Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(11): 117106    DOI: 10.1088/1674-1056/25/11/117106
Special Issue: TOPICAL REVIEW — Topological electronic states
TOPICAL REVIEW—Topological electronic states Prev   Next  

Topological nodal line semimetals

Chen Fang(方辰)1, Hongming Weng(翁红明)1,2, Xi Dai(戴希)1,2, Zhong Fang(方忠)1,2
1 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 Collaborative Innovation Center of Quantum Matter, Beijing, China
Abstract  

We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials; (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals, and other topological phases; and (v) we discuss the possible physical effects accessible to experimental probes in these materials.

Keywords:  topological semimetals      nodal band structures      topological invariatns  
Received:  11 September 2016      Revised:  24 October 2016      Accepted manuscript online: 
PACS:  71.20.-b (Electron density of states and band structure of crystalline solids)  
  73.20.-r (Electron states at surfaces and interfaces)  
Fund: 

Project partially supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302400 and 2016YFA0300604), partially by the National Natural Science Foundation of China (Grant Nos. 11274359 and 11422428), the National Basic Research Program of China (Grant No. 2013CB921700), and the "Strategic Priority Research Program (B)" of the Chinese Academy of Sciences (Grant No. XDB07020100).

Corresponding Authors:  Chen Fang, Hongming Weng     E-mail:  cfang@iphy.ac.cn;hmweng@iphy.ac.cn

Cite this article: 

Chen Fang(方辰), Hongming Weng(翁红明), Xi Dai(戴希), Zhong Fang(方忠) Topological nodal line semimetals 2016 Chin. Phys. B 25 117106

[1] Murakami S 2007 New J. Phys. 9 356
[2] Wan X, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B 83 205101
[3] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X and Fang Z 2012 Phys. Rev. B 85 195320
[4] Burkov A A, Hook M D and Balents L 2011 Phys. Rev. B 84 235126
[5] Chen Y, Xie Y, Yang S A, Pan H, Zhang F, Cohen M L and Zhang S 2015 Nano. Lett. 15 6974
[6] Xu G, Weng H M, Wang Z J, Dai X and Fang Z 2011 Phys. Rev. Lett. 107 186806
[7] Bzdušek T, Wu Q, Rüegg A, Sigrist M and Soluyanov A A 2016 Nature 538 75
[8] Lin J Y, Hu N C, Chen Y J, Lee C H and Zhang X 2016arXiv:1607.06524
[9] Chiu C K and Schnyder A P 2014 Phys. Rev. B 90 205136
[10] Yang B J, Bojesen T A, Morimoto T and Furusaki A 2016arXiv:1604.00843
[11] Bian G, Chang T R, Zheng H, Velury S, Xu S Y, Neupert T, Chiu C K, Sanchez D S, Belopolski I, Alidoust N, et al. 2015arXiv:1508.07521
[12] Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, et al. 2015arXiv:1505.03069
[13] Yamakage A, Yamakawa Y, Tanaka Y and Okamoto Y 2016 J. Phys. Soc. Jpn. 85 013708
[14] Weng H, Fang C, Fang Z and Dai X 2016arXiv:1605.05186
[15] Weng H, Liang Y, Xu Q, Yu R, Fang Z, Dai X and Kawazoe Y 2015 Phys. Rev. B 92 045108
[16] Xie L S, Schoop L M, Seibel E M, Gibson Q D, Xie W and Cava R J 2015 APL Mater. 3 083602
[17] Chan Y H, Chiu C K, Chou M Y and Schnyder A P 2016 Phys. Rev. B 93 205132
[18] Kim Y, Wieder B J, Kane C L and Rappe A M 2015 Phys. Rev. Lett. 115 036806
[19] Yu R, Weng H, Fang Z, Dai X and Hu X 2015 Phys. Rev. Lett. 115 036807
[20] Zeng M, Fang C, Chang G, Chen Y A, Hsieh T, Bansil A, Lin H and Fu L 2015arXiv:1504.03492
[21] Hirayama M, Okugawa R, Miyake T and Murakami S 2016 arXive:1602.06501
[22] Li R, Cheng X, Ma H, Wang S, Li D, Zhang Z, Li Y and Chen X Q 2016arXiv:1603.03974
[23] Du Y, Tang F, Wang D, Sheng L, Kan E j, Duan C G, Savrasov S Y and Wan X 2016arXiv:1605.07998
[24] Huang H, Liu J, Vanderbilt D and Duan W 2016 Phys. Rev. B 93 201114
[25] Zhao J, Yu R, Weng H and Fang Z 2015arXiv:1511.05704
[26] Xu Q, Yu R, Fang Z, Dai X and Weng H 2016 arXiv:1608.03172
[27] Carter J M, Shankar V V, Zeb M A and H Y Kee 2012 Phys. Rev. B 85 115105
[28] C Fang, Y Chen, H Y Kee and L Fu 2015 Phys. Rev. B 92 081201
[29] Liang Q F, Zhou J, Yu R, Wang Z and Weng H 2016 Phys. Rev. B 93 085427
[30] Weng H, Fang C, Fang Z, Bernevig B A and Dai X 2015 Phys. Rev. X 5 011029
[31] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B K, Alidoust N, Bian G, Neupane M, Zhang C, et al. 2014 Nat. Commun. 6 7373
[32] Fang C, Lu L, Liu J and Fu L 2016 Nat. Phys. 12 936
[33] Hu J, Tang Z, Liu J, Liu X, Zhu Y, Graf D, Myhro K, Tran S, Lau C N, Wei J, et al. 2016 Phys. Rev. Lett. 117 016602
[34] Huh Y, Moon E G and Kim Y B 2016 Phys. Rev. B 93 035138
[35] Han S, Cho G Y and Moon E G 2016arXiv:1601.00975
[36] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[37] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
[38] Fu L, Kane C and Mele E 2007 Phys. Rev. Lett. 98 106803
[39] Moore J E and Balents L 2007 Phys. Rev. B 75 121306
[40] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[41] Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802
[42] Fang C, Gilbert M J, Dai X and Bernevig B A 2012 Phys Rev. Lett. 108 266802
[43] Wang Z, Weng H, Wu Q, Dai X and Fang Z 2013 Phys. Rev. B 88 125427
[44] Heikkilä T T and Volovik G E 2015 New J. Phys. 17 093019
[45] Hyart T and Heikkilä T T 2016 Phys. Rev. B 93 235147
[46] Yang B J, Morimoto T and Furusaki A 2015 Phys. Rev. B 92 165120
[47] Kobayashi S and Sato M 2015 Phys. Rev. Lett. 115 187001
[48] Mikitik G P and Sharlai Y V 2006 Phys. Rev. B 73 235112
[49] Mikitik G P and Sharlai Y V 2008 Low Temperature Physics 34 794
[50] Ezawa M 2016 Phys. Rev. Lett. 116 127202
[51] Wang J T, Weng H, Nie S, Fang Z, Kawazoe Y and Chen C 2016 Phys. Rev. Lett. 116 195501
[52] Chen Y, Kim H S and Kee H Y 2016 Phys. Rev. B 93 155140
[53] Watanabe H, Po H C, Zaletel M P and Vishwanath A 2016 Phys. Rev. Lett. 117 096404
[54] Liu J and Balents L 2016 arXiv:1609.05529
[55] J W Rhim and Y B Kim 2015 Phys. Rev. B 92 045126
[56] Mullen K, Uchoa B and Glatzhofer D T 2015 Phys. Rev. Lett. 115 026403
[1] Two-dimensional topological semimetals
Xiaolong Feng(冯晓龙), Jiaojiao Zhu(朱娇娇), Weikang Wu(吴维康), and Shengyuan A. Yang(杨声远). Chin. Phys. B, 2021, 30(10): 107304.
[2] SymTopo:An automatic tool for calculating topological properties of nonmagnetic crystalline materials
Yuqing He(贺雨晴), Yi Jiang(蒋毅), Tiantian Zhang(张田田), He Huang(黄荷), Chen Fang(方辰), Zhong Jin(金钟). Chin. Phys. B, 2019, 28(8): 087102.
[3] Structural, elastic, and electronic properties of topological semimetal WC-type MX family by first-principles calculation
Sami Ullah, Lei Wang(王磊), Jiangxu Li(李江旭), Ronghan Li(李荣汉), Xing-Qiu Chen(陈星秋). Chin. Phys. B, 2019, 28(7): 077105.
No Suggested Reading articles found!