自旋涨落与非常规超导配对

李建新

doi:10.7498/aps.70.20202180

摘要

铜氧化物高温超导、铁基高温超导、重费米子超导和κ-型层状有机超导等超导体的超导态都与磁性有序态相邻, 且超导能隙在动量空间一般存在变号. 因此, 这些超导体的超导机理被认为有别于常规BCS超导中的电子交换声子导致的各向同性s-波配对. 在这些非常规超导中, 自旋涨落被认为是导致电子形成库珀对的主要起源之一. 本文主要以铜基和铁基高温超导为例简要综述非常规超导中的自旋序和自旋涨落性质, 二维哈伯徳模型中超导的起因及在解释铜基和铁基高温超导配对对称性的应用, 以及与非常规超导紧密相关的中子自旋共振模性质和理论解释. 我们认为, 尽管磁性和超导性的相互影响已经过多年研究, 但仍是当前一个富有挑战的活跃研究领域.

关键词:

Abstract

High-T_c cuprates, iron-based superconductors, heavy-fermion superconductors and κ-type layered organic superconductors share some common features − the proximity of the superconducting state to the magnetic ordered state and the non-s-wave superconducting pairing function. It is generally believed that the Cooper pairings in these unconventional superconductors are mediated by spin fluctuations. In this paper, we present a brief overview on the spin dynamics and unconventional pairing, focusing on high-T_c cuprates and iron-based superconductors. In particular, we will overview the properties of the neutron spin resonance and its possible origin, the pairing mechanism in Hubbard model within the weak-coupling framework and its application to the aforesaid unconventional superconductors. We point out that the interplay between magnetism and superconductivity is still an area of active research.

Keywords:

作者及机构信息

李建新^1,2

1.
南京大学物理学院, 固体微结构物理国家重点实验室, 南京　210093

2.
南京大学, 人工微结构科学与技术协同创新中心, 南京　210093

通信作者: 李建新, jxli@nju.edu.cn

基金项目: 国家重点基础研究发展计划(批准号: 2016YFA0300401)和国家自然科学基金(批准号: 11774152)资助的课题.

Authors and contacts

Li Jian-Xin^1,2

1.
National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China

2.
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Corresponding author: Li Jian-Xin, jxli@nju.edu.cn

Funds: Project supported by the National Basic Research Program of China (Grant No. 2016YFA0300401) and the National Natural Science Foundation of China (Grant No. 11774152)

文章全文 : translate this paragraph

参考文献

[1]	Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W, Schaefer H 1979 Phys. Rev. Lett. 43 1892 Google Scholar
[2]	Bednorz J G, Müller K A 1986 Z. Phys. B: Condens. Matter 64 189 Google Scholar
[3]	Kamihara Y, Hiramatsu H, Hirano M, Kawamura R, Yanagi H, Kamiya T, Hosono H 2006 J. Am. Chem. Soc. 128 10012 Google Scholar
[4]	Kamihara Y, Watanabe T, Hirano M, Hosono H 2008 J. Am. Chem. Soc. 130 3296 Google Scholar
[5]	Kini A M, Geiser U, Wang H H, Carlson K D, Williams J M, Kwok W K, Vandervoort K G, Thompson J E, Stupka D, Jung D, Whangbo M H 1990 Inorg. Chem. 29 2555 Google Scholar
[6]	Maeno Y, Hashimoto H, Yoshida K, Nishizaki S, Fujita T, Bednorz J G, Lichtenberg F 1994 Nature 372 532 Google Scholar
[7]	Takada K, Sakurai H, Takayama-Muromachi E, Izumi F, Dilanian R A, Sasaki R 2003 Nature 422 53 Google Scholar
[8]	Wu M K, Ashburn J R, Torng C J, Hor P H, Meng R L, Gao L, Huang Z J, Wang Y Q, Chu C W 1987 Phys. Rev. Lett. 58 908 Google Scholar
[9]	Zhao Z X, Chen L Q, Yang Q S, Huang Y H, Chen G H, Tang R M, Liu G R, Cui C G, Chen L, Wang L H, Guo S Q, Li S L, Bi J Q 1987 Chin. Sci. Bull. 32 661
[10]	Chen X H, Wu T, Wu G, Liu R H, Chen H, Fang D F 2008 Nature 453 761 Google Scholar
[11]	Ren Z A, Lu W, Yang J, Yi W, Shen X L, Zheng C, Che G C, Dong X L, Sun L L, Zhou F, Zhao Z X 2008 Chin. Phys. Lett. 25 2215 Google Scholar
[12]	Stewart G R 2017 Adv. Phys. 66 75 Google Scholar
[13]	Scalapino D J 2012 Rev. Mod. Phys. 84 1383 Google Scholar
[14]	Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17 Google Scholar
[15]	Chen X H, Dai P, Feng D L, Xiang T, Zhang F C 2014 Nat. Sci. Rev. 1 371 Google Scholar
[16]	Dai P C 2015 Rev. Mod. Phys. 87 855 Google Scholar
[17]	Si Q, Yu R, Abrahams E 2016 Nat. Rev. Mater. 1 16017 Google Scholar
[18]	Rossat-Mignod J, Regnault L P, Vettier C, Bourges C, Burlet C, Bossy J, Henry J Y, Lapertot G 1991 Physica C 185-189 86 Google Scholar
[19]	Christianson A D, Goremychkin E A, Osborn R, Rosenkranz S, Lumsden M D, Malliakas C D, Todorov I S, Claus H, Chung D Y, Kanatzidis M G, Bewley R I, Guidi T 2008 Nature 456 930 Google Scholar
[20]	Stock C, Broholm C, Hudis J, Kang H J, Petrovic C 2008 Phys. Rev. Lett. 100 087001 Google Scholar
[21]	Avci S, Chmaissem O, Chung D Y, Rosenkranz S, Goremychkin E A, Castellan J P, Todorov I S, Schlueter J A, Claus H, Daoud-Aladine A, Khalyavin D D, Kanatzidis M G, Osborn R 2012 Phys. Rev. B 85 184507 Google Scholar
[22]	Nandi S, Kim M G, Kreyssig A, Fernandes R M, Pratt D K, Thaler A, Ni N, Bud’ko S L, Canfield P C, Schmalian J, McQueeney R J, and Goldman A I 2010 Phys. Rev. Lett. 104 057006 Google Scholar
[23]	Nicklas M, Stockert O, Park T, Habicht K, Kiefer K, Pham L D, Thompson J D, Fisk Z, Steglich F 2007 Phys. Rev. B 76 052401
[24]	Nam M S, Ardavan A, Blundell S J, Schlueter J A 2007 Nature 449 584 Google Scholar
[25]	Tranquada J M 2007 Handbook of High-Temperature Superconductivity: Theory and Experiment (New York: Spnnger), also in arXiv: 0512115
[26]	Eschrig M 2006 Adv. Phys. 55 47 Google Scholar
[27]	Bourges P, Regnault L P, Sidis Y, Vettier C 1996 Phys. Rev. B 53 876 Google Scholar
[28]	Mazzone D G, Raymond S, Gavilano J L, Steffens P, Schneidewind A, Lapertot G, Kenzelmann M 2017 Phys. Rev. Lett. 119 187002 Google Scholar
[29]	Savrasov S Y, Andersen O K 1996 Phys. Rev. Lett. 77 4430 Google Scholar
[30]	Boeri L, Dolgov O V, Golubov A A 2008 Phys. Rev. Lett. 101 026403 Google Scholar
[31]	Berk N F, Schrieffer J R 1966 Phys. Rev. Lett. 17 433 Google Scholar
[32]	Emery V J 1986 Synth. Met. 13 21 Google Scholar
[33]	Miyake K, Schmitt-Rink S, Varma C M 1986 Phys. Rev. B 34 6554 Google Scholar
[34]	Scalapino D J, Loh E, Hirsch J E 1986 Phys. Rev. B 34 8190 Google Scholar
[35]	Coldea R, Hayden S M, Aeppli G, Perring T G, Frost C D, Mason T E, Cheong S W, Fisk Z 2001 Phys. Rev. Lett. 86 5377 Google Scholar
[36]	Headings N S, Hayden S M, Coldea R, Perring T G 2010 Phys. Rev. Lett. 105 247001 Google Scholar
[37]	Piazza B D, Mourigal M, Christensen N B, Nilsen G J, Tregenna-Piggott P, Perring T G, Enderle M, McMorrow D F, Ivanov D A, Ronnow H M 2015 Nat. Phys. 11 62 Google Scholar
[38]	Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y, Sandvik A W 2017 Phys. Rev. X 7 041072
[39]	Yu S L, Wang W, Dong Z Y, Yao Z J, Li J X 2018 Phys. Rev. B 98 134410 Google Scholar
[40]	Singh R R P, Gelfand M P 1995 Phys. Rev. B 52 15695 Google Scholar
[41]	Sandvik A W, Singh R R P 2001 Phys. Rev. Lett. 86 528 Google Scholar
[42]	Powalski M, Schmidt K P, Uhrig G S 2018 SciPost Phys. 4 001 Google Scholar
[43]	Hayden S M, Mook H A, Dai P, Perring T G, Dogan F 2004 Nature 429 531 Google Scholar
[44]	Tranquada J M, Woo H, Perring T G, Goka H, Gu G D, Xu G, Fujita M, Yamada K 2004 Nature 429 534 Google Scholar
[45]	Yamada K, Lee C H, Kurahashi K, Wada J, Wakimoto S, Ueki S, Kimura H, Endoh Y, Hosoya S, Shirane G, Birgeneau R J, Greven M, Kastner M A, Kim Y J 1998 Phys. Rev. B 57 6165 Google Scholar
[46]	Dai P, Mook H A, Hunt R D, Dogan F 2001 Phys. Rev. B 63 054525 Google Scholar
[47]	Stock C, Buyers W J L, Cowley R A, Clegg P S, Coldea R, Frost C D, Liang R, Peets D, Bonn D, Hardy W N, Birgeneau R J 2005 Phys. Rev. B 71 024522 Google Scholar
[48]	韩汝珊, 向涛, 闻海虎编 2009 铜氧化物高温超导电性实验与理论研究 (北京: 科学出版社) 第295−315页 Han R S, Xiang T, Wen H H 2009 Experimental and Theoretical Studies on the High-T_c Cuprates (Beijing: Science Press) pp295−315 (in Chinese)
[49]	Kivelson S A, Bindloss I P, Fradkin E, Oganesyan V, Tranquada J M, Kapitulnik A, Howald C 2003 Rev. Mod. Phys. 75 1201 Google Scholar
[50]	Brinckman J, Lee P A 1999 Phys. Rev. Lett. 82 2915 Google Scholar
[51]	Li J X, Gong C D 2002 Phys. Rev. B 66 014506 Google Scholar
[52]	Wen J S, Xu G Y, Gu G D, Tranquada J M, Birgeneau R J 2011 Rep. Prog. Phys. 74 124503 Google Scholar
[53]	Johnston D C 2010 Adv. Phys. 59 803 Google Scholar
[54]	Dong J, Zhang H J, Xu G, Li Z, Li G, Hu W Z, Wu D, Chen G F, Dai X, Luo J L, Fang Z, Wang N L 2008 Europhys. Lett. 83 27006 Google Scholar
[55]	Harriger L W, Luo H Q, Liu M S, Frost C, Hu J P, Norman M R, Dai P 2011 Phys. Rev. B 84 054544 Google Scholar
[56]	Zhao J, Adroja D T, Yao D X, Bewley R, Li S L, Wang X F, Wu G, Chen X H, Hu J P, Dai P 2009 Nat. Phys. 5 555 Google Scholar
[57]	Hu J P, Xu B, Liu W M, Hao N N, Wang Y P 2012 Phys. Rev. B 85 144403 Google Scholar
[58]	Qiu Y, Bao W, Zhao Y, Broholm C, Stanev V, Tesanovic Z, Gasparovic Y C, Chang S, Hu J, Qian B, Fang M, Mao Z 2009 Phys. Rev. Lett. 103 067008 Google Scholar
[59]	Inosov D S, Park J T, Bourges P, Sun D L, Sidis Y, Schneidewind A, Hradil K, Haug D, Lin C T, Keimer B, Hinkov V 2010 Nat. Phys. 6 178 Google Scholar
[60]	Xie T, Gong D, Ghosh H, Ghosh A, Soda M, Masuda T, Itoh S, Bourdarot F, Regnault L P, Danilkin S, Li S, Luo H 2018 Phys. Rev. Lett. 120 137001 Google Scholar
[61]	Brinkman W F, Serene J W, Anderson P W 1974 Phys. Rev. A 10 2386 Google Scholar
[62]	Leggett A J 1975 Rev. Mod. Phys. 47 331 Google Scholar
[63]	Bickers N E, Scalapino D J, Scalettar R T 1987 Internat. J. Mod. Phys. B 1 687 Google Scholar
[64]	Monthoux P, Balatsky A V, Pines D 1991 Phys. Rev. Lett. 67 3448 Google Scholar
[65]	Moriya T, Ueda K 2003 Rep. Prog. Phys. 66 1299 Google Scholar
[66]	Abrikosov A A, GorKov L P, Dzyaloshinski I E 1963 Method of Quantum Field Theory in Statistical Physics (New York: Dover Publications, INC) pp280–291
[67]	Yu S L, Li J X 2013 Chin. Phys. B 22 087411 Google Scholar
[68]	Anderson P W 1987 Science 235 1196 Google Scholar
[69]	Zhang F C, Rice T M 1988 Phys. Rev. B 37 3759 Google Scholar
[70]	Qin M P, Chung C M, Shi H, Vitali E, Hubig C, Schollwock U, White S R, Zhang S W 2020 Phys. Rev. X 10 031016
[71]	Jiang H C, Devereaux T P 2019 Science 365 1424 Google Scholar
[72]	Gull E, Parcollet O, Millis A J 2013 Phys. Rev. Lett. 110 216405 Google Scholar
[73]	Shih C T, Chen Y C, Lin H Q, Lee T K 1998 Phys. Rev. Lett. 81 1294 Google Scholar
[74]	Mazin I I, Singh D J, Johannes M D, Du M H 2008 Phys. Rev. Lett. 101 057003 Google Scholar
[75]	Raghu S, Qi X L, Liu C X, Scalapino D J, Zhang S C 2008 Phys. Rev. B 77 220503 Google Scholar
[76]	Yao Z J, Li J X, Wang Z D 2009 New J. Phys. 11 025009 Google Scholar
[77]	Ding H, Richard P, Nakayama K, Sugawara K, Arakane T, Sekiba Y, Takayama A, Souma S, Sato T, Takahashi T, Wang Z, Dai X, Fang Z, Chen G F, Luo J L, Wang N L 2008 EPL 83 47001 Google Scholar
[78]	Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004 Google Scholar
[79]	Wang F, Zhai H, Ran Y, Vishwanath A, Lee D H 2009 Phys. Rev. Lett. 102 047005 Google Scholar
[80]	Graser S, Maier T A, Hirschfeld P J, Scalapino D J 2009 New J. Phys. 11 025016 Google Scholar
[81]	McKenzie R H 1997 Science 278 820 Google Scholar
[82]	Kino H, Fukuyama H 1995 J. Phys. Soc. Jpn. 64 2726 Google Scholar
[83]	Schmalian J 1998 Phys. Rev. Lett. 81 4232 Google Scholar
[84]	Oike, H, Miyagawa K, Taniguchi H, Kanoda K 2015 Phys. Rev. Lett. 114 067002 Google Scholar
[85]	Kawasugi Y, Seki K, Edagawa Y, Sato Y, Pu J, Takenobu T, Yunoki S, Yamamoto H M, Kato R 2016 Nat. Commun. 7 12356 Google Scholar
[86]	Watanabe H, Seo H, Yunoki S 2019 Nat. Commun. 10 3167 Google Scholar
[87]	Park W K, Sarrao J L, Thompson J D, Greene L H 2008 Phys. Rev. Lett. 100 177001
[88]	Allan M P, Massee F, Morr D K, Van Dyke J, Rost A W, Mackenzie A P, Petrovic C, Davis J C 2013 Nat. Phys. 9 468 Google Scholar
[89]	Zhou B B, Misra S, da Silva Neto E H, Aynajian P, Baumbach R E, Thompson J D, Bauer E D, Yazdani A 2013 Nat. Phys. 9 474 Google Scholar
[90]	An K, Sakakibara T, Settai R, Onuki Y, Hiragi M, Chioka M, Machida K 2010 Phys. Rev. Lett. 104 037002 Google Scholar
[91]	Monthoux P, Lonzarich G G 2001 Phys. Rev. B 63 054529 Google Scholar
[92]	Nishiyama S, Miyake K, Varma C M 2013 Phys. Rev. B 88 014510 Google Scholar
[93]	谢武, 沈斌, 张勇军, 郭春煜, 许嘉诚, 路欣, 袁辉球 2019 物理学报 68 177101 Google Scholar Xie W, Shen B, Zhang Y J, Guo C Y, Xu J C, Lu X, Yuan H Q 2019 Acta Phys. Sin. 68 177101 Google Scholar
[94]	杨义峰, 李宇 2019 物理学报 64 217401 Yang Y F, Li Y 2019 Acta Phys. Sin. 64 217401
[95]	Fong H F, Keimer B, Anderson P W, Reznik D, Dogan F, Aksay I A 1995 Phys. Rev. Lett. 75 316 Google Scholar
[96]	He H, Bourges P, Sidis Y, Ulrich C, Regnault L, Pailhes S, Berzigiarova N, Kolesnikov N, Keimer B 2002 Science 295 1045 Google Scholar
[97]	Wilson S D, Dai P, Li S, Chi S, Kang H J, Lynn J W 2006 Nature 442 59 Google Scholar
[98]	Blumberg G, Stojkovic B P, Klein M V 1995 Phys. Rev. B 52 741
[99]	Liu D Z, Zha Y, Levin K 1995 Phys. Rev. Lett. 75 4130 Google Scholar
[100]	Li J X, Yin W G, Gong C D 1998 Phys. Rev. B. 58 2895
[101]	Yu G, Li Y, Motoyama E M, Greven M 2009 Nat. Phys. 5 873 Google Scholar
[102]	Tinkham M 1992 Introduction to Superconductivity (2nd Edition) (New York: McGraw-Hill, Inc.) pp79–82
[103]	Korshunov M M, Eremin I 2008 Phys. Rev. B 78 140509(R)Google Scholar
[104]	Maier T A, Scalapino D J 2008 Phys. Rev. B 78 020514(R)Google Scholar
[105]	Matan K, Ibuka S, Morinaga R, Chi S, Lynn J W, Christianson A D, Lumsden M D, Sato T J 2010 Phys. Rev. B 82 054515 Google Scholar
[106]	Castellan J P, Rosenkranz S, Goremychkin E A, Chung D Y, Todorov I S, Kanatzidis M G, Eremin I, Knolle J, Chubukov A V, Maiti S, Norman M R, Weber F, Claus H, Guidi T, Bewley R I, Osborn R 2011 Phys. Rev. Lett. 107 177003 Google Scholar
[107]	Lee C H, Kihou K, Park J T, Horigane K, Fujita K, Wasser F, Qureshi N, Sidis Y, Akimitsu J, Braden M 2016 Sci. Rep. 6 23424 Google Scholar
[108]	Shen S D, Zhang X W, Wo H L, Shen Y, Feng Y, Schneidewind A, Cermák P, Wang W B, Zhao J 2020 Phys. Rev. Lett. 124 017001 Google Scholar
[109]	Zhang Y, Yang L X, Xu M, Ye Z R, Chen F, He C, Xu H C, Jiang J, Xie B P, Ying J J, Wang X F, Chen X H, Hu J P, Matsunami M, Kimura S, Feng D L 2011 Nat. Mater. 10 273 Google Scholar
[110]	Dong J K, Zhou S Y, Guan T Y, Zhang H, Dai Y F, Qiu X, Wang X F, He Y, Chen X H, Li S Y 2010 Phys. Rev. Lett. 104 087005 Google Scholar
[111]	Reid J H, Tanatar M A, Juneau-Fecteau A, Gordon R T, René de Cotret S, Doiron-Leyraud N, Saito T, Fukazawa H, Kohori Y, Kihou K, Lee C H, Iyo A, Eisaki H, Prozorov R, Taillefer L 2012 Phys. Rev. Lett. 109 087001 Google Scholar
[112]	Richard P, Qian T, Ding H 2015 J. Phys.: Condens. Matter 27 293203 Google Scholar
[113]	Chubukov A V, Gor’kov L P 2008 Phys. Rev. Lett. 101 147004 Google Scholar
[114]	Song Y, Dyke J V, Lum I K, White B D, Jang S, Yazici D, Shu L, Schneidewind A, Cermák P, Qiu Y, Maple M B, Morr D K, Dai P 2016 Nat. Commun. 7 12774 Google Scholar
[115]	Zhang S C 1997 Science 275 1089 Google Scholar
[116]	Demler E, Zhang S C 1995 Phys. Rev. Lett. 75 4126 Google Scholar
[117]	Li J X 2003 Phys. Rev. Lett. 91 037002 Google Scholar
[118]	Kee H Y, Kivelson S, Aeppli G 2002 Phys. Rev. Lett. 88 257002 Google Scholar
[119]	Ardavan A, Brown S, Kagoshima S, Kanoda K, Kuroki K, Mori H, Ogata, M, Uji S, Wosnitza J 2012 J. Phys. Soc. Jpn. 81 011004 Google Scholar
[120]	Kang J, Yu S L, Xiang T, Li J X 2011 Phys. Rev. B 84 064520 Google Scholar
[121]	Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G 2003 Phys. Rev. Lett. 91 107001 Google Scholar
[122]	Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K 2008 Nat. Phys. 4 459 Google Scholar
[123]	Uchoa B, Castro Neto A H 2007 Phys. Rev. Lett. 98 146801 Google Scholar
[124]	Honerkamp C 2008 Phys. Rev. Lett. 100 146404 Google Scholar
[125]	Nandkishore R, Levitov L S, Chubukov A V 2012 Nat. Phys. 8 158 Google Scholar
[126]	Wang W S, Xiang Y Y, Wang Q H, Wang F, Yang F, Lee D H 2012 Phys. Rev. B 85 035414 Google Scholar
[127]	Yu S L, Li J X 2012 Phys. Rev. B 85 144402 Google Scholar
[128]	Xu X Y, Wessel S, Meng Z Y 2016 Phys. Rev. B 94 115105 Google Scholar
[129]	Fradkin E, Kivelson S A, Tranquada J M 2015 Rev. Mod. Phys. 87 457 Google Scholar
[130]	Jiang Y F, Jiang H C 2020 Phys. Rev. Lett. 125 157002 Google Scholar
[131]	Jiang Y F, Yao H, Yang F 2020 arXiv: 2003.02850 (unpublished)
[132]	Anderson P W 1973 Mater. Res. Bull. 8 153 Google Scholar
[133]	Zhou Y, Kanoda K, Ng T K 2017 Rev. Mod. Phys. 89 025003 Google Scholar
[134]	Wen J S, Yu S L, Li S Y, Yu W Q, Li J X 2019 NPJ Quantum Mater. 4 12 Google Scholar
[135]	Broholm C, Cava R J, Kivelson S A, Nocera D G, Norman M R, Senthil T 2020 Science 367 263

施引文献

图 1 铜氧化物高温超导La_2–xSr_xCuO₄/Na_2–xCe_xCuO₄、铁基超导Ba_1–xK_xFe₂As₂/Ba(Fe_1–xCo_x)₂As₂、重费米子超导CeCo(In_1–xCd_x)₅以及层状有机超导κ-(BEDT-TTF)₂X (标记为Mott insulator的相区在这里表示反铁磁绝缘体)的典型相图. 图分别来自文献[14,16,23,24]

Fig. 1. Typical phase diagrams for high-T_c cuprates, iron-based superconductors, heavy fermion superconductors and κ-typed layered organic superconductors. The figures are reproduced from Refs. [14,16,23,24].

下载: 全尺寸图片幻灯片

图 2 铜氧化物高温超导母体La₂CuO₄的自旋波色散和自旋波强度与二维波矢的依赖关系, 波矢方向见插图. (a)和(c)表示色散, (b)和(d)表示自旋波强度. 其中的实线是线性自旋波理论的计算结果(见文中介绍). 图(a)和图(b)来自文献[35], 图(c)和图(d)来自文献[36]

Fig. 2. (a), (c) Spin-wave dispersion in La₂CuO₄ along high symmetry directions in the two dimensional Brillouin zone as indicated in the inset. (b), (d) Spin-wave intensity as a function of the wave vector. Line is the prediction of the linear spin-wave theory. Fig. (a) and Fig. (b) are reproduced from Ref. [35], Fig. (c) and Fig. (d) from Ref. [36].

下载: 全尺寸图片幻灯片

图 3 中子散射实验揭示的掺杂铜氧化物高温超导自旋激发普适色散—沙漏状色散. 图(b)用于比较掺杂和未掺杂体系自旋激发谱的变化, 其中的实线表示未掺杂体系的自旋激发色散(纵轴的单位为meV). 图(a)和图(b)分别来自文献[25]和文献[47]

Fig. 3. The universality of the spin excitations in doped high-T_c cuprates—the hourglass dispersion revealed by neutron scattering experiments. Figure (b) is shown for a comparison with the dispersion in the undoped system, which is represented schematically by the solid lines. The figures are reproduced from Ref. [25] and Ref. [47], respectively.

下载: 全尺寸图片幻灯片

图 4 中子散射实验揭示的铜氧化物高温超导YaBa₂Cu₃O_6.6自旋激发在动量空间的分布　(a)激发能$ E = 24\;{\rm{meV}} $; (b)激发能 $ E = 34\;{\rm{meV}} $; (c)激发能 $ E = 75\;{\rm{meV}} $. 其中$ 34\;{\rm{meV}} $对应于自旋共振模能量. 图来自文献[43]

Fig. 4. Images of spin excitations in the momentum space for YaBa₂Cu₃O_6.6 revealed by neutron scattering experiments, at different excitation energies: (a) $ E = 24\;{\rm{meV}} $; (b) $ 34\;{\rm{meV}} $; (c) $ 75\;{\rm{meV}} $. $ 34\;{\rm{meV}} $ is the energy of the spin resonance. Figures are reproduced from Reference [43].

下载: 全尺寸图片幻灯片

图 5 铁基高温超导母体BaFe₂As₂沿着$ (\pi, q _{y}) $和$ (q_{x}, 0) $方向的自旋波色散. 图(a)中的实线表示利用各向异性海森伯模型计算的结果, 参数为$SJ_{1 {\rm a}} = 59.2 \pm 2.0,\; SJ_{1 {\rm b}} = -9.2 \pm 1.2,\; SJ_{2} = 13.6 \pm 1.0,\; SJ_{\rm c} = 1.8 \pm 0.3$ meV. 图(a)中的虚线代表利用各向同性海森伯模型计算的结果, 参数为$SJ_{1 {\rm a}} = SJ_{1 {\rm b}} = 18.3 \pm 1.4,\; SJ_{2} = 28.7 \pm 0.5, \;SJ_{\rm c} = 1.8$ meV. 其中S表示自旋. 图来自文献[55]

Fig. 5. Figures show spin wave dispersions in BaFe₂As₂ along the $ (\pi, q_{y}) $ and $ (q_{x}, 0) $ directions, respectively. In the panel (a), the solid line is a Heisenberg model calculation using anisotropic exchange couplings $SJ_{1 {\rm a}} = 59.2 \pm 2.0,\; SJ_{1 {\rm b}} = -9.2 \pm 1.2,\; SJ_{2} = 13.6 \pm 1.0,\; SJ_{\rm c} = 1.8 \pm 0.3$ meV, and the dotted line is that assuming isotropic exchange coupling $SJ_{1 {\rm a}} = SJ_{1 {\rm b}} = 18.3 \pm 1.4,\; SJ_{2} = 28.7 \pm 0.5,\; SJ_{\rm c} = 1.8$ meV. S is the spin of the system. Figures are reproduced from Ref. [55].

下载: 全尺寸图片幻灯片

图 6 哈伯德相互作用导致的粒子-粒子通道散射梯型费曼图. 其中的虚线表示哈伯德库仑互作用U　(a)自旋单态通道的散射; (b)自旋三重态通道的散射. 图来自文献[67]

Fig. 6. Ladder Feynman diagram in the particle-particle channel coming from the Hubbard interaction, where the dotted lines denote the Hubbard interaction U: (a) The spin-single channel; (b) the spin-triplet channel. Figures are reproduced from Ref. [67].

下载: 全尺寸图片幻灯片

图 7 (a)由(3)式计算的有效电子间相互作用势$ V_{\rm s}({ q}) $沿着四方晶格布里渊区高对称方向的分布. 计算参数为12%空穴掺杂, 并取次近邻跃迁参数$ t' = -0.3 t $和$ U = 2 t $; (b)$ V_{\rm s}({ q}) $经傅里叶变换后在实空间的分布. 图(b)来自文献[67]

Fig. 7. (a) Effective interaction $ V_{\rm s}({ q}) $ between electrons arising from the exchanges of spin fluctuations along the high symmetry directions in the Brillouin zone, calculated by Eq.(3) with the next-nearest-neighbor hopping $ t' = -0.3 t $, $ U = 2 t $ and 12% hole doping; (b) Fourier transformation of $ V_{\rm s}({ q}) $. Figure (b) is reproduced from Ref. [67].

下载: 全尺寸图片幻灯片

图 8 利用哈伯徳模型的弱耦合计算方法(方程(3)和方程(5))得到的最有利能隙函数在布里渊区的分布. 其中的粗黑线表示电子费米面, 点线表示配对能隙函数的节点(能隙为零的点). 计算参数基于对铜氧化物高温超导的近似描述, 具体见图7的说明文字. 图来自文献[67]

Fig. 8. The most favorable pairing function obtained from the weak-coupling approach to the Hubbard model Eqs.(3) and (5). The solid lines denote the Fermi surface and dotted lines denote the gap nodes. The parameters are the same as those given in the caption of Fig. 7, which are thought to describe approximately high-T_c cuprates. Figure is reproduced from Ref. [67].

下载: 全尺寸图片幻灯片

图 9 (a)自旋激发率$ \chi ({{q}}, \omega = 0) $, (b)电子型能带和(c)空穴型能带上最有利配对函数在动量空间的分布. 这些结果基于对描写铁基超导最简单的两带哈伯徳模型^[75]的弱耦合理论计算^[76]. (d)费米面, 其中$ Q_{\rm{AF}} $表示围绕Γ的空穴费米面与围绕M的电子费米面之间的套叠波矢. 图来自文献[76]

Fig. 9. Momentum dependence of the spin susceptibility $ \chi ({{q}}, \omega = 0) $ (a), the most favorable pairing functions on the electron Fermi pocket (b) and hole Fermi pocket (c). The results are obtained from the weak-coupling approach to the two-band Hubbard model ^[76], which is thought to be the simplest model describing iron iron pnictides ^[75]. (d) The Fermi surface in which $ Q_{\rm{AF}} $ denote the nesting wavevector between the hole pocket around Γ and electron pocket around M. Figures are reproduced from Ref. [76].

下载: 全尺寸图片幻灯片

图 10 中子散射实验在(a)铜氧化物超导YBa₂Cu₃O_6.92, (b)铁基超导BaFe_1.85Co_0.15As₂和(c)重费米子超导CeCoIn₅中测量的自旋极化率Im$ \chi ({{q}}, \omega) $与能量的依赖关系. 其中不同符号点标志的曲线表示不同温度的结果. 图来自文献[18,59, 20]

Fig. 10. Spin susceptibility Im$ \chi ({{q}}, \omega) $ measured by neutron scattering on (a) YBa₂Cu₃O_6.92, (b) BaFe_1.85Co_0.15As₂ and (c) CeCoIn₅ for different temperatures below and above the superconducting transition temperature. Figures are reproduced from Refs. [18, 59, 20], respectively.

下载: 全尺寸图片幻灯片

图 11 (a)铜氧化物超导YBa₂Cu₃O_6.97, (b)铁基超导Ba_0.6K_0.4Fe₂As₂和(c)重费米子超导Nd_0.05Ce_0.95CoIn₅中自旋共振峰强度随温度的依赖关系. 图分别来自文献[27, 19, 28]

Fig. 11. Temperature evolution of the neutron intensity around the spin resonance in (a) the high-T_c cuprate YBa₂Cu₃O_6.97, (b) iron-based superconductor Ba_0.6K_0.4Fe₂As₂ and (c) heavy fermion superconductor Nd_0.05Ce_0.95CoIn₅. Figures are reproduced from References [27, 19, 28], respectively.

下载: 全尺寸图片幻灯片

[1]	Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W, Schaefer H 1979 Phys. Rev. Lett. 43 1892 Google Scholar
[2]	Bednorz J G, Müller K A 1986 Z. Phys. B: Condens. Matter 64 189 Google Scholar
[3]	Kamihara Y, Hiramatsu H, Hirano M, Kawamura R, Yanagi H, Kamiya T, Hosono H 2006 J. Am. Chem. Soc. 128 10012 Google Scholar
[4]	Kamihara Y, Watanabe T, Hirano M, Hosono H 2008 J. Am. Chem. Soc. 130 3296 Google Scholar
[5]	Kini A M, Geiser U, Wang H H, Carlson K D, Williams J M, Kwok W K, Vandervoort K G, Thompson J E, Stupka D, Jung D, Whangbo M H 1990 Inorg. Chem. 29 2555 Google Scholar
[6]	Maeno Y, Hashimoto H, Yoshida K, Nishizaki S, Fujita T, Bednorz J G, Lichtenberg F 1994 Nature 372 532 Google Scholar
[7]	Takada K, Sakurai H, Takayama-Muromachi E, Izumi F, Dilanian R A, Sasaki R 2003 Nature 422 53 Google Scholar
[8]	Wu M K, Ashburn J R, Torng C J, Hor P H, Meng R L, Gao L, Huang Z J, Wang Y Q, Chu C W 1987 Phys. Rev. Lett. 58 908 Google Scholar
[9]	Zhao Z X, Chen L Q, Yang Q S, Huang Y H, Chen G H, Tang R M, Liu G R, Cui C G, Chen L, Wang L H, Guo S Q, Li S L, Bi J Q 1987 Chin. Sci. Bull. 32 661
[10]	Chen X H, Wu T, Wu G, Liu R H, Chen H, Fang D F 2008 Nature 453 761 Google Scholar
[11]	Ren Z A, Lu W, Yang J, Yi W, Shen X L, Zheng C, Che G C, Dong X L, Sun L L, Zhou F, Zhao Z X 2008 Chin. Phys. Lett. 25 2215 Google Scholar
[12]	Stewart G R 2017 Adv. Phys. 66 75 Google Scholar
[13]	Scalapino D J 2012 Rev. Mod. Phys. 84 1383 Google Scholar
[14]	Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17 Google Scholar
[15]	Chen X H, Dai P, Feng D L, Xiang T, Zhang F C 2014 Nat. Sci. Rev. 1 371 Google Scholar
[16]	Dai P C 2015 Rev. Mod. Phys. 87 855 Google Scholar
[17]	Si Q, Yu R, Abrahams E 2016 Nat. Rev. Mater. 1 16017 Google Scholar
[18]	Rossat-Mignod J, Regnault L P, Vettier C, Bourges C, Burlet C, Bossy J, Henry J Y, Lapertot G 1991 Physica C 185-189 86 Google Scholar
[19]	Christianson A D, Goremychkin E A, Osborn R, Rosenkranz S, Lumsden M D, Malliakas C D, Todorov I S, Claus H, Chung D Y, Kanatzidis M G, Bewley R I, Guidi T 2008 Nature 456 930 Google Scholar
[20]	Stock C, Broholm C, Hudis J, Kang H J, Petrovic C 2008 Phys. Rev. Lett. 100 087001 Google Scholar
[21]	Avci S, Chmaissem O, Chung D Y, Rosenkranz S, Goremychkin E A, Castellan J P, Todorov I S, Schlueter J A, Claus H, Daoud-Aladine A, Khalyavin D D, Kanatzidis M G, Osborn R 2012 Phys. Rev. B 85 184507 Google Scholar
[22]	Nandi S, Kim M G, Kreyssig A, Fernandes R M, Pratt D K, Thaler A, Ni N, Bud’ko S L, Canfield P C, Schmalian J, McQueeney R J, and Goldman A I 2010 Phys. Rev. Lett. 104 057006 Google Scholar
[23]	Nicklas M, Stockert O, Park T, Habicht K, Kiefer K, Pham L D, Thompson J D, Fisk Z, Steglich F 2007 Phys. Rev. B 76 052401
[24]	Nam M S, Ardavan A, Blundell S J, Schlueter J A 2007 Nature 449 584 Google Scholar
[25]	Tranquada J M 2007 Handbook of High-Temperature Superconductivity: Theory and Experiment (New York: Spnnger), also in arXiv: 0512115
[26]	Eschrig M 2006 Adv. Phys. 55 47 Google Scholar
[27]	Bourges P, Regnault L P, Sidis Y, Vettier C 1996 Phys. Rev. B 53 876 Google Scholar
[28]	Mazzone D G, Raymond S, Gavilano J L, Steffens P, Schneidewind A, Lapertot G, Kenzelmann M 2017 Phys. Rev. Lett. 119 187002 Google Scholar
[29]	Savrasov S Y, Andersen O K 1996 Phys. Rev. Lett. 77 4430 Google Scholar
[30]	Boeri L, Dolgov O V, Golubov A A 2008 Phys. Rev. Lett. 101 026403 Google Scholar
[31]	Berk N F, Schrieffer J R 1966 Phys. Rev. Lett. 17 433 Google Scholar
[32]	Emery V J 1986 Synth. Met. 13 21 Google Scholar
[33]	Miyake K, Schmitt-Rink S, Varma C M 1986 Phys. Rev. B 34 6554 Google Scholar
[34]	Scalapino D J, Loh E, Hirsch J E 1986 Phys. Rev. B 34 8190 Google Scholar
[35]	Coldea R, Hayden S M, Aeppli G, Perring T G, Frost C D, Mason T E, Cheong S W, Fisk Z 2001 Phys. Rev. Lett. 86 5377 Google Scholar
[36]	Headings N S, Hayden S M, Coldea R, Perring T G 2010 Phys. Rev. Lett. 105 247001 Google Scholar
[37]	Piazza B D, Mourigal M, Christensen N B, Nilsen G J, Tregenna-Piggott P, Perring T G, Enderle M, McMorrow D F, Ivanov D A, Ronnow H M 2015 Nat. Phys. 11 62 Google Scholar
[38]	Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y, Sandvik A W 2017 Phys. Rev. X 7 041072
[39]	Yu S L, Wang W, Dong Z Y, Yao Z J, Li J X 2018 Phys. Rev. B 98 134410 Google Scholar
[40]	Singh R R P, Gelfand M P 1995 Phys. Rev. B 52 15695 Google Scholar
[41]	Sandvik A W, Singh R R P 2001 Phys. Rev. Lett. 86 528 Google Scholar
[42]	Powalski M, Schmidt K P, Uhrig G S 2018 SciPost Phys. 4 001 Google Scholar
[43]	Hayden S M, Mook H A, Dai P, Perring T G, Dogan F 2004 Nature 429 531 Google Scholar
[44]	Tranquada J M, Woo H, Perring T G, Goka H, Gu G D, Xu G, Fujita M, Yamada K 2004 Nature 429 534 Google Scholar
[45]	Yamada K, Lee C H, Kurahashi K, Wada J, Wakimoto S, Ueki S, Kimura H, Endoh Y, Hosoya S, Shirane G, Birgeneau R J, Greven M, Kastner M A, Kim Y J 1998 Phys. Rev. B 57 6165 Google Scholar
[46]	Dai P, Mook H A, Hunt R D, Dogan F 2001 Phys. Rev. B 63 054525 Google Scholar
[47]	Stock C, Buyers W J L, Cowley R A, Clegg P S, Coldea R, Frost C D, Liang R, Peets D, Bonn D, Hardy W N, Birgeneau R J 2005 Phys. Rev. B 71 024522 Google Scholar
[48]	韩汝珊, 向涛, 闻海虎编 2009 铜氧化物高温超导电性实验与理论研究 (北京: 科学出版社) 第295−315页 Han R S, Xiang T, Wen H H 2009 Experimental and Theoretical Studies on the High-T_c Cuprates (Beijing: Science Press) pp295−315 (in Chinese)
[49]	Kivelson S A, Bindloss I P, Fradkin E, Oganesyan V, Tranquada J M, Kapitulnik A, Howald C 2003 Rev. Mod. Phys. 75 1201 Google Scholar
[50]	Brinckman J, Lee P A 1999 Phys. Rev. Lett. 82 2915 Google Scholar
[51]	Li J X, Gong C D 2002 Phys. Rev. B 66 014506 Google Scholar
[52]	Wen J S, Xu G Y, Gu G D, Tranquada J M, Birgeneau R J 2011 Rep. Prog. Phys. 74 124503 Google Scholar
[53]	Johnston D C 2010 Adv. Phys. 59 803 Google Scholar
[54]	Dong J, Zhang H J, Xu G, Li Z, Li G, Hu W Z, Wu D, Chen G F, Dai X, Luo J L, Fang Z, Wang N L 2008 Europhys. Lett. 83 27006 Google Scholar
[55]	Harriger L W, Luo H Q, Liu M S, Frost C, Hu J P, Norman M R, Dai P 2011 Phys. Rev. B 84 054544 Google Scholar
[56]	Zhao J, Adroja D T, Yao D X, Bewley R, Li S L, Wang X F, Wu G, Chen X H, Hu J P, Dai P 2009 Nat. Phys. 5 555 Google Scholar
[57]	Hu J P, Xu B, Liu W M, Hao N N, Wang Y P 2012 Phys. Rev. B 85 144403 Google Scholar
[58]	Qiu Y, Bao W, Zhao Y, Broholm C, Stanev V, Tesanovic Z, Gasparovic Y C, Chang S, Hu J, Qian B, Fang M, Mao Z 2009 Phys. Rev. Lett. 103 067008 Google Scholar
[59]	Inosov D S, Park J T, Bourges P, Sun D L, Sidis Y, Schneidewind A, Hradil K, Haug D, Lin C T, Keimer B, Hinkov V 2010 Nat. Phys. 6 178 Google Scholar
[60]	Xie T, Gong D, Ghosh H, Ghosh A, Soda M, Masuda T, Itoh S, Bourdarot F, Regnault L P, Danilkin S, Li S, Luo H 2018 Phys. Rev. Lett. 120 137001 Google Scholar
[61]	Brinkman W F, Serene J W, Anderson P W 1974 Phys. Rev. A 10 2386 Google Scholar
[62]	Leggett A J 1975 Rev. Mod. Phys. 47 331 Google Scholar
[63]	Bickers N E, Scalapino D J, Scalettar R T 1987 Internat. J. Mod. Phys. B 1 687 Google Scholar
[64]	Monthoux P, Balatsky A V, Pines D 1991 Phys. Rev. Lett. 67 3448 Google Scholar
[65]	Moriya T, Ueda K 2003 Rep. Prog. Phys. 66 1299 Google Scholar
[66]	Abrikosov A A, GorKov L P, Dzyaloshinski I E 1963 Method of Quantum Field Theory in Statistical Physics (New York: Dover Publications, INC) pp280–291
[67]	Yu S L, Li J X 2013 Chin. Phys. B 22 087411 Google Scholar
[68]	Anderson P W 1987 Science 235 1196 Google Scholar
[69]	Zhang F C, Rice T M 1988 Phys. Rev. B 37 3759 Google Scholar
[70]	Qin M P, Chung C M, Shi H, Vitali E, Hubig C, Schollwock U, White S R, Zhang S W 2020 Phys. Rev. X 10 031016
[71]	Jiang H C, Devereaux T P 2019 Science 365 1424 Google Scholar
[72]	Gull E, Parcollet O, Millis A J 2013 Phys. Rev. Lett. 110 216405 Google Scholar
[73]	Shih C T, Chen Y C, Lin H Q, Lee T K 1998 Phys. Rev. Lett. 81 1294 Google Scholar
[74]	Mazin I I, Singh D J, Johannes M D, Du M H 2008 Phys. Rev. Lett. 101 057003 Google Scholar
[75]	Raghu S, Qi X L, Liu C X, Scalapino D J, Zhang S C 2008 Phys. Rev. B 77 220503 Google Scholar
[76]	Yao Z J, Li J X, Wang Z D 2009 New J. Phys. 11 025009 Google Scholar
[77]	Ding H, Richard P, Nakayama K, Sugawara K, Arakane T, Sekiba Y, Takayama A, Souma S, Sato T, Takahashi T, Wang Z, Dai X, Fang Z, Chen G F, Luo J L, Wang N L 2008 EPL 83 47001 Google Scholar
[78]	Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani H, Aoki H 2008 Phys. Rev. Lett. 101 087004 Google Scholar
[79]	Wang F, Zhai H, Ran Y, Vishwanath A, Lee D H 2009 Phys. Rev. Lett. 102 047005 Google Scholar
[80]	Graser S, Maier T A, Hirschfeld P J, Scalapino D J 2009 New J. Phys. 11 025016 Google Scholar
[81]	McKenzie R H 1997 Science 278 820 Google Scholar
[82]	Kino H, Fukuyama H 1995 J. Phys. Soc. Jpn. 64 2726 Google Scholar
[83]	Schmalian J 1998 Phys. Rev. Lett. 81 4232 Google Scholar
[84]	Oike, H, Miyagawa K, Taniguchi H, Kanoda K 2015 Phys. Rev. Lett. 114 067002 Google Scholar
[85]	Kawasugi Y, Seki K, Edagawa Y, Sato Y, Pu J, Takenobu T, Yunoki S, Yamamoto H M, Kato R 2016 Nat. Commun. 7 12356 Google Scholar
[86]	Watanabe H, Seo H, Yunoki S 2019 Nat. Commun. 10 3167 Google Scholar
[87]	Park W K, Sarrao J L, Thompson J D, Greene L H 2008 Phys. Rev. Lett. 100 177001
[88]	Allan M P, Massee F, Morr D K, Van Dyke J, Rost A W, Mackenzie A P, Petrovic C, Davis J C 2013 Nat. Phys. 9 468 Google Scholar
[89]	Zhou B B, Misra S, da Silva Neto E H, Aynajian P, Baumbach R E, Thompson J D, Bauer E D, Yazdani A 2013 Nat. Phys. 9 474 Google Scholar
[90]	An K, Sakakibara T, Settai R, Onuki Y, Hiragi M, Chioka M, Machida K 2010 Phys. Rev. Lett. 104 037002 Google Scholar
[91]	Monthoux P, Lonzarich G G 2001 Phys. Rev. B 63 054529 Google Scholar
[92]	Nishiyama S, Miyake K, Varma C M 2013 Phys. Rev. B 88 014510 Google Scholar
[93]	谢武, 沈斌, 张勇军, 郭春煜, 许嘉诚, 路欣, 袁辉球 2019 物理学报 68 177101 Google Scholar Xie W, Shen B, Zhang Y J, Guo C Y, Xu J C, Lu X, Yuan H Q 2019 Acta Phys. Sin. 68 177101 Google Scholar
[94]	杨义峰, 李宇 2019 物理学报 64 217401 Yang Y F, Li Y 2019 Acta Phys. Sin. 64 217401
[95]	Fong H F, Keimer B, Anderson P W, Reznik D, Dogan F, Aksay I A 1995 Phys. Rev. Lett. 75 316 Google Scholar
[96]	He H, Bourges P, Sidis Y, Ulrich C, Regnault L, Pailhes S, Berzigiarova N, Kolesnikov N, Keimer B 2002 Science 295 1045 Google Scholar
[97]	Wilson S D, Dai P, Li S, Chi S, Kang H J, Lynn J W 2006 Nature 442 59 Google Scholar
[98]	Blumberg G, Stojkovic B P, Klein M V 1995 Phys. Rev. B 52 741
[99]	Liu D Z, Zha Y, Levin K 1995 Phys. Rev. Lett. 75 4130 Google Scholar
[100]	Li J X, Yin W G, Gong C D 1998 Phys. Rev. B. 58 2895
[101]	Yu G, Li Y, Motoyama E M, Greven M 2009 Nat. Phys. 5 873 Google Scholar
[102]	Tinkham M 1992 Introduction to Superconductivity (2nd Edition) (New York: McGraw-Hill, Inc.) pp79–82
[103]	Korshunov M M, Eremin I 2008 Phys. Rev. B 78 140509(R)Google Scholar
[104]	Maier T A, Scalapino D J 2008 Phys. Rev. B 78 020514(R)Google Scholar
[105]	Matan K, Ibuka S, Morinaga R, Chi S, Lynn J W, Christianson A D, Lumsden M D, Sato T J 2010 Phys. Rev. B 82 054515 Google Scholar
[106]	Castellan J P, Rosenkranz S, Goremychkin E A, Chung D Y, Todorov I S, Kanatzidis M G, Eremin I, Knolle J, Chubukov A V, Maiti S, Norman M R, Weber F, Claus H, Guidi T, Bewley R I, Osborn R 2011 Phys. Rev. Lett. 107 177003 Google Scholar
[107]	Lee C H, Kihou K, Park J T, Horigane K, Fujita K, Wasser F, Qureshi N, Sidis Y, Akimitsu J, Braden M 2016 Sci. Rep. 6 23424 Google Scholar
[108]	Shen S D, Zhang X W, Wo H L, Shen Y, Feng Y, Schneidewind A, Cermák P, Wang W B, Zhao J 2020 Phys. Rev. Lett. 124 017001 Google Scholar
[109]	Zhang Y, Yang L X, Xu M, Ye Z R, Chen F, He C, Xu H C, Jiang J, Xie B P, Ying J J, Wang X F, Chen X H, Hu J P, Matsunami M, Kimura S, Feng D L 2011 Nat. Mater. 10 273 Google Scholar
[110]	Dong J K, Zhou S Y, Guan T Y, Zhang H, Dai Y F, Qiu X, Wang X F, He Y, Chen X H, Li S Y 2010 Phys. Rev. Lett. 104 087005 Google Scholar
[111]	Reid J H, Tanatar M A, Juneau-Fecteau A, Gordon R T, René de Cotret S, Doiron-Leyraud N, Saito T, Fukazawa H, Kohori Y, Kihou K, Lee C H, Iyo A, Eisaki H, Prozorov R, Taillefer L 2012 Phys. Rev. Lett. 109 087001 Google Scholar
[112]	Richard P, Qian T, Ding H 2015 J. Phys.: Condens. Matter 27 293203 Google Scholar
[113]	Chubukov A V, Gor’kov L P 2008 Phys. Rev. Lett. 101 147004 Google Scholar
[114]	Song Y, Dyke J V, Lum I K, White B D, Jang S, Yazici D, Shu L, Schneidewind A, Cermák P, Qiu Y, Maple M B, Morr D K, Dai P 2016 Nat. Commun. 7 12774 Google Scholar
[115]	Zhang S C 1997 Science 275 1089 Google Scholar
[116]	Demler E, Zhang S C 1995 Phys. Rev. Lett. 75 4126 Google Scholar
[117]	Li J X 2003 Phys. Rev. Lett. 91 037002 Google Scholar
[118]	Kee H Y, Kivelson S, Aeppli G 2002 Phys. Rev. Lett. 88 257002 Google Scholar
[119]	Ardavan A, Brown S, Kagoshima S, Kanoda K, Kuroki K, Mori H, Ogata, M, Uji S, Wosnitza J 2012 J. Phys. Soc. Jpn. 81 011004 Google Scholar
[120]	Kang J, Yu S L, Xiang T, Li J X 2011 Phys. Rev. B 84 064520 Google Scholar
[121]	Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G 2003 Phys. Rev. Lett. 91 107001 Google Scholar
[122]	Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K 2008 Nat. Phys. 4 459 Google Scholar
[123]	Uchoa B, Castro Neto A H 2007 Phys. Rev. Lett. 98 146801 Google Scholar
[124]	Honerkamp C 2008 Phys. Rev. Lett. 100 146404 Google Scholar
[125]	Nandkishore R, Levitov L S, Chubukov A V 2012 Nat. Phys. 8 158 Google Scholar
[126]	Wang W S, Xiang Y Y, Wang Q H, Wang F, Yang F, Lee D H 2012 Phys. Rev. B 85 035414 Google Scholar
[127]	Yu S L, Li J X 2012 Phys. Rev. B 85 144402 Google Scholar
[128]	Xu X Y, Wessel S, Meng Z Y 2016 Phys. Rev. B 94 115105 Google Scholar
[129]	Fradkin E, Kivelson S A, Tranquada J M 2015 Rev. Mod. Phys. 87 457 Google Scholar
[130]	Jiang Y F, Jiang H C 2020 Phys. Rev. Lett. 125 157002 Google Scholar
[131]	Jiang Y F, Yao H, Yang F 2020 arXiv: 2003.02850 (unpublished)
[132]	Anderson P W 1973 Mater. Res. Bull. 8 153 Google Scholar
[133]	Zhou Y, Kanoda K, Ng T K 2017 Rev. Mod. Phys. 89 025003 Google Scholar
[134]	Wen J S, Yu S L, Li S Y, Yu W Q, Li J X 2019 NPJ Quantum Mater. 4 12 Google Scholar
[135]	Broholm C, Cava R J, Kivelson S A, Nocera D G, Norman M R, Senthil T 2020 Science 367 263

[1]	杨金颖, 王彬彬, 刘恩克. 磁性拓扑材料中贝利曲率驱动的非常规电输运行为. 物理学报, 2023, 72(17): 177103. doi: 10.7498/aps.72.20230995
[2]	王朝, 张铭, 张持, 王如志, 严辉. n = 2 Ruddlesden-Popper Sr₃B₂Se₇ (B = Zr, Hf) 非常规铁电性的第一性原理研究. 物理学报, 2021, 70(11): 116302. doi: 10.7498/aps.70.20202142
[3]	胡江平. 探索非常规高温超导体. 物理学报, 2021, 70(1): 017101. doi: 10.7498/aps.70.20202122
[4]	顾开元, 罗天创, 葛军, 王健. 拓扑材料中的超导. 物理学报, 2020, 69(2): 020301. doi: 10.7498/aps.69.20191627
[5]	李宏, 张斯淇, 郭明, 李美萱, 宋立军. Fabry-Perot腔与光学参量放大复合系统中实现可调谐的非常规光子阻塞. 物理学报, 2019, 68(12): 124203. doi: 10.7498/aps.68.20190154
[6]	谢武, 沈斌, 张勇军, 郭春煜, 许嘉诚, 路欣, 袁辉球. 重费米子材料与物理. 物理学报, 2019, 68(17): 177101. doi: 10.7498/aps.68.20190801
[7]	赵国栋, 杨亚利, 任伟. 钙钛矿型氧化物非常规铁电研究进展. 物理学报, 2018, 67(15): 157504. doi: 10.7498/aps.67.20180936
[8]	龚冬良, 罗会仟. 铁基超导体中的反铁磁序和自旋动力学. 物理学报, 2018, 67(20): 207407. doi: 10.7498/aps.67.20181543
[9]	程金光. 高压调控的磁性量子临界点和非常规超导电性. 物理学报, 2017, 66(3): 037401. doi: 10.7498/aps.66.037401
[10]	李世超, 甘远, 王靖珲, 冉柯静, 温锦生. 铁基超导体Fe1+yTe1-xSex中磁性的中子散射研究. 物理学报, 2015, 64(9): 097503. doi: 10.7498/aps.64.097503
[11]	陈俊, 於亚飞, 张智明. 利用信息流方法优化多激发自旋链中的量子态传输. 物理学报, 2015, 64(16): 160305. doi: 10.7498/aps.64.160305
[12]	张民仓. 相对论性非球谐振子势场中的赝自旋对称性. 物理学报, 2009, 58(1): 61-65. doi: 10.7498/aps.58.61
[13]	张民仓. 类Quesne环状球谐振子势场中的赝自旋对称性. 物理学报, 2009, 58(2): 712-716. doi: 10.7498/aps.58.712
[14]	张永祥, 孔贵芹, 俞建宁. 振动筛系统的两类余维三分岔与非常规混沌演化. 物理学报, 2008, 57(10): 6182-6187. doi: 10.7498/aps.57.6182
[15]	蒋建军, 张松俊, 刘拥军. 阻挫对准一维非对称子格反铁磁链自旋波激发的影响. 物理学报, 2006, 55(9): 4888-4892. doi: 10.7498/aps.55.4888
[16]	曹天德, 徐丽娜. 配对对称性与带间作用. 物理学报, 2005, 54(3): 1406-1409. doi: 10.7498/aps.54.1406
[17]	陈志谦, 郑仁蓉. 金属小粒子不同自旋态超导电性统计系综研究. 物理学报, 2002, 51(7): 1604-1607. doi: 10.7498/aps.51.1604
[18]	陈善宝, 张志强. 磁性薄膜畴壁短波长自旋波模式激发. 物理学报, 1996, 45(12): 2068-2072. doi: 10.7498/aps.45.2068
[19]	孙久勋, 章立源. s+d混合波对称性下联合模型的超导电性. 物理学报, 1996, 45(11): 1913-1920. doi: 10.7498/aps.45.1913
[20]	钱昆明, 林肇华, 戴道生. 自旋波共振激发的新模型. 物理学报, 1983, 32(12): 1547-1556. doi: 10.7498/aps.32.1547

计量

文章访问数: 12440
PDF下载量: 966
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

自旋涨落与非常规超导配对