• Acta Physica Sinica
  • Vol. 68, Issue 22, 227101-1 (2019)
Shan-Shan Wang1、*, Wei-Kang Wu2, and Sheng-Yuan Yang2
Author Affiliations
  • 1School of Physics, Southeast University, Nanjing 211189, China
  • 2Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
  • show less
    DOI: 10.7498/aps.68.20191538 Cite this Article
    Shan-Shan Wang, Wei-Kang Wu, Sheng-Yuan Yang. Progress on topological nodal line and nodal surface[J]. Acta Physica Sinica, 2019, 68(22): 227101-1 Copy Citation Text show less
    References

    [1] von Klitzing K, Dorda G, Pepper M[J]. Phys. Rev. Lett., 45, 494(1980).

    [2] Thouless D J, Kohmoto M, Nightingale M P, den Nijs M[J]. Phys. Rev. Lett., 49, 405(1982).

    [3] Haldane F D M[J]. Phys. Rev. Lett., 61, 2015(1988).

    [4] Kane C L, Mele E J[J]. Phys. Rev. Lett., 95, 146802(2005).

    [5] Kane C L, Mele E J[J]. Phys. Rev. Lett., 95, 226801(2005).

    [6] Geim A K, Novoselov K S[J]. Nat. Mater., 6, 183(2007).

    [7] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A[J]. Science, 306, 666(2004).

    [8] Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L, MacDonald A H[J]. Phys. Rev. B, 74, 165310(2006).

    [9] Yao Y, Ye F, Qi X L, Zhang S C, Fang Z[J]. Phys. Rev. B, 75, 041401(2007).

    [10] Bernevig B A, Hughes T L, Zhang S C[J]. Science, 314, 1757(2006).

    [11] König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C[J]. Science, 318, 766(2007).

    [12] Fu L, Kane C L, Mele E J[J]. Phys. Rev. Lett., 98, 106803(2007).

    [13] Hasan M Z, Kane C L[J]. Rev. Mod. Phys., 82, 3045(2010).

    [14] Fu L[J]. Phys. Rev. Lett., 106, 106802(2011).

    [15] Essin A M, Moore J E, Vanderbilt D[J]. Phys. Rev. Lett., 102, 146805(2009).

    [16] Schnyder A P, Ryu S, Furusaki A, Ludwig A W[J]. Phys. Rev. B, 78, 195125(2008).

    [17] Chiu C K, Teo J C Y, Schnyder A P, Ryu S[J]. Rev. Mod. Phys., 88, 035005(2006).

    [18] Xiao D, Chang M C, Niu Q[J]. Rev. Mod. Phys., 82, 1959(2010).

    [19] Niu Q, Chang M C, Wu B, Xiao D, Cheng R[J]. Physical Effects of Geometric Phases(2017).

    [20] Hořava P[J]. Phys. Rev. Lett., 95, 016405(2005).

    [21] Zhao Y X, Wang Z D[J]. Phys. Rev. Lett., 110, 240404(2013).

    [22] Wan X, Turner A M, Vishwanath A, Savrasov S Y[J]. Phys. Rev. B, 83, 205101(2011).

    [23] Nielsen H B, Ninomiya M[J]. Phys. Lett. B, 130, 389(1983).

    [24] Volovik G E[J]. The Universe in A Helium Droplet, 117(2003).

    [25] Guan S, Yu Z M, Liu Y, Liu G B, Dong L, Lu Y, Yao Y, Yang S A[J]. npj Quant. Mater., 2, 23(2017).

    [26] Yang S A[J]. SPIN, 6, 1640003(2016).

    [27] Young S M, Zaheer S, Teo J C, Kane C L, Mele E J, Rappe A M[J]. Phys. Rev. Lett., 108, 140405(2012).

    [28] Xu G, Weng H, Wang Z, Dai X, Fang Z[J]. Phys. Rev. Lett., 107, 186806(2011).

    [29] Weng H, Fang C, Fang Z, Dai X[J]. Phys. Rev. B, 93, 241202(2016).

    [30] Zhu Z, Winkler G W, Wu Q, Li J, Soluyanov A A[J]. Phys. Rev. X, 6, 031003(2016).

    [31] Chang G, Xu S Y, Huang S M, Sanchez D S, Hsu C H, Bian G, Yu Z M, Belopolski L, Alidoust N, Zheng H, Chang T R, Jeng H T, Yang S A, Neupert T, Lin H, Hasan M Z[J]. Sci. Rep., 7, 1688(2017).

    [32] Bradlyn B, Cano J, Wang Z, Vergniory M G, Felser C, Cava R J, Bernevig B A[J]. Science, 353, aaf5037(2016).

    [33] Wieder B J, Kim Y, Rappe A M, Kane C L[J]. Phys. Rev. Lett., 116, 186402(2016).

    [34] Kennett M P, Komeilizadeh N, Kaveh K, Smith P M[J]. Phys. Rev. A, 83, 053636(2011).

    [35] Roy B, Smith P M, Kennett M P[J]. Phys. Rev. B, 85, 235119(2012).

    [36] Chen C, Wang S S, Liu L, Yu Z M, Sheng X L, Chen Z, Yang S A[J]. Phys. Rev. Mater., 1, 044201(2017).

    [37] Liu Q, Zunger A[J]. Phys. Rev. X, 7, 021019(2017).

    [38] Yu W C, Zhou X, Chuang F C, Yang S A, Lin H, Bansil A[J]. Phys. Rev. Mater., 2, 051201(2018).

    [39] Zhu Z, Liu Y, Yu Z M, Wang S S, Zhao Y X, Feng Y, Sheng X L, Yang S A[J]. Phys. Rev. B, 98, 125104(2018).

    [40] Son D T, Spivak B Z[J]. Phys. Rev. B, 88, 104412(2013).

    [41] Gao Y, Yang S A, Niu Q[J]. Phys. Rev. B, 95, 165135(2017).

    [42] Luo Y, McDonald R D, Rosa P F S, Scott B, Wakeham N, Ghimire N J, Bauer E D, Thompson J D, Ronning F[J]. Sci. Rep., 6, 27294(2016).

    [43] Li Y, Li L, Wang J, Wang T, Xu X, Xi C, Cao C, Dai J[J]. Phys. Rev. B, 94, 121115(2016).

    [44] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X, Fang Z[J]. Phys. Rev. B, 85, 195320(2012).

    [45] Wang Z, Weng H, Wu Q, Dai X, Fang Z[J]. Phys. Rev. B, 88, 125427(2013).

    [46] Weng H, Fang C, Fang Z, Bernevig B A, Dai X[J]. Phys. Rev. X, 5, 011029(2015).

    [47] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Wang B K, Alidoust N, Bian G, Neupane M, Zhang C, Jia S, Bansil A, Lin H, Hasan M Z[J]. Nat. Commun., 6, 7373(2015).

    [48] Tang F, Po H C, Vishwanath A, Wan X[J]. Nature, 566, 486(2019).

    [49] Zhang T, Jiang Y, Song Z, Huang H, He Y, Fang Z, Weng H, Fang C[J]. Nature, 566, 475(2019).

    [50] Vergniory M G, Elcoro L, Felser C, Regnault N, Bernevig B A, Wang Z[J]. Nature, 566, 480(2019).

    [51] Yang S A, Pan H, Zhang F[J]. Phys. Rev. Lett, 113, 046401(2014).

    [52] Weng H, Liang Y, Xu Q, Yu R, Fang Z, Dai X, Kawazoe Y[J]. Phys. Rev. B, 92, 045108(2015).

    [53] Mullen K, Uchoa B, Glatzhofer D T[J]. Phys. Rev. Lett., 115, 026403(2015).

    [54] Yu R, Weng H, Fang Z, Dai X, Hu X[J]. Phys. Rev. Lett., 115, 036807(2015).

    [55] Kim Y, Wieder B J, Kane C L, Rappe A M[J]. Phys. Rev. Lett., 115, 036806(2015).

    [56] Chen Y, Xie Y, Yang S A, Pan H, Zhang F, Cohen M, Zhang S[J]. Nano Lett., 15, 6974(2015).

    [57] Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Wang B, Lee C C, Jeng H T, Bandil A, Chou F, Lin H, Hasan M Z[J]. arXiv: 1505.03069(2015).

    [58] Fang C, Chen Y, Kee H Y, Fu L[J]. Phys. Rev. B, 92, 081201(2015).

    [59] Zhong C, Chen Y, Xie Y, Yang S A, Cohen M L, Zhang S B[J]. Nanoscale, 8, 7232(2016).

    [60] Liang Q F, Zhou J, Yu R, Wang Z, Weng H[J]. Phys. Rev. B, 93, 085427(2016).

    [61] Li S, Yu Z M, Liu Y, Guan S, Wang S S, Zhang X, Yao Y, Yang S A[J]. Phys. Rev. B: Rapid Comm., 96, 081106(2017).

    [62] Lu Y, Zhou D, Chang G, Guan S, Chen W, Jiang Y, Jiang J, Wang X S, Yang S A, Feng Y P, Kawazoe Y, Lin H[J]. npj Comput. Mater., 2, 16011(2016).

    [63] Wu W, Liu Y, Li S, Zhong C, Yu Z M, Sheng X L, Zhao Y X, Yang S A[J]. Phys. Rev. B, 97, 115125(2018).

    [64] Zhang X, Yu Z M, Lu Y, Sheng X L, Yang H Y, Yang S A[J]. Phys. Rev. B, 97, 125143(2018).

    [65] Xu Q, Yu R, Fang Z, Dai X, Weng H[J]. Phys. Rev. B, 95, 045136(2017).

    [66] Chan Y H, Chiu C K, Chou M Y, Schnyder A P[J]. Phys. Rev. B, 93, 205132(2016).

    [67] Du Y, Tang F, Wang D, Sheng L, Kan E J, Duan C G, Savrasov S Y, Wan X[J]. npj Quantum Mater., 2, 3(2017).

    [68] Huang H, Liu J, Vanderbilt D, Duan W[J]. Phys. Rev. B, 93, 201114(2016).

    [69] Li S, Liu Y, Fu B, Yu Z M, Yang S A, Yao Y[J]. Phys. Rev. B, 97, 245148(2018).

    [70] Li R, Ma H, Cheng X, Wang S, Li D, Zhang Z, Li Y, Chen X Q[J]. Phys. Rev. Lett., 117, 096401(2016).

    [71] Bian G, Chang T R, Sankar R, Xu S Y, Zheng H, Neupert T, Chiu C K, Huang S M, Chang G, Belopolski I, Sanchez D S, Neupane M, Alidoust N, Liu C, Wang B, Lee C C, Jeng H T, Zhang C, Yuan Z, Jia S, Bansil A, Chou F, Lin H, Hasan M Z[J]. Nat. Commun., 7, 10556(2016).

    [72] Young S M, Kane C L[J]. Phys. Rev. Lett., 115, 126803(2015).

    [73] Wang S S, Liu Y, Yu Z M, Sheng X L, Yang S A[J]. Nat. Commun., 8, 1844(2017).

    [74] Li S, Liu Y, Wang S S, Yu Z M, Guan S, Sheng X L, Yao Y, Yang S A[J]. Phys. Rev. B, 97, 045131(2018).

    [75] Bzdušek T, Wu Q, Rüegg A, Sigrist M, Soluyanov A A[J]. Nature, 538, 7623(2016).

    [76] Sato T, Wang Z, Nakayama K, Souma S, Takane D, Nakata Y, Iwasawa H, Cacho C, Timur K, Takahashi T, Ando Y[J]. Phys. Rev. B, 98, 121111(2018).

    [77] An L, Zhang H, Hu J, Zhu X, Gao W, Zhang J, Xi C, Ning W, Mao Z, Tan M[J]. Phys. Rev. B, 97, 235133(2018).

    [78] Soluyanov A A, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig B A[J]. Nature, 527, 495(2015).

    [79] Xu Y, Zhang F, Zhang C[J]. Phys. Rev. Lett., 115, 265304(2015).

    [80] Zhang X, Jin L, Dai X, Liu G[J]. J. Phys. Chem. Lett., 8, 4814(2017).

    [81] Chang T R, Pletikosic I, Kong T, Bian G, Huang A, Denlinger J, Kushwaha S K, Sinkovic B, Jeng H T, Valla T, Xie W, Cava R J[J]. Adv. Sci., 6, 1800897(2018).

    [82] Li Z H, Wang W, Zhou P, Ma Z S, Sun L Z[J]. New J. Phys., 21, 033018(2019).

    [83] Yu Z M, Wu W, Sheng X L, Zhao Y X, Yang S A[J]. Phys. Rev. B. Rapid Comm., 99, 121106(2019).

    [84] Zhong C, Wu W, He J, Ding G, Liu Y, Li D, Yang S A, Zhang G[J]. Nanoscale, 11, 2468(2019).

    [85] Wang S S, Yu Z M, Liu Y, Jiao Y, Guan S, Sheng X L, Yang S A[J]. Phys. Rev. Mater., 3, 084201(2019).

    [86] Zeng M, Fang C, Chang G, Chen Y A, Hsieh T, Bansil A, Lin H, Fu L[J]. arXiv: 1504.03492(2015).

    [87] Kobayashi S, Yamakawa Y, Yamakage A, Inohara T, Okamoto Y, Tanaka Y[J]. Phys. Rev. B, 95, 245208(2017).

    [88] Gong C, Xie Y, Chen Y, Kim H S, Vanderbilt D[J]. Phys. Rev. Lett., 120, 106403(2018).

    [89] Sheng X L, Yu Z M, Yu R, Weng H, Yang S A[J]. J. Phys. Chem. Lett., 8, 3506(2017).

    [90] Zhong C, Chen Y, Yu Z -M, Xie Y, Wang H, [J]. Nat. Commun., 8, 15641(2017).

    [91] Chang G, Xu S Y, Zhou X, Huang S M, Singh B, Wang B, Belopolski I, Yin J, Zhang S, Bansil A, Lin H, Hasan M Z[J]. Phys. Rev. Lett., 119, 156401(2017).

    [92] Kim K S, Zhao Y, Jang H, Lee S Y, Kim J M, Kim K S, Ahn J H, Kim P, Choi J Y, Hong B H[J]. Nature, 457, 706(2009).

    [93] Lee C, Wei X, Kysar J W, Hone J[J]. Science, 321, 385(2008).

    [94] Wu W, Jiao Y, Li S, Sheng X L, Yu Z -M, Yang S A[J]. Phys. Rev. Materials, 3, 054203(2019).

    [95] You J Y, Chen C, Zhang Z, Sheng X L, Yang S A, Su G[J]. Phys. Rev. B, 100, 064408(2019).

    [96] Guan S, Liu Y, Yu Z M, Wang S S, Yao Y, Yang S A[J]. Phys. Rev. Materials, 1, 054003(2017).

    [97] Jin Y J, Wang R, Zhao J Z, Du Y P, Zheng C D, Gan L Y, Liu J F, Xu H, Tong S Y[J]. Nanoscale, 9, 13112(2017).

    [98] Zhou P, Ma Z S, Sun L Z[J]. Journal of Materials Chemistry C, 6, 1206(2018).

    [99] Feng B, Fu B, Kasamatsu S, Ito S, Cheng P, Liu C C, Feng Y, Wu S, Mahatha S K, Sheverdyaeva P, Moras O, Arita M, Sugino O, Chiang T C, Shimada K, Miyamoto K, Okuda T, Wu K, Chen L, Yao Y[J]. Nat. Commun., 8, 1007(2017).

    [100] Gao L, Sun J T, Lu J C, Li H, Qian K, Zhang S, Zhang Y Y, Qian T, Ding H, Lin X, Du S, Gao H J[J]. Adv. Mater., 30, 1707055(2018).

    [101] Li R, Xu Y, He J, Ullah S, Li J, Liu J M, Li D, Franchini C, Weng H, Chen X Q[J]. arXiv: 1610.07142(2016).

    [102] Shi Y, Guo Y, Wang X, Princep A J, Khalyavin D, Manuel P, Michiue Y, Sato A, Tsuda K, Arai M[J]. Nature Mater., 12, 1024(2013).

    [103] Chang G, Xu S Y, Zheng H, Singh B, Hsu C H, Bian G, Alidoust N, Belopolski I, Sanchez D S, Zhang S, Lin H, Hasan M Z[J]. Sci. Rep., 6, 38839(2016).

    [104] Zhang R W, Zhang Z, Liu C C, Yao Y[J]. arXiv: 1907.01130(2019).

    [105] Wang R, Zhao J Z, Jin Y J, Du Y P, Zhao Y X, Xu H, Tong S Y[J]. Phys. Rev. B, 97, 241111(2018).

    [106] Chen C, Yu Z M, Li S, Chen Z, Sheng X L, Yang S A[J]. Phys. Rev. B, 99, 075131(2019).

    [107] Wang J[J]. Phys. Rev. B, 96, 081107(2017).

    [108] Hosen M M, Dhakal G, Dimitri K, Maldonado P, Aperis A, Firoza K, Christopher S, Riseborough P, Oppeneer P M, Kaczorowski D, Durakiewicz T, Neupane M[J]. Sci. Rep., 8, 13283(2018).

    [109] Zhou X, Zhang R W, Zhang Z, Ma D S, Feng W, Mokrousov Y, Yao Y[J]. J. Phys. Chem. Lett., 10, 3101(2019).

    [110] Feng B, Zhang R W, Feng Y, Fu B, Wu S, Miyamoto K, He S, Chen L, Wu K, Shimada K, Okuda T, Yao Y[J]. Phy. Rev. Lett., 123, 116401(2019).

    [111] Heikkilä T T, Kopnin N B, Volovik G E[J]. JETP Lett., 94, 233(2011).

    [112] Liu J, Balents L[J]. Phys. Rev. B, 95, 075426(2017).

    [113] Bzdušek T, Sigrist M[J]. Phys. Rev. B, 96, 155105(2017).

    [114] Xiao M, Sun X Q, Fan S[J]. Phys. Rev. B, 99, 094206(2019).

    [115] Zhang X, Yu Z M, Zhu Z, Wu W, Wang S S, Sheng X L, Yang S A[J]. Phys. Rev. B, 97, 235150(2018).

    [116] Zhao Y X, Schnyder A P[J]. Phys. Rev. B, 94, 195109(2016).

    [117] Yu Z M, Wu W, Zhao Y X, Yang S A[J]. Phys. Rev. B, 100, 041118(2019).

    [118] Nielsen H B, Ninomiya M[J]. Nucl. Phys. B, 185, 20(1981).

    [119] Nielsen H B, Ninomiya M[J]. Nucl. Phys. B, 193, 173(1981).

    [120] Rhim J W, Kim Y B[J]. Phys. Rev. B, 92, 045126(2015).

    [121] Liu Y, Yang S A, Zhang F[J]. Phys. Rev. B, 97, 035153(2018).

    Shan-Shan Wang, Wei-Kang Wu, Sheng-Yuan Yang. Progress on topological nodal line and nodal surface[J]. Acta Physica Sinica, 2019, 68(22): 227101-1
    Download Citation