The role of the coherence length for the establishment of global phase coherence in arrays of ultra-thin superconducting nanowires

Abstract

We have fabricated 5 nm ultra-thin NbN nanowires that form a dense and regular array in the linear channels of mesoporous SBA-15 silica substrates. Bulk NbN is a well-known classical superconductor with Tc of 16 K. We show that, by being incorporated into this nanostructure, the composite material exhibits typical quasi-one-dimensional characteristics. We compare the superconducting properties with those of superconducting Pb nanowires of same dimensionality in identical configuration within the linear SBA-15 pores. While Pb nanowire arrays show a pronounced crossover from 1D superconductivity at high temperatures to a 3D bulk superconducting state in the low temperature regime with true zero resistance triggered by transversal Josephson interaction, this transition appears to be completely absent in the NbN nanowire array. The small coherence length in NbN, which strongly suppresses the Josephson coupling is discussed as the origin of this difference.A quasi one-dimensional (quasi-1D) superconductor is a superconducting material which is confined in a 1D geometry of lateral dimensionality equal to or less than the superconducting coherence length of the corresponding bulk material [1,2]. Such nanowires or linear atomic chains can either be realized in the form of individual free-standing nanowires [2,3], or can be arranged to form an array of parallel 1D nano-elements [1,[4][5][6][7]. The latter was realized in the form of artificially grown nanostructures [1,5,6,8,9] or found in intrinsic quasi-1D superconducting materials such as Tl2Mo6Se6 [10] or Sc3CoC4 [11,12]. The latter contain many parallel conducting 1D atomic chains separated by either insulating layers or a non-superconducting metallic host. Dependent on the superconducting coherence

Electron–electron interactions of the multi-Cooper-pairs in the 1D limit and their role in the formation of global phase coherence in quasi-one-dimensional superconducting nanowire arrays

“…We Table 1, assuming that the coherence length is longer than the insulating separation width [15]. Although the onset c T of the NbN nanowires array is the largest, its low electron concentration is one of the main reasons that BKT T is as low as 0.007K, which agrees with recent experimental observations [21]. In contrast, the BKT T of Sn nanowires almost matches the experimentally observed c T value in networks of freestanding Sn nanowires [2].…”

“…The phase-slips along the nanowire cause a finite electrical resistance below Tc, although Cooper pairs are already well formed [20]. However, this limitation can be overcome by arranging the nanowires to form dense parallel arrays [1,5,7,21] or even random networks [2], which is also realized by superconducting atomic chains in some intrinsic quasi-1D superconductors including Sc3CoC4 [3] and Tl2Mo6Se6 [4]. In order to completely suppress the phase fluctuations and create a phasecoherent three-dimensional (3D) superconducting bulk state in the array, the superconducting order parameters in the individual 1D superconducting elements must undergo a macroscopic phase ordering transition that can only be triggered when there is a significant coupling.…”

“…In order to completely suppress the phase fluctuations and create a phasecoherent three-dimensional (3D) superconducting bulk state in the array, the superconducting order parameters in the individual 1D superconducting elements must undergo a macroscopic phase ordering transition that can only be triggered when there is a significant coupling. This can be achieved by Josephson coupling between parallel nanowires embedded in an insulating host, such as AlPO4-5 (AFI) zeolite [4,7] or mesoporous SBA-15 silica [1,21], or in the form of the proximity effect, such as realized in Tl2Mo6Se6 [4]. This phase ordering transition triggers a dimensional crossover in the array from a 1D fluctuating superconducting state with finite resistance at high temperatures to a zero-resistance 3D bulk phase-coherent superconducting state in the low temperature regime.…”

Two-level systems in superconducting quantum devices due to trapped quasiparticles

“…In thin films, the gap is also nonuniformly suppressed by the Altshuler-Aronov effect due to impurity scattering (25,34) as well as thickness variations (35), particularly relevant for Al (36), where recent experiments also reveal subgap states and charge localization across multiple grains (37). The clean, low-resistance NbN films that we chose to study in this work are characterized by a low carrier density (38). In such materials, it is very likely that the density of states (DOS) varies significantly, resulting in gap variations.…”

Dimensional crossover in the quasi-one-dimensional superconductor Tl2Mo6Se6

“…Furthermore, the pairing temperature obtained independently from the phase slip fitting lies consistently in the 5.9-6.1 K range, supporting our identification of T p ∼ 5.9 K as the pairing temperature in Tl 2 Mo 6 Se 6 . Our analysis leads us to a striking conclusion: despite its homogeneous monocrystalline nature, above T ons 3D , Tl 2 Mo 6 Se 6 experiences strong 1D fluctuations similar to a bundle of weakly-coupled superconducting nanowires [63][64][65][66] .…”