二维有机拓扑绝缘体的研究进展

高艺璇; 张礼智; 张余洋; 杜世萱

doi:10.7498/aps.67.20181711

摘要

新材料的发现促进了科学与技术的进步.拓扑绝缘体是近期材料领域新的研究热点，相关研究的进一步深入，不仅加深了人们对材料物理性质的理解，也为其在自旋电子学和量子计算机等领域的潜在应用提供了有价值的参考.近年来，理论工作预测了一系列由金属和有机物构筑的二维有机拓扑绝缘体，本文主要介绍六角对称的金属有机晶格与Kagome金属有机晶格两类典型的二维有机拓扑绝缘体的研究进展，其中重点介绍了理论预测的氰基配位二维本征有机拓扑绝缘体.除了理论计算方面的工作，还简要介绍了关于二维有机拓扑绝缘体材料合成方面的实验工作.二维有机拓扑绝缘体的理论与实验研究不仅拓展了拓扑绝缘体的研究体系，还为寻找新的拓扑绝缘体材料提供了思路.

关键词:

Abstract

The discovery of new materials promotes the progress in science and technique. Among these new materials, topological materials have received much attention in recent years. Topological phases represent the advances both in the fundamental understanding of materials and in the broad applications in spintronics and quantum computing. The two-dimensional (2D) topological insulator (TI), also called quantum spin Hall insulator, is a promising material which has potential applications in future electronic devices with low energy consumption. The 2D TI has a bulk energy gap and a pair of gapless metallic edge states that are protected by the time reversal symmetry. To date, most of topological insulators are inorganic materials. Organic materials have potential advantages of low cost, easy fabrications, and mechanical flexibility. Historically, inorganic materials and devices have always found their organic counterparts, such as organic superconductors, organic light emitting diodes and organic spintronics. Recently, it has been predicted that some metal-organic lattices belong in an interesting class of 2D organic topological insulator (OTI). In this review, we present the progress of OTIs mainly in two typical types of them. In the first group, metal atoms bond with three neighboring molecules to form a hexagonal lattice, while they bond with two neighboring molecules to form a Kagome lattice. The electronic properties show that the Dirac band around Fermi level mainly comes from the hexagonal sites, and the flat band around Fermi level mainly is from Kagome lattice. It has been found that some of the materials from the first group could be intrinsic OTIs. However, none of the 2D OTIs predicted in the second group with a Kagome lattice is intrinsic. To obtain intrinsic OTIs from those non-intrinsic ones, in the heavy doping of material (one or two electrons per unit cell) it is required to move the Fermi level inside the gap opened by spin-orbit coupling, which is hard to realize in experiment. Therefore, many efforts have been made to search for intrinsic OTIs. It has been reported that the first group of 2D OTIs with a hexagonal lattice is found to be more possible to be intrinsic. By performing an electron counting and analyzing the orbital hybridization, an existing experimentally synthesized Cu-dicyanoanthracene (DCA) metal-organic framework is predicted to be an intrinsic OTI. Furthermore, like Cu-DCA, the structures consisting of molecules with cyanogen groups and noble metal atoms could be intrinsic OTIs. Finally, we discuss briefly possible future research directions in experimental synthesis and computational design of topological materials. We envision that OTIs will greatly broaden the scientific and technological influence of topological insulators and become a hot research topic in condensed matter physics.

Keywords:

作者及机构信息

1. 中国科学院物理研究所, 纳米物理与器件实验室, 北京 100190;

2. 中国科学院物理研究所, 松山湖材料实验室, 东莞 523808;

3. 中国科学院大学, 中国科学院拓扑量子计算卓越创新中心, 真空物理重点实验室, 北京 100049

基金项目: 国家重点研发计划（批准号：2016YFA0202300）、国家自然科学基金（批准号：61390501）、中国科学院战略性先导科技专项（B类）（批准号：XDB30000000）和中国科学院率先行动百人计划资助的课题.

Authors and contacts

1. Nanoscale Physics and Devices Laboratory, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

2. Songshan Lake Materials Laboratory, Institute of Physics, Chinese Academy of Sciences, Dongguan 523808, China;

3. Key Laboratory of Vacuum Physics, Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Project supported by the National Key Research and Development Projects of China (Grant No. 2016YFA0202300), the National Natural Science Foundation of China (Grant No. 61390501), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000), and the Chinese Academy of Sciences Pioneer Hundred Talents Program.

参考文献

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[2]	Yennie D R 1987 Rev. Mod. Phys. 59 781
[3]	Huckestein B 1995 Rev. Mod. Phys. 67 357
[4]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[5]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[6]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[7]	Ren Y F, Qiao Z H, Niu Q 2016 Rep. Prog. Phys. 79 066501
[8]	Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[9]	Knez I, Du R R, Sullivan G 2011 Phys. Rev. Lett. 107 136603
[10]	Murakami S 2006 Phys. Rev. Lett. 97 236805
[11]	Hirahara T, Bihlmayer G, Sakamoto Y, Yamada M, Miyazaki H, Kimura S, Blugel S, Hasegawa S 2011 Phys. Rev. Lett. 107 166801
[12]	Liu Z, Liu C X, Wu Y S, Duan W H, Liu F, Wu J 2011 Phys. Rev. Lett. 107 136805
[13]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C H, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801
[14]	Wang Z F, Yao M Y, Ming W M, Miao L, Zhu F F, Liu C H, Gao C L, Qian D, Jia J F, Liu F 2013 Nat. Commun. 4 2387
[15]	Zhang X, Zhang H J, Wang J, Felser C, Zhang S C 2012 Science 335 1464
[16]	Zhou M, Ming W M, Liu Z, Wang Z F, Li P, Liu F 2014 Proc. Natl. Acad. Sci. USA 111 14378
[17]	Hsu C H, Huang Z Q, Chuang F C, Kuo C C, Liu Y T, Lin H, Bansil A 2015 New J. Phys. 17 025005
[18]	Reis F, Li G, Dudy L, Bauernfeind M, Glass S, Hanke W, Thomale R, Schafer J, Claessen R 2017 Science 357 287
[19]	Jerome D, Mazaud A, Ribault M, Bechgaard K 1980 J. Phys. Lett. 41 L95
[20]	Tang C W, Vanslyke S A 1987 Appl. Phys. Lett. 51 913
[21]	Koezuka H, Tsumura A, Ando T 1987 Synthetic Met. 18 699
[22]	Wang Z F, Liu Z, Liu F 2013 Nat. Commun. 4 2451
[23]	Wang Z F, Liu Z, Liu F 2013 Phys. Rev. Lett. 110 196801
[24]	Liu Z, Wang Z F, Mei J W, Wu Y S, Liu F 2013 Phys. Rev. Lett. 110 106804
[25]	Wang Z F, Su N H, Liu F 2013 Nano Lett. 13 2842
[26]	Zhou Q H, Wang J L, Chwee T S, Wu G, Wang X B, Ye Q, Xu J W, Yang S W 2015 Nanoscale 7 727
[27]	Zhao B, Zhang J Y, Feng W X, Yao Y G, Yang Z Q 2014 Phys. Rev. B 90 201403
[28]	Zhang X M, Zhao M W 2015 RSC Adv. 5 9875
[29]	Ma Y D, Dai Y, Li X R, Sun Q L, Huang B B A 2014 Carbon 73 382
[30]	Zhang X M, Wang Z H, Zhao M W, Liu F 2016 Phys. Rev. B 93 165401
[31]	Zhang X M, Zhao M W 2015 Sci. Rep. 5 14098
[32]	Wei L, Zhang X M, Zhao M W 2016 Phys. Chem. Chem. Phys. 18 8059
[33]	Kim H J, Li C, Feng J, Cho J H, Zhang Z Y 2016 Phys. Rev. B 93 041404
[34]	Dong L, Kim Y, Er D, Rappe A M, Shenoy V B 2016 Phys. Rev. Lett. 116 096601
[35]	Kambe T, Sakamoto R, Hoshiko K, Takada K, Miyachi M, Ryu J H, Sasaki S, Kim J, Nakazato K, Takata M, Nishihara H 2013 J. Am. Chem. Soc. 135 2462
[36]	Sheberla D, Sun L, Blood-Forsythe M A, Er S, Wade C R, Brozek C K, Aspuru-Guzik A, Dinca M 2014 J. Am. Chem. Soc. 136 8859
[37]	Cui J S, Xu Z T 2014 Chem. Commun. 50 3986
[38]	Campbell M G, Sheberla D, Liu S F, Swager T M, Dinca M 2015 Angew. Chem. Int. Edit. 54 4349
[39]	Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[40]	Sancho M P L, Sancho J M L, Rubio J 1985 J. Phys. F: Met. Phys. 15 851
[41]	Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430
[42]	Sakamoto J, van Heijst J, Lukin O, Schluter A D 2009 Angew. Chem. Int. Edit. 48 1030
[43]	Grill L, Dyer M, Lafferentz L, Persson M, Peters M V, Hecht S 2007 Nat. Nanotechnol. 2 687
[44]	Cote A P, Benin A I, Ockwig N W, O'Keeffe M, Matzger A J, Yaghi O M 2005 Science 310 1166
[45]	Colson J W, Woll A R, Mukherjee A, Levendorf M P, Spitler E L, Shields V B, Spencer M G, Park J, Dichtel W R 2011 Science 332 228
[46]	Shi Z L, Liu J, Lin T, Xia F, Liu P N, Lin N 2011 J. Am. Chem. Soc. 133 6150
[47]	Schlickum U, Decker R, Klappenberger F, Zoppellaro G, Klyatskaya S, Ruben M, Silanes I, Arnau A, Kern K, Brune H, Barth J V 2007 Nano Lett. 7 3813
[48]	Yan L H, Xia B W, Zhang Q S, Kuang G W, Xu H, Liu J, Liu P N, Lin N 2018 Angew. Chem. Int. Edit. 57 4617
[49]	Tang E, Mei J W, Wen X G 2011 Phys. Rev. Lett. 106 236802
[50]	Yao Y G, Kleinman L, MacDonald A H, Sinova J, Jungwirth T, Wang D S, Wang E G, Niu Q 2004 Phys. Rev. Lett. 92 037204
[51]	Yao Y G, Fang Z 2005 Phys. Rev. Lett. 95 156601
[52]	Xiong Z H, Wu D, Vardeny Z V, Shi J 2004 Nature 427 821
[53]	Liu Z, Zou X L, Mei J W, Liu F 2015 Phys. Rev. B 92 220102
[54]	Kambe T, Sakamoto R, Kusamoto T, Pal T, Fukui N, Hoshiko K, Shimojima T, Wang Z F, Hirahara T, Ishizaka K, Hasegawa S, Liu F, Nishihara H 2014 J. Am. Chem. Soc. 136 14357
[55]	Zhang L Z, Wang Z F, Huang B, Cui B, Wang Z M, Du S X, Gao H J, Liu F 2016 Nano Lett. 16 2072
[56]	Pawin G, Wong K L, Kim D, Sun D Z, Bartels L, Hong S, Rahman T S, Carp R, Marsella M 2008 Angew. Chem. Int. Edit. 47 8442
[57]	Zhang J, Shchyrba A, Nowakowska S, Meyer E, Jung T A, Muntwiler M 2014 Chem. Commun. 50 12289
[58]	Kumar A, Banerjee K, Foster A S, Liljeroth P 2017 arXiv Preprint arXiv:1711.01128
[59]	Liljeroth P, Swart I, Paavilainen S, Repp J, Meyer G 2010 Nano Lett. 10 2475
[60]	Zhou M, Liu Z, Ming W M, Wang Z F, Liu F 2014 Phys. Rev. Lett. 113 236802
[61]	Pivetta M, Pacchioni G E, Schlickum U, Barth J V, Brune H 2013 Phys. Rev. Lett. 110 086102
[62]	Pacchioni G E, Pivetta M, Brune H 2015 J. Phys. Chem. C 119 25442
[63]	Meyer J, Nickel A, Ohmann R, Lokamani, Toher C, Ryndyk D A, Garmshausen Y, Hecht S, Moresco F, Cuniberti G 2015 Chem. Commun. 51 12621
[64]	Stepanow S, Lin N, Payer D, Schlickum U, Klappenberger F, Zoppellaro G, Ruben M, Brune H, Barth J V, Kern K 2007 Angew. Chem. Int. Edit. 46 710

施引文献

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[2]	Yennie D R 1987 Rev. Mod. Phys. 59 781
[3]	Huckestein B 1995 Rev. Mod. Phys. 67 357
[4]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[5]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[6]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[7]	Ren Y F, Qiao Z H, Niu Q 2016 Rep. Prog. Phys. 79 066501
[8]	Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[9]	Knez I, Du R R, Sullivan G 2011 Phys. Rev. Lett. 107 136603
[10]	Murakami S 2006 Phys. Rev. Lett. 97 236805
[11]	Hirahara T, Bihlmayer G, Sakamoto Y, Yamada M, Miyazaki H, Kimura S, Blugel S, Hasegawa S 2011 Phys. Rev. Lett. 107 166801
[12]	Liu Z, Liu C X, Wu Y S, Duan W H, Liu F, Wu J 2011 Phys. Rev. Lett. 107 136805
[13]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C H, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801
[14]	Wang Z F, Yao M Y, Ming W M, Miao L, Zhu F F, Liu C H, Gao C L, Qian D, Jia J F, Liu F 2013 Nat. Commun. 4 2387
[15]	Zhang X, Zhang H J, Wang J, Felser C, Zhang S C 2012 Science 335 1464
[16]	Zhou M, Ming W M, Liu Z, Wang Z F, Li P, Liu F 2014 Proc. Natl. Acad. Sci. USA 111 14378
[17]	Hsu C H, Huang Z Q, Chuang F C, Kuo C C, Liu Y T, Lin H, Bansil A 2015 New J. Phys. 17 025005
[18]	Reis F, Li G, Dudy L, Bauernfeind M, Glass S, Hanke W, Thomale R, Schafer J, Claessen R 2017 Science 357 287
[19]	Jerome D, Mazaud A, Ribault M, Bechgaard K 1980 J. Phys. Lett. 41 L95
[20]	Tang C W, Vanslyke S A 1987 Appl. Phys. Lett. 51 913
[21]	Koezuka H, Tsumura A, Ando T 1987 Synthetic Met. 18 699
[22]	Wang Z F, Liu Z, Liu F 2013 Nat. Commun. 4 2451
[23]	Wang Z F, Liu Z, Liu F 2013 Phys. Rev. Lett. 110 196801
[24]	Liu Z, Wang Z F, Mei J W, Wu Y S, Liu F 2013 Phys. Rev. Lett. 110 106804
[25]	Wang Z F, Su N H, Liu F 2013 Nano Lett. 13 2842
[26]	Zhou Q H, Wang J L, Chwee T S, Wu G, Wang X B, Ye Q, Xu J W, Yang S W 2015 Nanoscale 7 727
[27]	Zhao B, Zhang J Y, Feng W X, Yao Y G, Yang Z Q 2014 Phys. Rev. B 90 201403
[28]	Zhang X M, Zhao M W 2015 RSC Adv. 5 9875
[29]	Ma Y D, Dai Y, Li X R, Sun Q L, Huang B B A 2014 Carbon 73 382
[30]	Zhang X M, Wang Z H, Zhao M W, Liu F 2016 Phys. Rev. B 93 165401
[31]	Zhang X M, Zhao M W 2015 Sci. Rep. 5 14098
[32]	Wei L, Zhang X M, Zhao M W 2016 Phys. Chem. Chem. Phys. 18 8059
[33]	Kim H J, Li C, Feng J, Cho J H, Zhang Z Y 2016 Phys. Rev. B 93 041404
[34]	Dong L, Kim Y, Er D, Rappe A M, Shenoy V B 2016 Phys. Rev. Lett. 116 096601
[35]	Kambe T, Sakamoto R, Hoshiko K, Takada K, Miyachi M, Ryu J H, Sasaki S, Kim J, Nakazato K, Takata M, Nishihara H 2013 J. Am. Chem. Soc. 135 2462
[36]	Sheberla D, Sun L, Blood-Forsythe M A, Er S, Wade C R, Brozek C K, Aspuru-Guzik A, Dinca M 2014 J. Am. Chem. Soc. 136 8859
[37]	Cui J S, Xu Z T 2014 Chem. Commun. 50 3986
[38]	Campbell M G, Sheberla D, Liu S F, Swager T M, Dinca M 2015 Angew. Chem. Int. Edit. 54 4349
[39]	Mostofi A A, Yates J R, Lee Y S, Souza I, Vanderbilt D, Marzari N 2008 Comput. Phys. Commun. 178 685
[40]	Sancho M P L, Sancho J M L, Rubio J 1985 J. Phys. F: Met. Phys. 15 851
[41]	Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430
[42]	Sakamoto J, van Heijst J, Lukin O, Schluter A D 2009 Angew. Chem. Int. Edit. 48 1030
[43]	Grill L, Dyer M, Lafferentz L, Persson M, Peters M V, Hecht S 2007 Nat. Nanotechnol. 2 687
[44]	Cote A P, Benin A I, Ockwig N W, O'Keeffe M, Matzger A J, Yaghi O M 2005 Science 310 1166
[45]	Colson J W, Woll A R, Mukherjee A, Levendorf M P, Spitler E L, Shields V B, Spencer M G, Park J, Dichtel W R 2011 Science 332 228
[46]	Shi Z L, Liu J, Lin T, Xia F, Liu P N, Lin N 2011 J. Am. Chem. Soc. 133 6150
[47]	Schlickum U, Decker R, Klappenberger F, Zoppellaro G, Klyatskaya S, Ruben M, Silanes I, Arnau A, Kern K, Brune H, Barth J V 2007 Nano Lett. 7 3813
[48]	Yan L H, Xia B W, Zhang Q S, Kuang G W, Xu H, Liu J, Liu P N, Lin N 2018 Angew. Chem. Int. Edit. 57 4617
[49]	Tang E, Mei J W, Wen X G 2011 Phys. Rev. Lett. 106 236802
[50]	Yao Y G, Kleinman L, MacDonald A H, Sinova J, Jungwirth T, Wang D S, Wang E G, Niu Q 2004 Phys. Rev. Lett. 92 037204
[51]	Yao Y G, Fang Z 2005 Phys. Rev. Lett. 95 156601
[52]	Xiong Z H, Wu D, Vardeny Z V, Shi J 2004 Nature 427 821
[53]	Liu Z, Zou X L, Mei J W, Liu F 2015 Phys. Rev. B 92 220102
[54]	Kambe T, Sakamoto R, Kusamoto T, Pal T, Fukui N, Hoshiko K, Shimojima T, Wang Z F, Hirahara T, Ishizaka K, Hasegawa S, Liu F, Nishihara H 2014 J. Am. Chem. Soc. 136 14357
[55]	Zhang L Z, Wang Z F, Huang B, Cui B, Wang Z M, Du S X, Gao H J, Liu F 2016 Nano Lett. 16 2072
[56]	Pawin G, Wong K L, Kim D, Sun D Z, Bartels L, Hong S, Rahman T S, Carp R, Marsella M 2008 Angew. Chem. Int. Edit. 47 8442
[57]	Zhang J, Shchyrba A, Nowakowska S, Meyer E, Jung T A, Muntwiler M 2014 Chem. Commun. 50 12289
[58]	Kumar A, Banerjee K, Foster A S, Liljeroth P 2017 arXiv Preprint arXiv:1711.01128
[59]	Liljeroth P, Swart I, Paavilainen S, Repp J, Meyer G 2010 Nano Lett. 10 2475
[60]	Zhou M, Liu Z, Ming W M, Wang Z F, Liu F 2014 Phys. Rev. Lett. 113 236802
[61]	Pivetta M, Pacchioni G E, Schlickum U, Barth J V, Brune H 2013 Phys. Rev. Lett. 110 086102
[62]	Pacchioni G E, Pivetta M, Brune H 2015 J. Phys. Chem. C 119 25442
[63]	Meyer J, Nickel A, Ohmann R, Lokamani, Toher C, Ryndyk D A, Garmshausen Y, Hecht S, Moresco F, Cuniberti G 2015 Chem. Commun. 51 12621
[64]	Stepanow S, Lin N, Payer D, Schlickum U, Klappenberger F, Zoppellaro G, Ruben M, Brune H, Barth J V, Kern K 2007 Angew. Chem. Int. Edit. 46 710

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