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磁场穿透深度是联系超导体宏观电动力学与微观机制的重要物理量, 其精确测量对于研究超导机理以及探索超导应用具有重要意义. 在众多的磁场穿透深度测量方法中, 双线圈互感法具有测量精度高、技术相对成熟、对样品没有破坏等优点, 可被用于细致地研究超导薄膜的磁场穿透深度对温度、掺杂、外延应力等参量的依赖关系. 本文首先简要介绍了双线圈互感法的基本原理, 指出该方法的测量精度主要受系统几何参数及薄膜边缘漏磁的影响; 之后对自主设计搭建的透射型双线圈互感装置进行了系统的校验, 并详细说明了其测量精度: 对于厚度为100 nm, 穿透深度为150 nm的典型薄膜样品, 穿透深度绝对值的测量误差小于10%; 最后通过测量NbN超导薄膜的磁场穿透深度进一步检验了装置的精度, 分析表明穿透深度的测量值与文献报道结果符合.The magnetic penetration depth (λ) of a superconductor is an important parameter which connects the macroscopic electrodynamics with the microscopic mechanism of superconductivity. High-accuracy measurement of λ is of great significance for revealing the pairing mechanism of superconductivity and exploring the applications of superconductors. Among various methods used to measure λ of superconducting films, the two-coil mutual inductance (MI) technique has been widely adopted due to its high precision and simplicity. In this paper, we start with introducing the principle of MI technique and pointing out that its accuracy is mainly limited by the uncertainties in the geometric parameters (e.g. the distance between two coils) and the leakage flux around the film edge. On this basis, we build a homemade transmission-type MI device with a delicate design to achieve high-accuracy. Two coils are fixed by a single-crystal sapphire block machined with high precisions to minimize the uncertainty in geometry. As a result, the reproducibility in induced voltage measured with sample remounted is better than 4%. Besides, the flux leakage around the film edge is accurately determined by measuring a thick Nb film and Nb foils. The voltage induced by leakage flux is only around 1% of that measured in the normal state. Therefore, the absolute value of λ can be accurately extracted after flux leakage subtraction and normalization. It is shown that the error of the measured λ is less than 10% for a typical superconducting film with a thickness of 100 nm and a penetration depth of 150 nm. Furthermore, the performance of our apparatus is tested on epitaxial NbN films with thickness of 6.5 nm. The results show that the low temperature variation of superfluid density is well described by the dirty s-wave BCS theory, and at temperatures close to Tc, the superfluid density decrease drastically, owing to the Berezinski-Kosterlitz-Thouless transition transition. Moreover, the zero-temperature magnetic penetration depth and the superconducting energy gap extracted from the fitting parameters are both consistent with the reported values. Our device provides an ideal platform for carrying out detailed studies of the dependence of λ on temperature, chemical composition and epitaxial strain, etc. It could also be utilized to characterize other parameters of superconductor such as the critical current density, and when combined with the ionic liquid gating technique, our device offers an efficient route for revealing the microscopic mechanism of superconductivity.
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Keywords:
- magnetic penetration depth /
- two-coil mutual inductance technique /
- NbN superconducting film /
- Meissner effect
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图 1 (a)双线圈互感装置示意图; (b)等效电路图
Fig. 1. Schematic illustration (a) and equivalent circuit (b) of the two-coil mutual inductance apparatus.
图 2 (a) d = 100 nm, λ = 150 nm的超导薄膜的互感系数随薄膜半径R的变化曲线; (b)基于不同的线圈间距(h = 0.9, 4.5, 9.0 mm) 得到的穿透深度计算值随薄膜半径R的变化曲线, 虚线代表实际穿透深度λ = 150 nm
Fig. 2. (a) The mutual inductance as a function of film radii R calculated for the typical superconducting film with d = 100 nm, λ = 150 nm; (b) calculations of penetration depth λcal vs film radii R for different spacings between two coils (h = 0.9, 4.5, 9.0 mm). The real penetration depth (λ = 150 nm) is indicated by the dotted line.
图 3 (a)两次测量同一片铌膜得到的感生电压Vx, 1(T)及Vx, 2(T); (b)铌膜的感生电压V(T = 4.5 K)随频率的依赖关系
Fig. 3. (a) The induced voltage data Vx, 1(T) and Vx, 2(T) taken from the same Nb film with sample remounted; (b) the frequency dependence of induced voltage V(T = 4.5 K) for the Nb film.
图 4 NbN薄膜(NbN#1, NbN#2, NbN#3, NbN#4)的双线圈互感测量结果 (a) NbN#1样品的感生电压曲线Vx(T)及Vy(T); (b)四个样品的穿透深度随温度变化曲线λ(T); (c) NbN#1样品的超流密度-温度曲线
${{\rm{\lambda }}^{ - 2}}\left( T \right) \propto {n_{\rm{s}}}\left( T \right)$ , 黑色实线是脏极限BCS理论的拟合结果; (d)四块样品的穿透深度零温外延值λ (T → 0)与Tc的关系, 符合文献报道趋势[38], 误差棒的长度小于数据点的标记尺寸Fig. 4. Two-coil mutual inductance measurement results of NbN films (NbN#1, NbN#2, NbN#3, NbN#4): (a) Temperature dependence of induced voltage Vx(T) and Vy(T) for NbN#1; (b) temperature-dependent penetration depth λ(T) of four NbN films; (c) temperature variation in superfluid density
${{\rm{\lambda }}^{ - 2}}\left( T \right) \propto {n_{\rm{s}}}\left( T \right)$ for NbN#1. The black line shows the dirty s-wave BCS theory fit to the data; (d) the value of λ (T → 0) for four NbN films, which shows a good agreement with the published value[38]. The length of error bar is shorter than the symbol size. -
[1] Meissner W, Ochsenfeld R 1933 Naturwissenschaften 21 787
[2] London F, London H 1935 Proc. R. Soc. A 149 71
Google Scholar
[3] Prozorov R, Giannetta R W 2006 Supercond. Sci. Technol. 19 R41
Google Scholar
[4] Prozorov R, Kogan V G 2011 Rep. Prog. Phys. 74 124505
Google Scholar
[5] Hardy W N, Bonn D A, Morgan D C, Liang R, Zhang K 1993 Phys. Rev. Lett. 70 3999
Google Scholar
[6] Skinta J A, Kim M S, Lemberger T R, Greibe T, Naito M 2002 Phys. Rev. Lett. 88 207005
Google Scholar
[7] Fletcher J D, Carrington A, Taylor O J, Kazakov S M, Karpinski J 2005 Phys. Rev. Lett. 95 097005
Google Scholar
[8] Emery V J, Kivelson S A 1995 Nature 374 434
Google Scholar
[9] Božović I, He X, Wu J, Bollinger A T 2016 Nature 536 309
Google Scholar
[10] Homes C C, Dordevic S V, Strongin M, Bonn D A, Liang R, Hardy W N, Komiya S, Ando Y, Yu G, Kaneko N, Zhao X, Greven M, Basov D N, Timusk T 2004 Nature 430 539
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Google Scholar
[16] Hashimoto K, Shibauchi T, Kasahara S, Ikada K, Tonegawa S, Kato T, Okazaki R, van der Beek C J, Konczykowski M, Takeya H, Hirata K, Terashima T, Matsuda Y 2009 Phys. Rev. Lett. 102 207001
Google Scholar
[17] Hashimoto K, Shibauchi T, Kato T, Ikada K, Okazaki R, Shishido H, Ishikado M, Kito H, Iyo A, Eisaki H, Shamoto S, Matsuda Y 2009 Phys. Rev. Lett. 102 017002
Google Scholar
[18] Pang G, Smidman M, Zhang J, Jiao L, Weng Z, Nica E M, Chen Y, Jiang W, Zhang Y, Xie W, Jeevan H S, Lee H, Gegenwart P, Steglich F, Si Q, Yuan H 2018 Proc. Natl. Acad. Sci. U.S.A. 115 5343
Google Scholar
[19] Van Degrift C T 1975 Rev. Sci. Instrum. 46 599
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[20] Weng Z F, Zhang J L, Smidman M, Shang T, Quintanilla J, Annett J F, Nicklas M, Pang G M, Jiao L, Jiang W B, Chen Y, Steglich F, Yuan H Q 2016 Phys. Rev. Lett. 117 027001
Google Scholar
[21] Okazaki R, Konczykowski M, van der Beek C J, Kato T, Hashimoto K, Shimozawa M, Shishido H, Yamashita M, Ishikado M, Kito H, Iyo A, Eisaki H, Shamoto S, Shibauchi T, Matsuda Y 2009 Phys. Rev. B 79 064520
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Google Scholar
[23] Tafuri F, Kirtley J R, Medaglia P G, Orgiani P, Balestrino G 2004 Phys. Rev. Lett. 92 157006
Google Scholar
[24] Luan L, Lippman T M, Hicks C W, Bert J A, Auslaender O M, Chu J H, Analytis J G, Fisher I R, Moler K A 2011 Phys. Rev. Lett. 106 067001
Google Scholar
[25] Hebard A F, Fiory A T 1980 Phys. Rev. Lett. 44 291
Google Scholar
[26] Jeanneret B, Gavilano J L, Racine G A, Leemann C, Martinoli P 1989 Appl. Phys. Lett. 55 2336
Google Scholar
[27] Kinney J, Garcia-Barriocanal J, Goldman A M 2015 Phys. Rev. B 92 100505
Google Scholar
[28] Claassen J H, Wilson M L, Byers J M, Adrian S 1997 J. Appl. Phys. 82 3028
Google Scholar
[29] Turneaure S J, Pesetski A A, Lemberger T R 1998 J. Appl. Phys. 83 4334
Google Scholar
[30] Turneaure S J, Ulm E R, Lemberger T R 1996 J. Appl. Phys. 79 4221
Google Scholar
[31] Fiory A T, Hebard A F, Mankiewich P M, Howard R E 1988 Appl. Phys. Lett. 52 2165
Google Scholar
[32] He X, Gozar A, Sundling R, Božović I 2016 Rev. Sci. Instrum. 87 113903
Google Scholar
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Google Scholar
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Google Scholar
[35] Lee J Y, Kim Y H, Hahn T S, Choi S S 1996 Appl. Phys. Lett. 69 1637
Google Scholar
[36] Duan M C, Liu Z L, Ge J F, Tang Z J, Wang G Y, Wang Z X, Guan D, Li Y Y, Qian D, Liu C, Jia J F 2017 Rev. Sci. Instrum. 88 073902
Google Scholar
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Google Scholar
Ding S Y 2009 Progress in Physics 29 239
Google Scholar
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Google Scholar
[39] Tinkham M 1996 Introduction to Superconductivity (2 nd Ed.) (New York: McGraw-Hill) p103
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Google Scholar
[41] Nelson D R, Kosterlitz J M 1977 Phys. Rev. Lett. 39 1201
Google Scholar
[42] Qin M Y, Zhang R Z, Feng Z P, Lin Z F, Wei X J, Alvarez S B, Dong C, Silhanek A V, Zhu B Y, Yuan J, Qin Q, Jin K 2020 J. Supercond. Novel Magn. 33 159
Google Scholar
[43] Draskovic J, Lemberger T R, Peters B, Yang F, Ku J, Bezryadin A, Wang S 2013 Phys. Rev. B 88 134516
Google Scholar
[44] Lemberger T R, Ahmed A 2013 Phys. Rev. B 87 214505
Google Scholar
[45] Claassen J H, Reeves M E, Soulen R J 1991 Rev. Sci. Instrum. 62 996
[46] Li D, Lee K, Wang B Y, Osada M, Crossley S, Lee H R, Cui Y, Hikita Y, Hwang H Y 2019 Nature 572 624
Google Scholar
[47] Logvenov G, Gozar A, Bozovic I 2009 Science 326 699
Google Scholar
[48] Nam H, Su P H, Shih C K 2018 Rev. Sci. Instrum. 89 043901
Google Scholar
[49] Zuev Y, Lemberger T R, Skinta J A, Greibe T, Naito M 2003 Phys. Status Solidi B 236 412
Google Scholar
[50] Cui Y T, Moore R G, Zhang A M, Tian Y, Lee J J, Schmitt F T, Zhang W H, Li W, Yi M, Liu Z K, Hashimoto M, Zhang Y, Lu D H, Devereaux T P, Wang L L, Ma X C, Zhang Q M, Xue Q K, Lee D H, Shen Z X 2015 Phys. Rev. Lett. 114 037002
Google Scholar
[51] Rout P K, Budhani R C 2010 Phys. Rev. B 82 024518
Google Scholar
[52] Kumar S, Kumar C, Jesudasan J, Bagwe V, Raychaudhuri P, Bose S 2013 Appl. Phys. Lett. 103 262601
Google Scholar
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