Onset of superconductivity in ultrathin granular metal films

Jaeger, Heinrich M.; Haviland, D. B.; Orr, Brian J.; Goldman, A. M.

doi:10.1103/physrevb.40.182

Cited by 378 publications

(310 citation statements)

References 82 publications

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“…* Electronic Mail: Sangita.Bose@fkf.mpg.de † Electronic Mail: pratap@tifr.res.in ‡ Electronic Mail: pushan@tifr.res.in 2 Superconductivity at reduced length scales has been a subject of intense research over the past few decades. 1,2,3,4,5,6,7,8,9,10,11 Though one may expect changes in the superconducting properties as the system size is reduced below the fundamental length scales such as the coherence length, ξ(T), and the penetration depth, λ L (T), it is now established that there is actually a third length scale that finally defines a zero dimensional superconductor. This is the critical particle diameter (D C ) at which the energy level spacing (δ) arising from the discretization of the energy bands (the "Kubo" gap) equals the superconducting energy gap (∆(0)).…”

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confidence: 99%

Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb

Bose

Galande

Chockalingam

et al. 2009

J. Phys.: Condens. Matter

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The superconducting transition temperature (T C ) in nanostructured Pb remains nearly constant as the particle size is reduced from 65 to 7nm, below which size the superconductivity is lost rather abruptly. In contrast, there is a large enhancement in the upper critical field (H C2 ) in the same size regime. We explore the origin of the unusual robustness of the T C over such a large particle size range in nanostructured Pb, by measuring the temperature dependence of the superconducting energy gap in planar tunnel junctions of Al/Al 2 O 3 /nano-Pb. We show that below 22nm, the electron phonon coupling strength increases monotonically with decreasing particle size, and almost exactly compensates for the quantum size effect, which is expected to suppress T C . # Present address: Max Planck Institute for Solid state Research, Nanoscale Science Department, Stuttgart, Germany. * Electronic Mail: Sangita.Bose@fkf.mpg.de † Electronic Mail: pratap@tifr.res.in ‡ Electronic Mail: pushan@tifr.res.in 2 Superconductivity at reduced length scales has been a subject of intense research over the past few decades. 1,2,3,4,5,6,7,8,9,10,11 Though one may expect changes in the superconducting properties as the system size is reduced below the fundamental length scales such as the coherence length, ξ(T), and the penetration depth, λ L (T), it is now established that there is actually a third length scale that finally defines a zero dimensional superconductor. This is the critical particle diameter (D C ) at which the energy level spacing (δ) arising from the discretization of the energy bands (the "Kubo" gap) equals the superconducting energy gap (∆(0)). Superconductivity is completely destabilized below this length scale. The existence of such an 'Anderson criterion' 2 has been successfully demonstrated in many elemental superconductors such as Al, 3 Sn,5 In, 12 Pb, 6,7 and Nb. 13 However, as the size of the superconductor approaches D C , the behavior of the superconducting transition temperature (T C ) is quite different in different systems: superconductors with a weak electron phonon coupling (In, Al, and Sn) show an increase in T C ; the intermediate coupling superconductorNb shows a gradual, monotonic decrease in T C ; while the T C in the strong coupling superconductor, Pb, shows almost no change.Two competing mechanisms control the T C in nanostructured superconductors. The first arises from the increase in surface to volume ratio with decreasing size. As the surface atoms have a smaller coordination number than the bulk atoms, surface phonons are softer than bulk phonons. This leads to an overall decrease in the phonon frequencies in nanoparticles, 14 resulting in an enhanced electron-phonon coupling strength 15 and a higher T C .Experimentally, an increase in the electron-phonon coupling can be detected by measuring the dimensionless quantity: 2∆(0)/k B T C , which monotonically increases with coupling 3 strength from its value of 3.52 in the weak coupling limit. This effect could be counteracted by the quantum si...

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confidence: 99%

Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb

Bose

Galande

Chockalingam

et al. 2009

J. Phys.: Condens. Matter

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“…(1) quantitatively fits well with the data from each material. This list, which surveys thin-film superconductors and presents their properties, also includes some superconductors that require more gentle treatment, for instance, superconductors that only qualitatively agree with the scaling dT c vs R s (e.g., MgB 2 [47]), as well as the few material sets that do not exhibit convincing agreement with this scaling (Ga [48], Sn [12], Nb 3 Sn, and V 3 Si [49]). …”

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Universal scaling of the critical temperature for thin films near the superconducting-to-insulating transition

et al. 2014

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Thin superconducting films form a unique platform for geometrically confined, strongly interacting electrons. They allow an inherent competition between disorder and superconductivity, which in turn enables the intriguing superconducting-to-insulating transition and is believed to facilitate the comprehension of high-T c superconductivity. Furthermore, understanding thin film superconductivity is technologically essential, e.g., for photodetectors and quantum computers. Consequently, the absence of established universal relationships between critical temperature (T c ), film thickness (d), and sheet resistance (R s ) hinders both our understanding of the onset of the superconductivity and the development of miniaturized superconducting devices. We report that in thin films, superconductivity scales as dT c (R s ). We demonstrated this scaling by analyzing the data published over the past 46 years for different materials (and facilitated this database for further analysis). Moreover, we experimentally confirmed the discovered scaling for NbN films, quantified it with a power law, explored its possible origin, and demonstrated its usefulness for nanometer-length-scale superconducting film-based devices. Relationships between low-temperature and normal-state properties are crucial for understanding superconductivity. For instance, the Bardeen-Cooper-Schrieffer theory (BCS) successfully associates the normal-to-superconducting transition temperature, T c , with material parameters, such as the Debye temperature ( D ) and the density of states at the Fermi level [N (0)]. Hence, the BCS model allows us to infer superconducting characteristics (i.e., T c ) from properties measured at higher temperatures [1]. In the BCS framework, superconductivity occurs when attractive phonon-mediated electron-electron interactions overcome the Coulomb repulsion, giving rise to paired electrons (Cooper pairs) with a binding energy gap:. Moreover, within a superconductor, all Cooper pairs are coupled, giving rise to a collective electron interaction. Such a collective state is described by a complex global order parameter with real amplitude ( ) and phase (ϕ): = e iϕ .Because superconductivity relies on a collective electron behavior, the onset of superconductivity occurs when the number of participating electrons is just enough to be considered collective, i.e., at the nanoscale [2-5]. Thus, it is known that the superconductivity-disorder interplay varies in thin films and is effectively tuned with the film thickness (d) or with the disorder in the system, which is represented by sheet resistance of the film at the normal state (R s ) [6][7][8][9][10]. The mechanism of superconductivity in thin films has been investigated since the 1930s [6] increase in T c with decreasing thickness in aluminum films in a study that pioneered the currently ongoing research of thin superconducting films. This enhancement of T c , which is still not completely understood, was later confirmed by Strongin et al. [12], who also reported the more common be...

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The superfluid transition in 4 He is associated with the onset of an order parameter that is a macroscopic wavefunction. This is similar to the onset of superconductivity in metals and alloys.

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Coupling and proximity effects in the superfluid transition in 4He dots

et al. 2010

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The superfluid transition in 4 He is associated with the onset of an order parameter that is a macroscopic wavefunction. This is similar to the onset of superconductivity in metals and alloys. Yet, some of the hallmark phenomena that are associated with wavefunctions, and are evident in superconductors, have not been identified in 4 He. Here we report proximity effects on the specific heat and superfluid density of a thin 4 He film in equilibrium with an array of larger boxes of 4 He. Comparison with previous data also enables us, by scaling, to deduce an excess specific heat associated with a collective behaviour of weakly coupled boxes. These effects should be relevant to the understanding of experiments where helium has been studied when confined in packed powders, porous materials or other inhomogeneous confinements, where proximity and collective effects must be present but not readily quantifiable 1,2 . Our work also forms a point of comparison and contrast with the case of superconductors 3,4 , and is relevant to studies of Josephson effects in superfluids, coupling effects in arrays of Bose-condensed atoms 5,6 , and magnetic systems where, because of chemical composition, two separate but interacting ordering transitions take place 7,8 .In the case of superconductors, coupling and proximity effects have been well understood for many years. The large correlationlength amplitude ξ 0 makes coupling between two superconductors easy to achieve. Weak links with dimensions of the order of ξ 0 , which can be a metal, an insulator or another superconductor, enable measurements of the familiar Josephson effects (see for instance ref. 9). With 4 He these effects are much more difficult to achieve because ξ 0 is of the order of interatomic dimensions. Furthermore, weak links and coupling between two regions of 4 He cannot be achieved through any material other than 4 He. We can, however, take advantage of the growth of the correlation length with temperature T and critical exponent ν, ξ = ξ 0 |1 − T /T λ | −ν ≡ ξ 0 t −ν near the transition temperature T λ and construct apertures whereby analogous Josephson effects can be realized 10,11 .We are unaware of any theory that describes the effects on thermodynamic properties of a 'grain' or dot of helium due to a coupling to another dot through a weak link, or, for that matter, how this coupling is affected by the geometry or 'strength' of this link. This question arose while attempting to verify finite-size scaling for zero-dimensional crossover 12 . We had measured the heat capacity of helium in arrays of (1 µm) 3 and (2 µm) 3 boxes linked by channels of 1 µm × 1 µm × 0.019 µm and 2 µm × 2 µm × 0.010 µm respectively. These data did not scale anywhere in the critical region 13 . The lack of scaling is unexpected, because for both twoand one-dimensional crossover, at least for T > T λ , other data do scale 14 . More significantly, an analysis of the zero-dimensional data suggested that the smaller boxes had a higher heat capacity than expected 13 . This might result from ...

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Onset of superconductivity in ultrathin granular metal films

Cited by 378 publications

References 82 publications

Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb

Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb

Universal scaling of the critical temperature for thin films near the superconducting-to-insulating transition

Coupling and proximity effects in the superfluid transition in 4He dots

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