Two-Cooper-pair problem and the Pauli exclusion principle

Journal Article · Sat May 01 00:00:00 EDT 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.81.174514· OSTI ID:21366815

Pogosov, Walter V ^[1]; Combescot, Monique ^[1]; Crouzeix, Michel ^[2]

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1. Institut des NanoSciences de Paris, Universite Pierre et Marie Curie-CNRS, Campus Boucicaut, 140 rue de Lourmel, 75015 Paris (France)
2. Institut de Recherche Mathematiques de Rennes, Universite de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex (France)

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's procedure, we here prove 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 in the pair binding while the gap increases strongly indicates that at odd with common belief, the average pair binding energy cannot be on the order of the gap.

• OSTI ID: 21366815
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 17; Other Information: DOI: 10.1103/PhysRevB.81.174514; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BCS THEORY
BINDING ENERGY
CHANNELING
COOPER PAIRS
ELECTRONS
EXCITATION
GROUND STATES
PAULI PRINCIPLE
SPIN
SUPERCONDUCTIVITY
ANGULAR MOMENTUM
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ELEMENTARY PARTICLES
ENERGY
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
FERMIONS
LEPTONS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES