Superconducting Penetration Depth of Niobium

Maxfield, B. W.; McLean, W.

doi:10.1103/physrev.139.a1515

Cited by 137 publications

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“…The same value is obtained from extrapolating the linear H c2 (T) dependence observed below 6 K and using the bulk expression for H c2 , H c2 (T) = φ 0 /[2πξ(T) 2 ]. This value is significantly smaller than the BCS coherence length of Nb, ξ 0 = 38 nm [11], indicating that our films are in the dirty limit with a electron mean free path of l = 1.38 ξ(0) 2 /ξ 0 ≈ 5 nm. The Ginzburg-Landau parameter, κ = λ/ξ, can be estimated using the dirty-limit expressions for the penetration depth and the coherence length to κ = 0.72 λ L /l ≈ 7; λ L = 39 nm is the London penetration depth of Nb [11].…”

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confidence: 75%

“…This value is significantly smaller than the BCS coherence length of Nb, ξ 0 = 38 nm [11], indicating that our films are in the dirty limit with a electron mean free path of l = 1.38 ξ(0) 2 /ξ 0 ≈ 5 nm. The Ginzburg-Landau parameter, κ = λ/ξ, can be estimated using the dirty-limit expressions for the penetration depth and the coherence length to κ = 0.72 λ L /l ≈ 7; λ L = 39 nm is the London penetration depth of Nb [11]. Ratios of ξ(0)/a ≈ 0.1 and λ(0)/a ≈ 0.7 are achieved which are substantially larger than in previous reports [1,2] have been studied in superconducting wire networks [7][8][9], Josephson junction arrays [12] and perforated Al films [13].…”

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confidence: 75%

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Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

et al. 2002

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Nb films containing extended arrays of holes with 45-nm diameter and 100-nm spacing have been fabricated using anodized aluminum oxide (AAO) as substrate. Pronounced matching effects in the magnetization and Little-Parks oscillations of the superconducting critical temperature have been observed in fields up to 9 kOe. Flux pinning in the patterned samples is enhanced by two orders of magnitude as compared to unpatterned reference samples in applied fields exceeding 5 kOe. Matching effects are a dominant contribution to vortex pinning at temperatures as low as 4.2 K due to the extremely small spacing of the holes.

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Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

et al. 2002

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“…The penetration depth is sensitive to film quality and thickness, and deviates significantly for films thinner than 50 nm [34]. For the 80 nm thick Nb film used, the dependence is less critical, and we use the bulk London penetration depth, 39 nm [35]. The investigated junctions are smaller than or comparable to the Josephson penetration depth, λ Φ πμ…”

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confidence: 99%

Geometric dependence of Nb-Bi₂Te₃-Nb topological Josephson junction transport parameters

Molenaar

Leusink

Wang

et al. 2014

Supercond. Sci. Technol.

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Superconductor-topological insulator-superconductor Josephson junctions have been fabricated in order to study the width dependence of the critical current, normal state resistance and flux periodicity of the critical current modulation in an external field. Previous literature reports suggest anomalous scaling in topological junctions due to the presence of Majorana bound states. However, for most realized devices, one would expect that trivial π 2 -periodic Andreev levels dominate transport. We also observe anomalous scaling behaviour of junction parameters, but the scaling can be well explained by mere geometric effects, such as the parallel bulk conductivity shunt and flux focusing.

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“…For commonly used SC Nb with λ L ≈ 50 nm [24] and nanoscale thicknesses d SC = 50 ÷ 250 nm, we obtain g * ≈ 200 ÷ 400, which exceeds the electron spin g-factor by at least two orders of magnitude. In contrast to the Zeeman spin splitting [18], the orbital effect considered here does not require high magnetic fields to generate spin splitting, as will be shown below.…”

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Superconducting quantum spin Hall systems with giant orbitalgfactors

2015

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Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. We examine hybrid QSHS/superconductor structures in an external magnetic field and predict a gapless superconducting state with protected edge modes. It originates entirely from the orbital magnetic-field effect caused by the locking of the electron spin to the momentum of the superconducting condensate flow. We show that such spin-momentum locking can generate a giant orbital g-factor of order of several hundreds, allowing one to achieve significant spin polarization in the QSHS in the fields well below the critical field of the superconducting material. We propose a three-terminal setup in which the spin-polarized edge superconductivity can be probed by Andreev reflection, leading to unusual transport characteristics: a non-monotonic excess current and a zerobias conductance splitting in the absence of the Zeeman interaction.PACS numbers: 72.25. Dc, 73.23.Ad, 74.45.+c Introduction. Spin-Hall effects are one of the most active fields in modern solid state physics [1][2][3][4][5][6][7][8]. In particular, the quantum spin-Hall effect [5, 6, 9, 10] allows one to generate and convert charge and spin currents in protected edge channels [11]. Combining quantum spin-Hall systems (QSHSs) with superconductors (SCs) leads to a broader spectrum of interesting observable phenomena [12][13][14]. These include quantum interference effects reported in [13,14], indicating superconducting transport through the edge states in the QSH regime. Understanding edge superconductivity in QSHS/SC hybrids is also instrumental to the proposals to realize Majorana zero modes in topological insulators (see, e.g., [15] and reviews [16,17]).In this paper we predict a unique magnetic-field response of QSHS/SC hybrids which is characterized by very large effective g-factors reaching the order of several hundreds. It originates from the locking of the electron spin to the momentum of the superconducting condensate flow generated by an external magnetic field. We show that this orbital effect has the form similar to the Zeeman spin splitting in thin superconducting films [18], but involves an effective g-factor determined by the parameters of the QSHS/SC structure, viz.: the edge-state velocity, v, the thickness of the SC material, d SC , and the London penetration depth, λ L :

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Superconducting Penetration Depth of Niobium

Cited by 137 publications

References 20 publications

Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

Geometric dependence of Nb-Bi₂Te₃-Nb topological Josephson junction transport parameters

Superconducting quantum spin Hall systems with giant orbitalgfactors

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Superconducting Penetration Depth of Niobium

Cited by 137 publications

References 20 publications

Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

Superconducting transition and vortex pinning in Nb films patterned with nanoscale hole arrays

Geometric dependence of Nb-Bi2Te3-Nb topological Josephson junction transport parameters

Superconducting quantum spin Hall systems with giant orbitalgfactors

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Geometric dependence of Nb-Bi₂Te₃-Nb topological Josephson junction transport parameters