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Order parameters of non-centrosymmetric superconductors

Zhang Jing-Lei Jiao Lin Pang Gui-Ming Yuan Hui-Qiu

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Order parameters of non-centrosymmetric superconductors

Zhang Jing-Lei, Jiao Lin, Pang Gui-Ming, Yuan Hui-Qiu
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  • The non-centrosymmetric (NCS) superconductors (SCs), a class of novel superconducting materials, have recently attracted considerable interests. As a result of antisymmetric spin-orbital coupling (ASOC) arising from the absence of inversion symmetry, the superconducting pairing state of these compounds allows the admixture of spin-singlet and spin-triplet components. This is in contrast to other previously studied superconductors, which usually possess an inversion symmetry in their crystal structure, and therefore their pairing state is of either spin-singlet/even parity or the spin-triplet/odd parity due to the restrictions of the Pauli principles and parity conservation.#br#Determination of the gap structure is crucial for unveiling the pairing state of NCS SCs. In this article, we first describe a method of measuring the precise temperature dependence of the changes in the London penetration depth using the tunnel-diode-oscillator (TDO), which provides an important evidence for the superconducting gap structures. Then the pairing states of NCS SCs are briefly reviewed, putting the emphasis on a few compounds with different ASOC strengths. It is proposed that the ASOC may tune the ratio of the spin-triplet to the spin-singlet component and, therefore, the spin-triplet state may become dominant while the ASOC effect is sufficiently strong in NCS SCs. However, our investigations demonstrate that the actual case is more complicated and there is no simple correspondence between the ASOC size and the pairing states. Instead, it is found that the band splitting due to the ASOC effect divided by the superconducting transition temperature Tc may better characterize of the superconducting pairing states in NCS SCs.
      Corresponding author: Yuan Hui-Qiu, hqyuan@zju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11474251), the National Basic Research Program of China (Grant No. 2011CBA00103), and the Fundamental Research Funds for the Central Universities.
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    Izawa K, Kasahara Y, Matsuda Y, Behnia K, Yasuda T, Settai R, ōnuki Y 2005 Phys. Rev. Lett. 94 197002

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    Hayashi N, Wakabayashi K, Frigeri P A, Sigrist M 2006 Phys. Rev. B 73 024504

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  • [1]

    Anderson P W 1958 J. Phys. Chem. Solids 11 26

    [2]

    Frigeri P A, Agterberg DF, Koga A, Sigrist M 2004 Phys. Rev. Lett. 92 097001

    [3]

    Gor'kov L P, Rashba E I 2001 Phys. Rev. Lett. 87 037004

    [4]

    Bauer E, Sigrist M 2012 Non-Centrosymmetric Superconductors: Introduction and Overview (Springer-Verlag, Berlin Heidelberg)

    [5]

    Kaur R P, Agterberg D F, Sigrist M 2005 Phys. Rev. Lett. 94 137002

    [6]

    Agterberg D F, Kaur R P 2007 Phys. Rev. B 75 064511

    [7]

    Sato M, Fujimoto S 2009 Phys. Rev. B 79 094504

    [8]

    Chadov S, Qi X, Kbler J, Fecher G H, Felser C, Zhang S C 2010 Nat. Mater. 9 541

    [9]

    Lin H, Wray L A, Xia Y, Xu S, Jia S, Cava R J, Bansil A, Hasan M Z 2010 Nat. Mater. 9 546

    [10]

    Bauer E, Hilscher G, Michor H, Paul Ch, Scheidt E W, Gribanov A, Seropegin Yu, Noël H, Sigrist M, Rogl R 2004 Phys. Rev. Lett. 92 027003

    [11]

    Akazawa T, Hidaka H, Fujiwara T, Kobayashi T C, Yamamoto E, Haga Y, Settai R, ōnuki Y 2004 J Phys.: Condens. Matter 16 L29

    [12]

    Sugitani I, Okuda Y, Shishido H, Yamada T, Thamizhavel A, Yamamoto E, Matsuda T D, Haga Y, Takeuchi T, Settai R, ōnuki Y 2006 J. Phys. Soc. Jpn. 75 043703

    [13]

    Kimura N, Ito K, Saitoh K, Umeda Y, Aoki H 2005 Phys. Rev. Lett. 95 247004

    [14]

    Kawai T, Muranaka H, Measson M A, Shimoda T, Doi Y, Matsuda T D, Haga Y, Knebel G, Lapertot G, Aoki D, Flouquet J, Takeuchi T, Settai R, Onuki Y 2008 J. Phys. Soc. Jpn. 77 064716

    [15]

    Bauer E, Khan R T, Michor H, Royanian E, Grytsiv A, Koblyuk N M, Rogl P, Reith D, Podloucky R, Scheidt R W, Wolf W, M Marsman 2009 Phys. Rev. B 80 064504

    [16]

    Eguchi G, Wadati H, Sugiyama T, Ikenaga E, Yonezawa S, Maeno Y 2012 Phys. Rev. B 86 184510

    [17]

    Togano K, Badica P, Nakamori Y, Orimo S, Takeya H, Hirata K 2004 Phys. Rev. Lett. 93 247004

    [18]

    Badica P, Kondo T, Togano K 2005 J. Phys. Soc. Jpn. 74 1014

    [19]

    Klimczuk T, Ronning F, Sidorov V, Cava R J, Thompson J D 2007 Phys. Rev. Lett. 99 257004

    [20]

    Bonalde I, Ribeiro R L,Brämer-Escamilla W, Mu G, Wen H H 2009 Phys. Rev. B 79 052506

    [21]

    Bauer E, Rogl G, Chen X G, Khan R T, Michor H, Hilscher G, Royanian E, Kumagai K, Li D Z, Li Y Y, Podloucky R, Rogl R 2010 Phys. Rev. B 82 064511

    [22]

    Wakui W, Akutagawa S, Kase N, Kawashima K, Muranaka T, Iwahori Y, ABE J, Akimitsu J 2009 J. Phys. Soc. Jpn. 78 034710

    [23]

    Joshi B, Thamizhavel A, Ramakrishnan S 2011 Phys. Rev. B 84 064518

    [24]

    Krupka M C, Giorgi A L, Krikorian N H, Szklarz E G 1969 J. Less-Common Met. 17 91

    [25]

    Mochiku T, Nakane T, Kito H, Takeya H, Harjo S, Ishigaki T, Kamiyama T, Wada T, Hirata K 2005 Physica C 421 426

    [26]

    Amano G, Akutagawa S, Muranak T, Zenitani Y, Akimitsu 2004 J. Phys. Soc. Jpn. 73 530

    [27]

    Zuev Y L, Kuznetsova V A, Prozorov R, Vannette M D, Lobanov M V, Christen D K, Thompson J R 2007 Phys. Rev. B 76 132508

    [28]

    Kase N, Akimitsu J 2009 J. Phys. Soc. Jpn 78 044710

    [29]

    Knapton A G 1959 J. Less-Common Met. 1 480

    [30]

    Yuan H Q, Agterberg D F, Hayashi N, Badica P, Vandervelde D, Togano K, Sigrist M, Salamon M B 2006 Phys. Rev. Lett. 97 017006

    [31]

    Yuan H Q, Salamon M B, Badica P, Togano K 2008 Physica B 403 1138

    [32]

    Nishiyama M, Inada Y, Zheng G Q 2007 Phys. Rev. Lett. 98 047002

    [33]

    Takeya H, ElMassalami M, Kasahara S, Hirata K 2007 Phys. Rev. B. 76 104506

    [34]

    Harada S, Zhou J J, Yao Y G, Inada Y, Zheng G Q 2012 Phys. Rev. B 86 220502

    [35]

    Jiao L, Zhang J L, Chen Y, Weng Z F, Shao Y M, Feng J Y, Joshi B, Thamizhavel A, Ramakrishnan S, Lu X, Yuan H Q 2014 Phys. Rev. B 89 060507

    [36]

    Sonier J, Brewer J, Kiefl R 2000 Rev. Mod. Phys. 72 769

    [37]

    Luan L, Lippman, Clifford T M, Hicks 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

    [38]

    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

    [39]

    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

    [40]

    Fiory A T, Hebard A F, Mankiewich P M, Howard R E 1988 Appl. Phys. Lett. 52 2165

    [41]

    Van Degrift C T 1975 Rev. Sci. Instrum. 46 599

    [42]

    Prozorov R, Giannetta R W 2006 Supercond. Sci. Technol. 19 R41

    [43]

    Zhang J L 2014 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [张警蕾 2014 博士学位论文 (浙江大学)]

    [44]

    Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W, Schäfer H 1979 Phys. Rev. Lett. 43 1892

    [45]

    Bonalde I, Brämer-Escamilla W, Bauer E 2005 Phys. Rev. Lett. 94 207002

    [46]

    Ribeiro R L, I. Bonalde I, Haga Y, Settai R, Onuki Y 2009 J. Phys. Soc. Jpn. 78 115002

    [47]

    Yogi M, Kitaoka Y, Hashimoto S, Yasuda T, Settai R, Matsuda T D, Haga Y, ōnuki Y, Rogl P, Bauer E 2004 Phys. Rev. Lett. 93 027003

    [48]

    Izawa K, Kasahara Y, Matsuda Y, Behnia K, Yasuda T, Settai R, ōnuki Y 2005 Phys. Rev. Lett. 94 197002

    [49]

    Hayashi N, Wakabayashi K, Frigeri P A, Sigrist M 2006 Phys. Rev. B 73 024504

    [50]

    Bauer E, Lackner R, Hilscher G, Michor H, Sieberer M, Eichler A, Gribanov A, SeropeginY, Rogl P 2005 J. Phys.: Condens. Matter 17 1877

    [51]

    Ribeiro R L, I. Bonalde I, Haga Y, Settai R, Onuki Y 2009 J. Phys. Soc. Jpn. 78 115002

    [52]

    Settai R, Miyauchi Y, Takeuchi T, Lévy F, Sheikin I and ōnuki Y 2008 J. Phys. Soc. Jpn. 77 073705

    [53]

    Peets D C, Eguchi G, Kriener M, Harada, Shamsuzzamen S K, Inada Y, Zheng G Q, Maeno Y 2011 Phys. Rev. B 84 054521

    [54]

    Lee K W, Pickett W E 2005 Phys. Rev. B 72 174505

    [55]

    Kuroiwa S, Saura Y, Akimitsu J, Hiyaishi M, Miyazaki M, Satoh K H, Takeshita S, Kadono R 2009 Phys. Rev. Lett. 100 097002

    [56]

    Akutagawa S, Akimitsu J 2007 J. Phys. Soc. Jpn. 76 024713

    [57]

    Harada A, Akutagawa S, Miyamichi Y, Mukuda H, Kitaoka Y, Akimitsu J 2007 J. Phys. Soc. Jpn. 76 023704

    [58]

    Chen J, Salamon M B, Akutagawa S, Akimitsu J, Singleton J, Zhang J L, Jiao L, Yuan H Q 2011 Phys. Rev. B 83 144529

    [59]

    Werthamer N R, Helfand E, Hohenberg P C 1966 Phys. Rev. 147 295

    [60]

    Tinkham M 1975 Introduction to Superconductivity, Krieger Publishing Company, Malabar, Florida.

    [61]

    Agterberg D F, Barzykin V, Gor'kov L P 1999 Phys. Rev. B 60 14868

    [62]

    Nishikayama Y, Shishidou T, Oguchi T 2007 J. Phys. Soc. Jpn. 76 064714

    [63]

    Bodak O I, Marusin E P 1979 DoklAkad. NaukUkr. SSR Ser. A 12 1048

    [64]

    Kotsanidis P, Jakinthos J K, Gamari-Seale E 1989 J. Less-Common Met. 152 287

    [65]

    Hillier A D, Quintanilla J, Cywinski R 2009 Phys. Rev. Lett. 102 117007

    [66]

    Quintanilla J, Hillier A D, Annett J F, Cywinski R 2010 Phys. Rev. B 82 174511

    [67]

    Hillier A D, Quintanilla J, Mazidian B, Annett J F, Cywinski R 2012 Phys. Rev. Lett. 109 097001

    [68]

    Bonalde I, Ribeiro R L, Syu K J, Sung H H, Lee W H 2011 New J. Phys. 13 123022

    [69]

    Pecharsky V K, Miller L L, Gschneidner K A 1998 Phys. Rev. B 58 497

    [70]

    Iwamoto Y, Iwasaki Y, Ueda K, Kohara T 1998 Phys. Lett. A 250 439

    [71]

    Chen J, Jiao L, Zhang J L, Chen Y, Yang L, Nicklas M, Steglich F, Yuan H Q 2013 New J. Phys. 15 053005

    [72]

    Hase I, Yanagisawa T 2009 J. Phys. Soc. Jpn. 78 084724

    [73]

    Iwamoto Y, Iwasaki Y, Ueda K, Kohara T 1998 Phys. Lett. A 250 439

    [74]

    Mondal M, Joshi B, Kumar S, Kamlapure A, Ganguli S C, Thamizhavel A, Mandal S, Ramakrishnan S, Raychaudhuri P 2012 Phys. Rev. B 86 094520

    [75]

    Matano K, Maeda S, Sawaoka H, Muro Y, Takabatake T, Joshi B, Ramakrishnan S, Kawashima S K, Akimitsu J, Zheng G Q 2013 J. Phys. Soc. Jpn. 82 084711

    [76]

    Sun Z X, Enayat M, Maldonado A, Lithgow C, Yelland E, Peets D C, Yaresko A, Schnyder A P, Wahl P 2015 Nat. Commun. 6 6633

    [77]

    Chen J, Jiao L, Zhang J L, Chen Y, Yang L, Nicklas M, Steglich F, Yuan H Q 2012 Phys. Rev. B 88 144510

    [78]

    Karki A B, Xiong Y M, Haldolaarachchige N, StadlerS, Vekhter I, Adams P W, Young D P, Phelan W A, Chan J Y 2011 Phys. Rev. B 83 144525

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Publishing process
  • Received Date:  18 June 2015
  • Accepted Date:  03 July 2015
  • Published Online:  05 November 2015

Order parameters of non-centrosymmetric superconductors

    Corresponding author: Yuan Hui-Qiu, hqyuan@zju.edu.cn
  • 1. High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China;
  • 2. Center for Correlated Matter, Zhejiang University, Hangzhou 310058, China;
  • 3. Department of Physics, Zhejiang University, Hangzhou 310027, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11474251), the National Basic Research Program of China (Grant No. 2011CBA00103), and the Fundamental Research Funds for the Central Universities.

Abstract: The non-centrosymmetric (NCS) superconductors (SCs), a class of novel superconducting materials, have recently attracted considerable interests. As a result of antisymmetric spin-orbital coupling (ASOC) arising from the absence of inversion symmetry, the superconducting pairing state of these compounds allows the admixture of spin-singlet and spin-triplet components. This is in contrast to other previously studied superconductors, which usually possess an inversion symmetry in their crystal structure, and therefore their pairing state is of either spin-singlet/even parity or the spin-triplet/odd parity due to the restrictions of the Pauli principles and parity conservation.#br#Determination of the gap structure is crucial for unveiling the pairing state of NCS SCs. In this article, we first describe a method of measuring the precise temperature dependence of the changes in the London penetration depth using the tunnel-diode-oscillator (TDO), which provides an important evidence for the superconducting gap structures. Then the pairing states of NCS SCs are briefly reviewed, putting the emphasis on a few compounds with different ASOC strengths. It is proposed that the ASOC may tune the ratio of the spin-triplet to the spin-singlet component and, therefore, the spin-triplet state may become dominant while the ASOC effect is sufficiently strong in NCS SCs. However, our investigations demonstrate that the actual case is more complicated and there is no simple correspondence between the ASOC size and the pairing states. Instead, it is found that the band splitting due to the ASOC effect divided by the superconducting transition temperature Tc may better characterize of the superconducting pairing states in NCS SCs.

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