size'' and the (prefactor of the T dependent) Ginzburg-Landau coherence length is pointed out: the two quantities are the same only in the BCS limit. The evolution of the collective modes from the BCS to the Bose regime is discussed together with the mixing of the amplitude and phase in the absence of a particle-hole symmetry.