Local evolutions of nodal points in two-dimensional systems with chiral symmetry

doi:10.1088/1674-1056/28/7/077101

中国物理B ›› 2019, Vol. 28 ›› Issue (7): 77101-077101.doi: 10.1088/1674-1056/28/7/077101

所属专题： SPECIAL TOPIC — Topological semimetals

• SPECIAL TOPIC—Topological semimetals • 上一篇下一篇

Local evolutions of nodal points in two-dimensional systems with chiral symmetry

Peiyuan Fu(符培源), Zhesen Yang(杨哲森), Jiangping Hu(胡江平)

1 Beijing National Laboratory for Condensed Matter Physics, and 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 Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
4 Collaborative Innovation Center of Quantum Matter, Beijing 100190, China

收稿日期:2019-04-09 出版日期:2019-07-05 发布日期:2019-07-05
通讯作者: Zhesen Yang E-mail:yangzs@iphy.ac.cn
基金资助:
Project supported by the National Basic Research Program of China (Grant Nos. 2015CB921300 and 2017YFA0303100), the National Natural Science Foundation of China (Grant Nos. 1190020, 11534014, and 11334012), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB07000000 and XDB28000000).

Local evolutions of nodal points in two-dimensional systems with chiral symmetry

Peiyuan Fu(符培源)^1,2, Zhesen Yang(杨哲森)^1,2, Jiangping Hu(胡江平)^1,3,4

1 Beijing National Laboratory for Condensed Matter Physics, and 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 Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
4 Collaborative Innovation Center of Quantum Matter, Beijing 100190, China

Received:2019-04-09 Online:2019-07-05 Published:2019-07-05
Contact: Zhesen Yang E-mail:yangzs@iphy.ac.cn
Supported by:
Project supported by the National Basic Research Program of China (Grant Nos. 2015CB921300 and 2017YFA0303100), the National Natural Science Foundation of China (Grant Nos. 1190020, 11534014, and 11334012), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB07000000 and XDB28000000).

摘要/Abstract

摘要：

Two-dimensional systems with chiral symmetry allow stable discrete band crossings (nodal points) in Brillouin zones. Here we study the local evolutions of these nodal points under chiral symmetry preserving perturbations. We find that these evolutions can be classified by different types of local k·p models around the nodal points. Several concrete examples are calculated to illustrate our results.

关键词: nodal points, chiral symmetry, k·p model

Abstract:

Key words: nodal points, chiral symmetry, k·p model

中图分类号: (Other topics in electronic structure)

71.90.+q

03.65.Vf (Phases: geometric; dynamic or topological)

符培源, 杨哲森, 胡江平. Local evolutions of nodal points in two-dimensional systems with chiral symmetry[J]. 中国物理B, 2019, 28(7): 77101-077101.

Peiyuan Fu(符培源), Zhesen Yang(杨哲森), Jiangping Hu(胡江平). Local evolutions of nodal points in two-dimensional systems with chiral symmetry[J]. Chin. Phys. B, 2019, 28(7): 77101-077101.

参考文献 41

[31]	Singh B, Ghosh B, Su C, Lin H, Agarwal A and Bansil A 2018 Phys. Rev. Lett. 121 226401 doi: 10.1103/PhysRevLett.121.226401
[1]	Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405 doi: 10.1103/PhysRevLett.49.405
[32]	Xu B, Zhao L X, Marsik P, Sheveleva E, Lyzwa F, Dai Y M, Chen G F, Qiu X G and Bernhard C 2018 Phys. Rev. Lett. 121 187401 doi: 10.1103/PhysRevLett.121.187401
[2]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 doi: 10.1103/PhysRevLett.61.2015
[33]	Chen R, Xu D H and Zhou B 2018 Phys. Rev. B 98 235159 doi: 10.1103/PhysRevB.98.235159
[3]	Kosterlitz J M and Thouless D J 1973 J. Phys. C: Solid State Phys. 6 1181 doi: 10.1088/0022-3719/6/7/010
[34]	Benito-Matias E and Molina R A 2019 Phys. Rev. B 99 075304 doi: 10.1103/PhysRevB.99.075304
[4]	Bernevig B A, Hughes T A and Zhang S C 2006 Science 314 1757 doi: 10.1126/science.1133734
[35]	Ominato Y, Tatsumi S and Nomura K 2019 Phys. Rev. B 99 085205 doi: 10.1103/PhysRevB.99.085205
[5]	Bernevig B A and Zhang S C 2006 Phys. Rev. Lett. 96 106802 doi: 10.1103/PhysRevLett.96.106802
[36]	Kim R, Yang B J and Kim C H 2019 Phys. Rev. B 99 045130 doi: 10.1103/PhysRevB.99.045130
[6]	Fu L, Kane C L and Mele E J 2006 Phys. Rev. Lett. 98 106803
[37]	Hu Y J, Aulestia E I P, Tse K F, Kuo C N, Zhu J Y, Lue C S, Lai K T and Goh S K 2018 Phys. Rev. B 98 035133 doi: 10.1103/PhysRevB.98.035133
[7]	Fu L and Kane C L 2007 Phys. Rev. B 76 045302 doi: 10.1103/PhysRevB.76.045302
[38]	Habe T and Koshino M 2018 Phys. Rev. B 98 125201 doi: 10.1103/PhysRevB.98.125201
[8]	Fu L 2011 Phys. Rev. Lett. 106 106802 doi: 10.1103/PhysRevLett.106.106802
[39]	Dana I, Avron Y and Zak J 1985 J. Phys. C 18 L679
[40]	Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005 doi: 10.1103/RevModPhys.88.035005
[9]	Burkov A A, Hook M D and Balents L 2011 Phys. Rev. B 84 235126 doi: 10.1103/PhysRevB.84.235126
[41]	Hořava P 2005 Phys. Rev. Lett. 95 016405 doi: 10.1103/PhysRevLett.95.016405
[10]	Wan X G, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B 83 205101 doi: 10.1103/PhysRevB.83.205101
[11]	Soluyanov A A, Gresch D, Wang Z J, Wu Q S, Troyer M, Dai X and Bernevig B A 2015 Nature 527 495 doi: 10.1038/nature15768
[12]	Young S M, Zaheer S, Teo J C Y, Kane C L, Mele E J and Rappe A M 2012 Phys. Rev. Lett. 108 140405 doi: 10.1103/PhysRevLett.108.140405
[13]	Bzdusek T, Wu Q, Ruegg A, Sigrist M and Soluyanov A 2016 Nature 538 75 doi: 10.1038/nature19099
[14]	Bradlyn B, Cano J, Wang Z, Vergniory M G, Felser C, Cava R J and Bernevig B A 2016 Science 353 5037 doi: 10.1126/science.aaf5037
[15]	Yan Z B, Bi R, Shen H T, Lu L, Zhang S C and Wang Z 2017 Phys. Rev. B 96 041103 doi: 10.1103/PhysRevB.96.041103
[16]	Yu R, Fang Z, Dai X and Weng H M 2017 Front. Phys. 12 127202 doi: 10.1007/s11467-016-0630-1
[17]	Yu R, Wu Q S, Fang Z and Weng H M 2017 Phys. Rev. Lett. 119 036401 doi: 10.1103/PhysRevLett.119.036401
[18]	Xu Q N, Yu R, Fang Z, Dai X and Weng H M 2017 Phys. Rev. B 95 045136 doi: 10.1103/PhysRevB.95.045136
[19]	Zhao J Z, Yu R, Weng H M and Fang Z 2016 Phys. Rev. B 94 195104 doi: 10.1103/PhysRevB.94.195104
[20]	Weng H M, Dai X and Fang Z 2016 J. Phys.: Condens. Matter 28 303001 doi: 10.1088/0953-8984/28/30/303001
[21]	Hasan M Z, Xu S Y and Bian G 2015 Phys. Scr. 2015 014001
[22]	Qin S S, Hu L H, Le C C, Zeng J F, Zhang F C, Fang C and Hu J P 2019 arXiv:1901.04932
[23]	Le C C, Wu X X, Qin S S, Li Y X, Thomale R, Zhang F C and Hu J P 2018 Pro. Natl. Acad. Sci. USA 115 8311 doi: 10.1073/pnas.1803599115
[24]	Le C C, Qin S S, Wu X X, Dai X, Fu P Y and Hu J P 2017 Phys. Rev. B 96 115121 doi: 10.1103/PhysRevB.96.115121
[25]	Xu X T, Kang Z B, Chang T R, Lin H, Bian G, Yuan Z J, Qu Z, Zhang J L and Jia S 2019 arXiv:1903.07901v1
[26]	Ito S, Arita M, Haruyama J, Feng B, Chen W C, Namatame H, Taniguchi M, Cheng C M, Bian G, Tang S J, Chiang T C, Sugino O, Komori F and Matsuda I 2019 arXiv:1903.07018v1
[27]	Vail O, Taylor P, Folkes P, Nichols B and de Coster G 2019 arXiv:1903.06723v1
[28]	Hamilton G A, Park M J and Gilbert M J 2019 arXiv:1903.00024v1
[29]	Ma J C, Deng K, Zheng L, Wu S F, Liu Z, Zhou S Y and Sun D 2019 arXiv:1902.06874v1
[30]	VanGennep D, Paul T A, Yerger C W, Weir S T, Vohra Y K and Hamlin J J 2019 Phys. Rev. B 99 085204)
[31]	Singh B, Ghosh B, Su C, Lin H, Agarwal A and Bansil A 2018 Phys. Rev. Lett. 121 226401 doi: 10.1103/PhysRevLett.121.226401
[32]	Xu B, Zhao L X, Marsik P, Sheveleva E, Lyzwa F, Dai Y M, Chen G F, Qiu X G and Bernhard C 2018 Phys. Rev. Lett. 121 187401 doi: 10.1103/PhysRevLett.121.187401
[33]	Chen R, Xu D H and Zhou B 2018 Phys. Rev. B 98 235159 doi: 10.1103/PhysRevB.98.235159
[34]	Benito-Matias E and Molina R A 2019 Phys. Rev. B 99 075304 doi: 10.1103/PhysRevB.99.075304
[35]	Ominato Y, Tatsumi S and Nomura K 2019 Phys. Rev. B 99 085205 doi: 10.1103/PhysRevB.99.085205
[36]	Kim R, Yang B J and Kim C H 2019 Phys. Rev. B 99 045130 doi: 10.1103/PhysRevB.99.045130
[37]	Hu Y J, Aulestia E I P, Tse K F, Kuo C N, Zhu J Y, Lue C S, Lai K T and Goh S K 2018 Phys. Rev. B 98 035133 doi: 10.1103/PhysRevB.98.035133
[38]	Habe T and Koshino M 2018 Phys. Rev. B 98 125201 doi: 10.1103/PhysRevB.98.125201
[39]	Dana I, Avron Y and Zak J 1985 J. Phys. C 18 L679
[40]	Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005 doi: 10.1103/RevModPhys.88.035005
[41]	Hořava P 2005 Phys. Rev. Lett. 95 016405 doi: 10.1103/PhysRevLett.95.016405

Local evolutions of nodal points in two-dimensional systems with chiral symmetry

Local evolutions of nodal points in two-dimensional systems with chiral symmetry

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