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We start this Lecture with the evaluation of the sign and magnitudeMagnitude of electron–phonon interactionElectron-phonon interactionInteractionelectron-phonon interaction close to the Fermi surfaceFermiFermi surfaceFermi surface and deep inside Fermi sphereFermiFermi sphereSphere. On the basis of these results, we solve the famous Cooper problemCooperCooper problemProblemCooper problem in the BCS theoryBardeen-Cooper-Schrieffer (BCS)BCS theoryTheoryBCS theory and find the binding energyBinding energyEnergybinding energy of the Cooper pairPairCooper pair. We determine the critical temperatureCriticalcritical temperatureTemperatureCritical temperature of the superconducting transition and the value of the superconducting gapSuperconducting gap as well. We analyze the role of strong electron–electron repulsion which is always present in metals and show that the superconductivity is not destroyed due to the presence of Tolmachev logarithmLogarithmTolmachev logarithmTolmachev logarithm in the effective coupling constant. In conclusion we provide a brief introduction to the unconventional superconductivity.

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Lecture 23. The Cooper Problem

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  • 发表日期：

    2026年

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  • Maxim Kagan

摘要

We start this Lecture with the evaluation of the sign and magnitudeMagnitude of electron–phonon interactionElectron-phonon interactionInteractionelectron-phonon interaction close to the Fermi surfaceFermiFermi surfaceFermi surface and deep inside Fermi sphereFermiFermi sphereSphere. On the basis of these results, we solve the famous Cooper problemCooperCooper problemProblemCooper problem in the BCS theoryBardeen-Cooper-Schrieffer (BCS)BCS theoryTheoryBCS theory and find the binding energyBinding energyEnergybinding energy of the Cooper pairPairCooper pair. We determine the critical temperatureCriticalcritical temperatureTemperatureCritical temperature of the superconducting transition and the value of the superconducting gapSuperconducting gap as well. We analyze the role of strong electron–electron repulsion which is always present in metals and show that the superconductivity is not destroyed due to the presence of Tolmachev logarithmLogarithmTolmachev logarithmTolmachev logarithm in the effective coupling constant. In conclusion we provide a brief introduction to the unconventional superconductivity.