Thermodynamic Properties of Small Superconducting Particles

Mühlschlegel, B.; Scalapino, D. J.; Denton, Richard V.

doi:10.1103/physrevb.6.1767

Cited by 314 publications

(237 citation statements)

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“…Models of this kind had previously been studied by Richardson [46][47][48][49][50][51][52][53][54], Strongin et al [93], Mühlschlegel et al [94,95] and Kawataba [96,97]. The first application to RBT's grains for h = 0 was by von Delft et al [21] and for h = 0 by Braun et al [21][22][23].…”

Section: A Simple Reduced Bcs Interaction Plus a Zeeman Termmentioning

confidence: 99%

“…First steps towards a more detailed answer were taken in the early 1970s by Strongin et al [93] and by Mühlschlegel et al [94], who calculated the thermodynamic properties of ensembles small superconducting grains. Experimental realizations of such ensembles were, e.g., the granular films studied by Giaver and Zeller [80,81] .…”

Section: Superconductivity: Crossover From the Bulk To The Limit Of Amentioning

confidence: 99%

“…approaches above is a direct consequence of the neglect of such fluctuations. A rather successful way of including fluctuations is the so-called static path approximation (SPA), pioneered by Mühlschlegel, Scalapino and Denton [94] and developed by various nuclear theorists [127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143], while recently an exact parity projection has also been incorporated [29][30][31][32]. A detailed and general discussion, including a complete list of relevant references, was given very recently by Rossignoli, Canosa and Ring [30].…”

Section: Static Path Approximationmentioning

confidence: 99%

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Spectroscopy of discrete energy levels in ultrasmall metallic grains

2001

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We review recent experimental and theoretical work on ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an individual grain can be measured by the technique of single-electron tunneling spectroscopy: the spectrum is extracted from the current-voltage characteristics of a single-electron transistor containing the grain as central island. We review experiments studying the influence on the discrete spectrum of superconductivity, nonequilibrium excitations, spin-orbit scattering and ferromagnetism. We also review the theoretical descriptions of these phenomena in ultrasmall grains, which require modifications or extensions of the standard bulk theories to include the effects of level discreteness.

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Section: A Simple Reduced Bcs Interaction Plus a Zeeman Termmentioning

confidence: 99%

Section: Superconductivity: Crossover From the Bulk To The Limit Of Amentioning

confidence: 99%

Section: Static Path Approximationmentioning

confidence: 99%

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Spectroscopy of discrete energy levels in ultrasmall metallic grains

2001

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“…The Ginzburg-Levanyuk criterion in 0D, under the assumption of the BCS condition for 0 , yields 1 c Ϸ 13.3 ͑T c / T F ͒ ͑ 0 3 / v͒ 1/2 , where T F is the Fermi temperature, and v the volume of the particle. Alternatively, the critical reduced temperature may be defined as the one below which the first-order fluctuation correction to the mean field behavior of ͉͗ ͉ 2 ͘ is no longer sufficient, 11 in which case one obtains c Ϸ 0.95 ͓N͑0͒vk B T c ͔ −1/2 where N͑0͒ is the singlespin density of states per unit volume. Assuming that the electron mean free path is limited by surface scattering, one then finds 8 c Ϸ͑6k B T c ͒ 1/2 / ͑d /2͒ 3/2 ͉T c dH c / dT͉ Tc .…”

Section: Analysis Of the Datamentioning

confidence: 99%

“…6,9 Fluctuation diamagnetism in aluminum nanoparticles was successfully studied in a pioneering experiment by Buhrman and Halperin 8 by measuring the magnetization as a function of temperature, in constant magnetic fields. The data were analyzed in terms of dia for H → 0, as derived in exact theories 10,11 for the GL free energy functional in 0D limit. The behavior of M dia ͑T Ϸ T c ͒ in nonzero magnetic fields was discussed by extending the zero-field equations with the replacement of the reduced temperature by ͑ + H 2 / H c 2 ͒, where H c is the size-dependent critical field.…”

Section: Introductionmentioning

confidence: 99%

Zero-dimensional superconducting fluctuations and fluctuating diamagnetism in lead nanoparticles

et al. 2006

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High-resolution superconducting quantum interference device magnetization measurements in lead nanoparticles with particle size d less than the superconducting coherence length are used to study zero-dimensional fluctuating diamagnetism. The diamagnetic magnetization M dia ͑H, T = const͒ as a function of the applied magnetic field H at constant temperature is reported in the critical region and compared with the observed behavior in the temperature range where the first-order fluctuation corrections are expected to hold. The magnetization curves are analyzed in the framework of exact fluctuation theories based on the GinzburgLandau functional for ӷ d. The role of the upturn field H up , where the slope of M dia ͑H͒ changes sign, is discussed. The relevance of the magnetization curves over a wide range of magnetic fields and the role of H up for the study of fluctuating diamagnetism, in particular, when the first-order fluctuation correction breaks down, is pointed out. The size and temperature dependences of H up in the critical region are obtained from the experimental data and compared to the theoretical derivations for M dia .

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