Cooper Pairs; Superconductors and Superfluids

MANUEL DE LLANO, Francisco J. Sevilla, S. Tapia

Although BCS pairs of fermions are known not to obey Bose-Einstein (BE) commutation relations nor BE statistics, we show how Cooper pairs (CPs), whether the simple original ones or the CPs recently generalized in a many-body Bethe-Salpeter approach, being clearly distinct from BCS pairs at least obey BE statistics. Hence, contrary to widespread popular belief, CPs can undergo BE condensation to account for superconductivity if charged, as well as for neutral-atom fermion superfluidity where CPs, but uncharged, are also expected to form. Keywords: Cooper pairs; Bose-Einstein condensation; superconductors; superfluids 1

A. J. Leggett

Naoum Karchev, T. Vetsov

In this paper, we address the impact of the electric field on superconductors which are insulators in the normal state, semiconductors at low carrier concentration and ultracold gas of fermions in the strongly interacting regime. The electric field penetrates these systems and effects on the Cooper pairs. We show that if there are Cooper pairs above the superconductor critical temperature, the electric field forces the Cooper pairs to Bose condensate and the onset of the superconductivity, thereby increasing the critical temperature. To study this phenomenon, we numerically solve the Maxwell equations for [Formula: see text]-wave superconductors obtained from the time-dependent Ginzburg–Landau theory. Our investigation designs an experimental way for verification of the pairing of Fermions preceding superconductivity and superfluidity.

Xiaotian Si, Wataru Kohno, Takafumi Kita

We improve the Bardeen-Cooper-Schrieffer wave function with a fixed particle number so as to incorporate many-body correlations beyond the mean-field treatment. It is shown that the correlations lower the ground-state energy far more than Cooper-pair condensation in the weak-coupling region. Moreover, they naturally bring a superposition over the number of condensed particles. Thus, Cooper-pair condensation is special among the various bound-state formations of quantum mechanics in that number fluctuations are necessarily present in the condensate through the dynamical exchange of particles with the non-condensate reservoir. On the basis of this result, we propose $\varDelta N_{\rm con}\cdot \varDelta ϕ\gtrsim 1$ as the uncertainty relation relevant to the number-phase fluctuations in superconductors and superfluids, where the number of condensed particles $N_{\rm con}$ is used instead of the total particle number $N$. The formula implies that a macroscopic phase $ϕ$ can be established even in number-fixed superconductors and superfluids since $\varDelta N_{\rm con}\gg 1$.