Theoretical Description of the Superconducting State of Nanostructures at Intermediate Temperatures: A Combined Treatment of Collective Modes and Fluctuations

Pedro Ribeiro; Antonio M. García-García

doi:10.1103/PhysRevLett.108.097004

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Theoretical Description of the Superconducting State of Nanostructures at Intermediate Temperatures: A Combined Treatment of Collective Modes and Fluctuations

Pedro Ribeiro, Antonio M. García-García

DOI 10.1103/PhysRevLett.108.097004 · Physical Review Letters

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Abstract

A rigorous treatment of the combined effect of thermal and quantum fluctuations in a zero-dimensional superconductor is considered one of the most relevant and still-unsolved problems in the theory of nanoscale superconductors. In this Letter, we notice that the divergences that plagued previous calculations are avoided by identifying and treating nonperturbatively a low-energy collective mode. In this way, we obtain for the first time closed expressions for the partition function and the superconducting order parameter which include both types of fluctuation and are valid at any temperature and to leading order in δ/Δ0, where δ is the mean level spacing and Δ0 is the bulk energy gap. Our results pave the way for a quantitative description of superconductivity in nanostructures at finite temperature and pairing in hot nuclei.