From one to $N$ Cooper pairs, step by step
| Autor: | Pogosov, W. V., Combescot, M. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Physica C 471, 566 (2011) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physc.2011.07.007 |
| Popis: | We extend the one-pair Cooper configuration towards Bardeen-Cooper-Schrieffer (BCS) model of superconductivity by adding one-by-one electron pairs to an energy layer where a small attraction acts. To do it, we solve Richardson's equations analytically in the dilute limit of pairs on the one-Cooper pair scale. We find, through only keeping the first order term in this expansion, that the $N$ correlated pair energy reads as the energy of $N$ isolated pairs within a $N(N-1)$ correction induced by the Pauli exclusion principle which tends to decrease the average pair binding energy when the pair number increases. Quite remarkably, extension of this first-order result to the dense regime gives the BCS condensation energy exactly. This leads us to suggest a different understanding of the BCS condensation energy with a pair number equal to the number of pairs feeling the potential and an average pair binding energy reduced by Pauli blocking to half the single Cooper pair energy - instead of the more standard but far larger superconducting gap. Comment: 14 pages, 2 figures |
| Databáze: | arXiv |
| Externí odkaz: |
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