For an electron gas with $\ensuremath{\delta}$-function attraction, we investigate the crossover from weak- to strong-coupling superconductivity in two and three dimensions. From mean-field theory we extract the stiffness of phase fluctuations and set up effective $\mathrm{XY}$ models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature ${T}_{c}$ as a monotonous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.For an electron gas with $\ensuremath{\delta}$-function attraction, we investigate the crossover from weak- to strong-coupling superconductivity in two and three dimensions. From mean-field theory we extract the stiffness of phase fluctuations and set up effective $\mathrm{XY}$ models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature ${T}_{c}$ as a monotonous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.

arXiv:cond-mat/9907138Physical review. B, Condensed matterMay 1, 199992 citations

Fermion Pairing and Superconductivity

Philippe A. Martin, FRANÇOIS ROTHEN

Springer eBooksJan 1, 20020 citations

Decay of superconducting correlations for gauged electrons in dimensions D ≤ 4

Yasuhiro Tada, Tohru Koma

We study lattice superconductors coupled to gauge fields, such as an attractive Hubbard model in electromagnetic fields, with a standard gauge fixing. We prove upper bounds for a two-point Cooper pair correlation at finite temperatures in spatial dimensions D ≤ 4. The upper bounds decay exponentially in three dimensions and by power law in four dimensions. These imply the absence of the superconducting long-range order for the Cooper pair amplitude as a consequence of fluctuations of the gauge fields. Since our results hold for the gauge fixing Hamiltonian, they cannot be obtained as a corollary of Elitzur’s theorem.We study lattice superconductors coupled to gauge fields, such as an attractive Hubbard model in electromagnetic fields, with a standard gauge fixing. We prove upper bounds for a two-point Cooper pair correlation at finite temperatures in spatial dimensions D ≤ 4. The upper bounds decay exponentially in three dimensions and by power law in four dimensions. These imply the absence of the superconducting long-range order for the Cooper pair amplitude as a consequence of fluctuations of the gauge fields. Since our results hold for the gauge fixing Hamiltonian, they cannot be obtained as a corollary of Elitzur’s theorem.

arXiv:1612.00619Journal of Mathematical PhysicsMar 1, 20181 citation

Fermion Pairing and Superconductivity

Philippe A. Martin, FRANÇOIS ROTHEN

Springer eBooksJan 1, 20040 citations

Superconductivity in Two and Three-dimensional Hubbard Model

H. Fukazawa

Mar 24, 20030 citations

Spin-fluctuation exchange study of superconductivity in two- and three-dimensional single-band Hubbard models

Ryotaro Arita, Kazuhiko Kuroki, Hideo Aoki

In order to identify the most favorable situation for superconductivity in the repulsive single-band Hubbard model, we have studied instabilities for d-wave pairing mediated by antiferromagnetic spin fluctuations and p-wave pairing mediated by ferromagnetic fluctuations with the fluctuation exchange approximation in both two dimensions and three dimensions. By systematically varying the band filling and band structure we have shown that (i) d pairing is stronger in two dimensions than in three dimensions and (ii) p pairing is much weaker than d pairing.In order to identify the most favorable situation for superconductivity in the repulsive single-band Hubbard model, we have studied instabilities for d-wave pairing mediated by antiferromagnetic spin fluctuations and p-wave pairing mediated by ferromagnetic fluctuations with the fluctuation exchange approximation in both two dimensions and three dimensions. By systematically varying the band filling and band structure we have shown that (i) d pairing is stronger in two dimensions than in three dimensions and (ii) p pairing is much weaker than d pairing.

arXiv:cond-mat/9909119Physical review. B, Condensed matterDec 1, 199976 citations

\mathrm{XY}

models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature

{T}_{c}

as a monotonous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.