Localization and interaction effects in ultrathin amorphous superconducting films

Graybeal, J. M.; Beasley, M. R.

doi:10.1103/physrevb.29.4167

Cited by 308 publications

(164 citation statements)

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“…For v F ∼ 1.5 × 10 8 cm/sec, this rate corresponds to a mean free path of ∼ 0.3 nm. This value, while small, is consistent with other estimates and is much less than the thickness of the films [6]. Hence surface scattering is not important, R ∝ 1/d, and the normal-state conductivity does not depend on sheet resistance.…”

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confidence: 91%

“…Several transport experiments have revealed a sharp reduction in the superconducting transition temperature T c with increasing R , even in the weakly localized regime [6,7,8,9]. The suppression of T c has been attributed to localization and an increase in the Coulomb interaction [3].…”

mentioning

confidence: 99%

“…For films prepared in similar fashion, no sign of crystalline inclusions were observed by x-ray and transmission electron microscopy. This procedure is known to yield uniform and homogeneous amorphous films of near ideal stoichiometry [6,7]. A thickness monitor gave the film thickness; the remaining parameters of our films, in Table I, were all determined from optical measurements, described below.…”

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Unusual thickness dependence of the superconducting transition ofα-MoGethin films

et al. 2008

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Thin films of α-MoGe show progressively reduced Tc's as the thickness is decreased below 30 nm and the sheet resistance exceeds 100 Ω/ . We have performed far-infrared transmission and reflection measurements for a set of α-MoGe films to characterize this weakened superconducting state. Our results show the presence of an energy gap with ratio 2∆0/kBTc = 3.8 ± 0.1 in all films studied, slightly higher than the BCS value, even though the transition temperatures decrease significantly as film thickness is reduced. The material properties follow BCS-Eliashberg theory with a large residual scattering rate except that the coherence peak seen in the optical scattering rate is found to be strongly smeared out in the thinner superconducting samples. A peak in the optical mass renormalization at 2∆0 is predicted and observed for the first time.PACS numbers: 74.81.Bd, Disorder and reduced dimensionality affect the physical properties of metallic systems in a number of ways. Anomalous diffusion leads to localization of electrons and a related enhancement of the Coulomb interaction via reduced screening[1, 2], seen as an increase in µ * , the renormalized Coulomb interaction parameter. In a system of lower dimensions, the coupling to disorder increases, and pronounced effects are expected. Disorder-driven localization and the related enhancement of the Coulomb interaction inherently compete with the attractive interaction in superconducting metals [3,4], described by the electron-phonon spectral density α 2 F (ω) [5]. This competition reduces the transition temperature. Of particular interest are two-dimensional (2D) superconductors in which the degree of disorder can be adjusted by varying the appropriate parameters. In an ideal 2D system, the relevant parameter is normally considered to be the sheet resistance, R . The sheet resistance is determined by two factors: the (possibly thickness dependent) conductivity σ and the film thickness d.Amorphous MoGe (α-MoGe) thin films are thought to be a model system for studying the interplay between superconductivity and disorder. Several transport experiments have revealed a sharp reduction in the superconducting transition temperature T c with increasing R , even in the weakly localized regime [6,7,8,9]. The suppression of T c has been attributed to localization and an increase in the Coulomb interaction [3]. In this Letter, we explore the T c suppression in α-MoGe thin films with different thickness via temperature-dependent far-infrared transmittance and reflectance. A strong suppression of T c with increasing R is observed. The superconducting energy gap is also reduced, but the ratio of gap energy to transition temperature and the normal-state conductivity, both of which could be dependent on the disorderdriven Coulomb interaction, are not affected at all.Our films were prepared by co-magnetron sputtering

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Unusual thickness dependence of the superconducting transition ofα-MoGethin films

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“…These data include NbN sets of films that were reported previously by other groups, each of which was reported to be in agreement with one of the models of the form T c (R s ) [17] or T c (d) [18,19]. Moreover, these data sets include some "classical" examples, such as the Bi films by Goldman et al [20], which were used for demonstrating a possible superconducting-to-insulating transition, and the homogeneous αMoGe films of Graybeal et al [46], which were used for demonstrating Finkel'stein's model [9]. The data and analysis of each of these materials are discussed in detail on a linear scale in the Supplemental Material [38] (e.g., a detailed analysis of αMoGe films is provided in section S7 in the Supplemental Material [38]).…”

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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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“…Unlike previous studies, 2,4 here we use fluorinated single-wall nanotubes (FSWNT), which are known to be insulating. 12 The substrate with suspended nanotubes was then sputtercoated 13 in one of two ways: (i) with amorphous 14 Mo 0.79 Ge 0.21 or (ii) with a slightly thinner amorphous Mo 0.79 Ge 0.21 film followed (in the same vacuum cycle) by a 2 nm Si film. Contact pads were defined using photolithography, followed by (i) wet etching in H 2 O 2 for MoGe or (ii) reactive ion etching followed by wet H 2 O 2 etching for Si-coated samples.…”

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Effect of morphology on the superconductor-insulator transition in one-dimensional nanowires

et al. 2004

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We study the effect of morphology on the low temperature behavior of superconducting nanowires of length ≈100 nm. A well-defined superconductor-insulator transition (SIT) is observed only in homogenous wires, in which case the transition occurs when the normal resistance is close to h/4e 2 . Inhomogeneous wires, on the other hand, exhibit a mixed behavior, such that signatures of the superconducting and insulating regimes can be observed in the same sample. The resistance versus temperature curves of inhomogeneous wires show multiple steps, each corresponding to a weak link constriction (WLC) present in the wire. Similarly, each WLC generates a differential resistance peak when the bias current reaches the critical current of the WLC. Due to the presence of WLCs an inhomogeneous wire splits into a sequence of weakly interacting segments where each segment can act as a superconductor or as an insulator. Thus the entire wire then shows a mixed behavior.PACS numbers: 74.48. Na, 74.81.Fa, 74.40.+k Evidence for a superconductor-insulator quantum phase transition (SIT) in one-dimensional (1D) wires has been found in a number of experiments. 1,2 Yet, other studies have demonstrated a crossover, as opposed to an SIT, in thin wires where superconductivity disappears gradually, as diameter is reduced, presumably due to an increasing number of quantum phase slips (QPS). 3,4,5 Thus the existence and possible origins of superconductor-insulator transitions in 1D remain important open problems. In particular it is not known how the SIT depends on the morphology of nanowires.In two-dimensional system, for example, the crucial role of morphology (i.e. granularity) on the SIT is well known. 6,7,8 For uniform films, as the film thickness is reduced, a reduction of the critical temperature is observed while the superconducting transition remains sharp. The SIT occurs when the square resistance of the film reaches a critical value close to the quantum resistance R Q =h/4e 2 =6.5 kΩ. 9 In nonhomogeneous (granular) films, on the other hand, a reduction of the film thickness results in a crossover between superconducting and insulating regimes, with very broad resistive transitions in the thinnest superconducting samples. 6,10,11 Our goal here is to determine the morphological requirements for 1D nanowires under which an SIT can occur.In this Communication, we present a comparative study of homogeneous and inhomogeneous nanotubetemplated wires and find a qualitatively different behavior at low temperatures. Homogeneous samples (of length ≈100 nm) show an SIT which occurs when the wire's normal resistance is close to R Q , confirming previous results where different nanotubes were utilized as substrates. 2 Inhomogeneous wires, on the other hand, exhibit a mixed behavior displaying properties of superconductors and insulators at once. Such samples frequently show multiple steps in the resistive transitions but no resistive tails typical of QPS. 3,4,5 We propose a model which regards the inhomogeneous wire as a sequence of weak link c...

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Localization and interaction effects in ultrathin amorphous superconducting films

Cited by 308 publications

References 9 publications

Unusual thickness dependence of the superconducting transition ofα-MoGethin films

Unusual thickness dependence of the superconducting transition ofα-MoGethin films

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

Effect of morphology on the superconductor-insulator transition in one-dimensional nanowires

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