Localization and interaction effects in ultrathin epitaxial NbN superconducting films

Abstract

For epitaxial NbN films with thickness d, 2.0 nm ≤ d ≤ 20.5 nm, we observed a sharp superconducting transition, for which the transition temperature T(c) monotonically decreased with increasing 1/d. Regarding the suppression of T(c), the sheet resistance R(sq) dependence of T(c) closely fitted the Finkel'stein formula from localization theory, with a reasonable value of the electron mean free path comparable to atomic distance, which was used as a fitting parameter. On the other hand, the critical sheet resistance R(c), at which the superconducting-insulator transition was expected, was approximately one-third of the universal value R(q) = h/4e(2) suggested by the dirty boson model for self-duality. It is concluded that T(c) depression in the present NbN system is determined by localization theory but not the dirty boson model.

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

“…(1), we show that this equation fits data gathered from the literature for ∼30 other superconductors studied over the past 46 years that summarize all of the reports from which we could extract d, R s , and T c [11,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In some cases, we merged data reported in different publications by the same authors.…”

“…As opposed to these three models, which suggest that T c depends merely on R s , competing models, such as the proximity effect [7] and the quantum size effect [10] theories, suggest that T c depends on d only, with no direct dependence on R s . Nevertheless, none of these models is sufficient to explain the entirety of the accumulated experimental data [11,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28], despite the long-standing attempt to do so either through a direct mathematical derivation as in the above model, or with the aid of empirical universal laws [29].…”

“…This observation began the race to understanding the superconductor insulator phase transition, which is believed by many researchers to be of a quantum nature [5]. To date, although much data for thin film superconductivity have been accumulated [11,12,[15][16][17][18][19][20][21][22][23][24][25][26][27][28], and the local disorder has already been observed directly [33], the mechanisms governing the collective behavior close to the superconducting-to-insulating transition, or near the onset of superconductivity have remained elusive. That is, a model equivalent to the BCS, but that is valid for thin films, is still missing.…”

“…We chose sputtered NbN as the material for this study for four main reasons: (a) It is widely researched, and experimental data collected for different growth methods and conditions are available; (b) there are contradicting reports about which of the existing models describes the T c suppression in NbN films-for instance, Kang et al [18] proposed that T c is suppressed due to the quantum size effect, Wang et al [17] suggested that the suppression follows Finkel'stein's model [9], Semenov et al [19] determined that the suppression is governed by the proximity effect, and Koushik et al [39] argued that the transition is of a BKT type; (c) the relatively high T c of NbN (16 K for a bulk NbN [40]) assists the experimental investigation; and (d) its properties make it useful for photodetectors [34,36,41,42].…”

“…Moreover, although there is an ongoing dispute of how to determine T c in thin films, usually the values for T c are measured in a consistent manner within a data set of a given material, allowing an examination of each data set at least with itself [45]. 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].…”