Unusual thickness dependence of the superconducting transition ofα-MoGethin films

Abstract

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

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.…”

“…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.…”

“…In addition, the complete presentation of the individual sets of data on a linear scale in the Supplemental Material [38] [15][16][17]; -NbN by Semenov et al [19]; -NbN by Kang et al [18]; -our NbN films (from Fig. 1); -Mo [50]; -Bi and -Pb by Haviland, Liu, and Goldman [20]; -Al from Cohen and Abeles [11]; -Nb [51]; -disordered TiN by Klapwijk et al [21,22]; -disordered TiN by Baturina et al [52]; -αNb 3 Ge [23]; -αMoGe from Graybeal and Beasley [53]; -αMoGe from Graybeal et al [24][25][26]; -αMoGe by Yazdani and Kapitulnik [27]; -αReW by Raffy et al [28]; while is Al, and , , , , , and are Pb films, corresponding to the same symbols used by Strongin et al [12]. A complete list of the data is given in the Supplemental Material [38].…”

“…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].…”

Zirconium Dodecaboride as the First Superconductor with the Improved Near-Surface Characteristics

“…В стандартной теории сверхпроводимости критическая температура T кр экспоненциально зависит от λ эф , поэтому даже небольшие вари-ации этого параметра приводят к сильным изменениям T кр , в то время как отношение 2Δ 0 /k B T кр меняется незначительно в соответ-ствии с изменениями λ эф (именно такое поведение и было обнаруже-но недавно на пленках MoGe [35]). Однако в данном случае, напро-тив, именно отношение 2Δ 0 /k B T кр растет, а критическая температу-ра практически остается неизменной.…”