Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator
Zhao-Kun Yang(杨兆昆)1, Jing-Rong Wang(王景荣)2, and Guo-Zhu Liu(刘国柱)1,†
1 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; 2 High Magnetic Field Laboratory of Anhui Province, Chinese Academy of Sciences, Hefei 230031, China
Abstract One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap. This kind of quantum phase transition is characterized by the change of certain topological invariant. A new gapless semimetallic state emerges at each topological quantum critical point. Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential. We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder. The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis, but becomes a compressible diffusive metal when other types of disorders exist.
Fund: Project supported by the Natural Science Foundation of Anhui Province, China (Grant No. 2208085MA11) and the National Natural Science Foundation of China (Grants Nos. 11974356, 12274414, and U1832209).
Corresponding Authors:
Guo-Zhu Liu
E-mail: gzliu@ustc.edu.cn
Cite this article:
Zhao-Kun Yang(杨兆昆), Jing-Rong Wang(王景荣), and Guo-Zhu Liu(刘国柱) Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator 2023 Chin. Phys. B 32 056401
[1] Vafek O and Vishwanath A 2014 Annu. Rev. Condens. Matter Phys.5 83 [2] Wehling T O, Black-Schaffer A M and Balatsky A V 2014 Adv. Phys.63 1 [3] Yang B J and Nagaosa N 2014 Nat. Commun.5 4898 [4] Weng H, Dai X and Fang Z 2016 J. Phys.-Condens. Matter28 303001 [5] Fang C, Weng H, Dai X and Fang Z 2016 Chin. Phys. B25 117106 [6] Armitage N P, Mele E J and Vishwanath A 2018 Rev. Mod. Phys.90 015001 [7] Lv B Q, Qian T and Ding H 2021 Rev. Mod. Phys.93 025002 [8] Hasan M Z, Chang G, Belopolski I, Bian G, Xu S Y and Yin J X 2021 Nat Rev Mater6 784 [9] Lu H Z and Shen S Q 2016 Chin. Phys. B25 117202 [10] Wang H and Wang J 2018 Chin. Phys. B27 107402 [11] Feng X L, Zhu J J, Wu W K and Yang S Y 2021 Chin. Phys. B 30 107304 [12] Son D T and Spivak B Z 2013 Phys. Rev. B88 104412 [13] Burkov A A 2017 Phys. Rev. B96 041110 [14] Nandy S, Sharma G, Taraphder A and Tewari S 2017 Phys. Rev. Lett. 119 176804 [15] Goswami P and Chakravarty S 2011 Phys. Rev. Lett. 107 196803 [16] Dietl P, Piéchon F and Montambaux G 2008 Phys. Rev. Lett.100 236405 [17] Montambaux G, Piéchon F, Fuchs J N and Goerbig M O 2009 Phys. Rev. B80 153412 [18] Isobe H, Yang B J, Chubukov A, Schmalian J and Nagaosa N 2016 Phys. Rev. Lett.116 076803 [19] Cho G Y and Moon E G 2016 Sci. Rep.6 19198 [20] Wang J R, Liu G Z and Zhang C J 2017 Phys. Rev. B95 075129 [21] Yang B J, Bahramy M S, Arita R, Isobe H, Moon E G and Nagaosa N 2013 Phys. Rev. Lett.110 086402 [22] Yang B J and Nagaosa N 2014 Nat. Commun.5 4898 [23] Wang J R, Liu G Z and Zhang C J 2019 Phys. Rev. B99 195119 [24] Han S E, Lee C, Moon E G and Min H 2019 Phys. Rev. Lett.122 187601 [25] Zhang S X, Jian S K and Yao H 2021 Phys. Rev. B103 165129 [26] Xu S Y, Xia Y, Wray L A, Jia S, Meier F, Dil J H, Osterwalder J, Slomski B, Bansil A, Lin H, Cava R J and Hasan M Z 2011 Science332 560 [27] Sato T, Segawa K, Kosaka K, Souma S, Nakayama K, Eto K, Minami T, Ando Y and Takahashi T 2011 Nat. Phys.7 840 [28] Wu L, Brahlek M, Aguilar R V, Stier A V, Morris C M, Lubashevsky Y, Bilbro L S, Bansal N, Oh S and Armitage N P 2013 Nat. Phys. 9 410 [29] Brahlek M, Bansal N, Koirala N, Xu S Y, Neupane M, Liu C, Hasan M Z and Oh S 2012 Phys. Rev. Lett.109 186403 [30] Xu G, Weng H, Wang Z, Dai X and Fang Z 2011 Phys. Rev. Lett.107 186806 [31] Fang C, Gilbert M J, Dai X and Bernevig B A 2012 Phys. Rev. Lett.108 266802 [32] Lai H H 2015 Phys. Rev. B91 235131 [33] Jian S K and Yao H 2015 Phys. Rev. B92 045121 [34] Bera S, Sau J D and Roy B 2016 Phys. Rev. B93 201302 [35] Sbierski B, Trescher M, Bergholtz E J and Brouwer P W 2017 Phys. Rev. B95 115104 [36] Roy B, Goswami P and Juričić V 2017 Phys. Rev. B95 201102 [37] Wang J R, Liu G Z and Zhang C J 2017 Phys. Rev. B96 165142 [38] Zhang S X, Jian S K and Yao H 2017 Phys. Rev. B96 241111 [39] Wang J R, Liu G Z and Zhang C J 2018 Phys. Rev. B98 205113 [40] Huang S M, Xu S Y, Belopolski I, Lee C C, Chang G, Chang T R, Wang B K, Alidoust N, Bian G, Neupane M, Sanchez D, Zheng H, Jeng H T, Bansil A, Neupert T, Lin H and Hasan M Z 2016 Proc. Natl. Acad. Sci. USA113 1180 [41] Liu Q and Zunger A 2017 Phys. Rev. X 7 021019 [42] Chen W J, Xiao M and Chan C T 2016 Nat. Commun.7 13038 [43] Chang M L, Xiao M, Chen W J and Chan C T 2017 Phys. Rev. B95 125136 [44] Ludwig A W W, Fisher M P A, Shankar R and Grinstein G 1994 Phys. Rev. B50 7526 [45] Nersesyan A A, Tsvelik A M and Wenger F 1994 Phys. Rev. Lett.72 2628 [46] Ostrovsky P M, Gornyi I V and Mirlin A D 2006 Phys. Rev. B74 235443 [47] Evers F and Mirlin A D 2008 Rev. Mod. Phys.80 1355 [48] Fradkin E 1986 Phys. Rev. B33 3263 [49] Shindou R and Murakami S 2009 Phys. Rev. B79 045321 [50] Ominato Y and Koshino M 2014 Phys. Rev. B89 054202 [51] Sbierski B, Pohl G, Bergholtz E J and Brouwer P W 2014 Phys. Rev. Lett.113 026602 [52] Roy B and Das Sarma S 2014 Phys. Rev. B90 241112 [53] Syzranov S V, Ostrovsky P M, Gurarie V and Radzihovsky L 2016 Phys. Rev. B93 155113 [54] Syzranov S V and Radzihovsky L 2018 Annu. Rev. Condens. Matter Phys.9 35 [55] Carpentier D, Fedorenko A A and Orignac E 2013 Euro. Phys. Lett.102 67010 [56] Sbierski B, Decker K S C and Brouwer P W 2016 Phys. Rev. B94 220202 [57] Zhao P L, Wang J R, Wang A M and Liu G Z 2016 Phys. Rev. B94 195114 [58] Nandkishore R M and Parameswaran S A 2017 Phys. Rev. B95 205106 [59] Sikkenk T S and Fritz L 2017 Phys. Rev. B96 155121 [60] Yang Z K, Wang J R and Liu G Z 2018 Phys. Rev. B98 195123 [61] Luo X, Xu B, Ohtsuki T and Shindou R 2018 Phys. Rev. B98 045129 [62] Luo X, Ohtsuki T and Shindou R 2018 Phys. Rev. B98 020201 [63] Roy B, Slager R J and Juričić V 2018 Phys. Rev. X 8 031076 [64] Ning Z, Fu B, Shi Q and Wang X 2020 Chin. Phys. B29 077202 [65] Wang J, Liu G Z and Kleinert H 2011 Phys. Rev. B83 214503 [66] Stauber T, Guinea F and Vozmediano M A H 2005 Phys. Rev. B71 041406 [67] Shankar R 1994 Rev. Mod. Phys.66 129 [68] Park M J, Basa B and Gilbert M J 2017 Phys. Rev. B95 094201 [69] Zhu W and Sheng D N 2019 Phys. Rev. Lett.123 056804 [70] Pixley J H, Goswami P and Das Sarma S 2015 Phys. Rev. Lett.115 076601 [71] Pixley J H, Wilson J H, Huse D A and Gopalakrishnan S 2018 Phys. Rev. Lett.120 207604 [72] Gonçalves M, Ribeiro P, Castro E V and Araújo M A N 2020 Phys. Rev. Lett.124 136405 [73] Fu B, Zhu W, Shi Q, Li Q, Yang J and Zhang Z 2017 Phys. Rev. Lett.118 146401
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