Two-Cooper-pair problem and the Pauli exclusion principle

Abstract

While the one-Cooper pair problem is now a textbook exercise, the energy of two pairs of electrons with opposite spins and zero total momentum has not been derived yet, the exact handling of Pauli blocking between bound pairs being not that easy for N=2 already. The two-Cooper pair problem however is quite enlightening to understand the very peculiar role played by the Pauli exclusion principle in superconductivity. Pauli blocking is known to drive the change from 1 to $N$ pairs, but no precise description of this continuous change has been given so far. Using Richardson procedure, we here show that Pauli blocking increases the free part of the two-pair ground state energy, but decreases the binding part when compared to two isolated pairs - the excitation gap to break a pair however increasing from one to two pairs. When extrapolated to the dense BCS regime, the decrease of the pair binding while the gap increases strongly indicates that, at odd with common belief, the average pair binding energy cannot be of the order of the gap.

9 pages, no figures, final version

References in corpus (4)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• LaFeAsO${}_{1-x}$F${}_x$: A low carrier density superconductor near itinerant magnetism
• Normal State Correlated Electronic Structure of Iron Pnictides

Cited by in corpus (11)

• "Probabilistic" approach to Richardson equations
• From one to $N$ Cooper pairs, step by step
• "Moth-eaten effect" driven by Pauli blocking, revealed for Cooper pairs
• BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function
• Coboson formalism for Cooper pairs used to derive Richardson's equations
• Effective forces between quantum bound states
• BCS ansatz for superconductivity in the canonical ensemble and the Pauli exclusion principle
• Multi-particle instability in a spin-imbalanced Fermi gas
• A mechanism for pair formation in strongly correlated systems
• Competition between BCS-pairing and "moth-eaten effect" in BEC-BCS crossover
• Electron pair forming in an integrable model