Measurement of magnetic penetration depth in superconducting films by two-coil mutual inductance technique

Zhang Ruo-Zhou; Qin Ming-Yang; Zhang Lu; You Li-Xing; Dong Chao; Sha Peng; Yuan Jie; Jin Kui

doi:10.7498/aps.69.20191758

Abstract

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 T_c, 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.

Keywords:

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
4.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
5.
Songshan Lake Materials Laboratory, Dongguan 523808, China

Corresponding author: Jin Kui, kuijin@iphy.ac.cn

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References

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Cited By

图 1 (a)双线圈互感装置示意图; (b)等效电路图

Figure 1. Schematic illustration (a) and equivalent circuit (b) of the two-coil mutual inductance apparatus.

DownLoad: Full-Size Img PowerPoint

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

Figure 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 λ_cal 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.

DownLoad: Full-Size Img PowerPoint

图 3 (a)两次测量同一片铌膜得到的感生电压V_{x, 1}(T)及V_{x, 2}(T); (b)铌膜的感生电压V(T = 4.5 K)随频率的依赖关系

Figure 3. (a) The induced voltage data V_{x, 1}(T) and V_{x, 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.

DownLoad: Full-Size Img PowerPoint

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V_x(T)及V_y(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T_c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

Figure 4. Two-coil mutual inductance measurement results of NbN films (NbN#1, NbN#2, NbN#3, NbN#4): (a) Temperature dependence of induced voltage V_x(T) and V_y(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.

DownLoad: Full-Size Img PowerPoint

[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 Google Scholar
[11]	Uemura Y J, Luke G M, Sternlieb B J, Brewer J H, Carolan J F, Hardy W N, Kadono R, Kempton J R, Kiefl R F, Kreitzman S R, Mulhern P, Riseman T M, Williams D L, Yang B X, Uchida S, Takagi H, Gopalakrishnan J, Sleight A W, Subramanian M A, Chien C L, Cieplak M Z, Xiao G, Lee V Y, Statt B W, Stronach C E, Kossler W J, Yu X H 1989 Phys. Rev. Lett. 62 2317 Google Scholar
[12]	Hashimoto K, Cho K, Shibauchi T, Kasahara S, Mizukami Y, Katsumata R, Tsuruhara Y, Terashima T, Ikeda H, Tanatar M A, Kitano H, Salovich N, Giannetta R W, Walmsley P, Carrington A, Prozorov R, Matsuda Y 2012 Science 336 1554 Google Scholar
[13]	Joshi K R, Nusran N M, Tanatar M A, Cho K, Bud’ko S L, Canfield P C, Fernandes R M, Levchenko A, Prozorov R 2019 arXiv: 1903.00053 [cond-mat.supr-con]
[14]	Wang C G, Li Z, Yang J, Xing L Y, Dai G Y, Wang X C, Jin C Q, Zhou R, Zheng G Q 2018 Phys. Rev. Lett. 121 167004 Google Scholar
[15]	Sonier J E, Brewer J H, Kiefl R F 2000 Rev. Mod. Phys. 72 769 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 Google Scholar
[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 Google Scholar
[22]	Ren C, Wang Z S, Luo H Q, Yang H, Shan L, Wen H H 2008 Phys. Rev. Lett. 101 257006 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
[33]	Dubuis G, He X, Božović I 2014 Rev. Sci. Instrum. 85 103902 Google Scholar
[34]	Clem J R, Coffey M W 1992 Phys. Rev. B 46 14662 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
[37]	丁世英 2009 物理学进展 29 239 Google Scholar Ding S Y 2009 Progress in Physics 29 239 Google Scholar
[38]	Kamlapure A, Mondal M, Chand M, Mishra A, Jesudasan J, Bagwe V, Benfatto L, Tripathi V, Raychaudhuri P 2010 Appl. Phys. Lett. 96 072509 Google Scholar
[39]	Tinkham M 1996 Introduction to Superconductivity (2 nd Ed.) (New York: McGraw-Hill) p103
[40]	Kosterlitz J M, Thouless D J 1972 J. Phys. C: Solid. State. Phys. 5 L124 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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Vol. 69, Issue 4 - 2020-02-20

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