摘要
In this study, we used the crystal structure search method and first-principles calculations to systematically explore the highpressure phase diagrams of the TaAs family(NbP, NbAs, TaP, and TaAs). Our calculation results show that NbAs and TaAs have similar phase diagrams, the same structural phase transition sequence I4_1 md→P6 m2→P2_1/c→Pm3 m, and slightly different transition pressures. The phase transition sequence of NbP and TaP differs somewhat from that of NbAs and TaAs, in which new structures emerge, such as the Cmcm structure in NbP and the Pmmn structure in TaP. Interestingly, we found that in the electronic structure of the high-pressure phase P6 m2-NbAs, there are coexistingWeyl points and triple degenerate points, similar to those found in high-pressure P6 m2-TaAs.
In this study, we used the crystal structure search method and first-principles calculations to systematically explore the highpressure phase diagrams of the TaAs family(NbP, NbAs, TaP, and TaAs). Our calculation results show that NbAs and TaAs have similar phase diagrams, the same structural phase transition sequence I4_1 md→P6 m2→P2_1/c→Pm3 m, and slightly different transition pressures. The phase transition sequence of NbP and TaP differs somewhat from that of NbAs and TaAs, in which new structures emerge, such as the Cmcm structure in NbP and the Pmmn structure in TaP. Interestingly, we found that in the electronic structure of the high-pressure phase P6 m2-NbAs, there are coexistingWeyl points and triple degenerate points, similar to those found in high-pressure P6 m2-TaAs.
引文
1 A.Bansil,H.Lin,and T.Das,Rev.Mod.Phys.88,021004(2016),arXiv:1603.03576.
2 C.K.Chiu,J.C.Y.Teo,A.P.Schnyder,and S.Ryu,Rev.Mod.Phys.88,035005(2016),arXiv:1505.03535.
3 H.Weng,X.Dai,and Z.Fang,J.Phys.-Condens.Matter 28,303001(2016),arXiv:1603.04744.
4 S.M.Young,S.Zaheer,J.C.Y.Teo,C.L.Kane,E.J.Mele,and A.M.Rappe,Phys.Rev.Lett.108,140405(2012),arXiv:1111.6483.
5 Z.Wang,Y.Sun,X.Q.Chen,C.Franchini,G.Xu,H.Weng,X.Dai,and Z.Fang,Phys.Rev.B 85,195320(2012).
6 Z.Wang,H.Weng,Q.Wu,X.Dai,and Z.Fang,Phys.Rev.B 88,125427(2013),arXiv:1305.6780.
7 H.Sun,and J.Zhao,Sci.China-Phys.Mech.Astron.59,107011(2016).
8 X.Wan,A.M.Turner,A.Vishwanath,and S.Y.Savrasov,Phys.Rev.B 83,205101(2011),arXiv:1007.0016.
9 G.Xu,H.Weng,Z.Wang,X.Dai,and Z.Fang,Phys.Rev.Lett.107,186806(2011),arXiv:1106.3125.
10 H.Weng,C.Fang,Z.Fang,B.A.Bernevig,and X.Dai,Phys.Rev.X5 ,011029(2015),arXiv:1501.00060.
11 Y.Sun,S.C.Wu,and B.Yan,Phys.Rev.B 92,115428(2015),arXiv:1508.06649.
12 C.C.Lee,S.Y.Xu,S.M.Huang,D.S.Sanchez,I.Belopolski,G.Chang,G.Bian,N.Alidoust,H.Zheng,M.Neupane,B.Wang,A.Bansil,M.Z.Hasan,and H.Lin,Phys.Rev.B 92,235104(2015).
13 D.T.Son,and B.Z.Spivak,Phys.Rev.B 88,104412(2013),arXiv:1206.1627.
14 P.Hosur,and X.Qi,C.R.Phys.14,857(2013),arXiv:1309.4464.
15 X.Huang,L.Zhao,Y.Long,P.Wang,D.Chen,Z.Yang,H.Liang,M.Xue,H.Weng,Z.Fang,X.Dai,and G.Chen,Phys.Rev.X 5,031023(2015),arXiv:1503.01304.
16 H.B.Nielsen,and M.Ninomiya,Phys.Lett.B 130,389(1983).
17 H.J.Kim,K.S.Kim,J.F.Wang,M.Sasaki,N.Satoh,A.Ohnishi,M.Kitaura,M.Yang,and L.Li,Phys.Rev.Lett.111,246603(2013),arXiv:1307.6990.
18 S.Y.Xu,I.Belopolski,N.Alidoust,M.Neupane,G.Bian,C.Zhang,R.Sankar,G.Chang,Z.Yuan,C.C.Lee,S.M.Huang,H.Zheng,J.Ma,D.S.Sanchez,B.K.Wang,A.Bansil,F.Chou,P.P.Shibayev,H.Lin,S.Jia,and M.Z.Hasan,Science 349,613(2015),arXiv:1502.03807.
19 B.Q.Lv,H.M.Weng,B.B.Fu,X.P.Wang,H.Miao,J.Ma,P.Richard,X.C.Huang,L.X.Zhao,G.F.Chen,Z.Fang,X.Dai,T.Qian,and H.Ding,Phys.Rev.X 5,031013(2015),arXiv:1502.04684.
20 D.F.Xu,Y.P.Du,Z.Wang,Y.P.Li,X.H.Niu,Q.Yao,P.Dudin,Z.A.Xu,X.G.Wan,and D.L.Feng,Chin.Phys.Lett.32,107101(2015),arXiv:1509.03847.
21 L.X.Yang,Z.K.Liu,Y.Sun,H.Peng,H.F.Yang,T.Zhang,B.Zhou,Y.Zhang,Y.F.Guo,M.Rahn,D.Prabhakaran,Z.Hussain,S.K.Mo,C.Felser,B.Yan,and Y.L.Chen,Nat.Phys.11,728(2015).
22 S.M.Huang,S.Y.Xu,I.Belopolski,C.C.Lee,G.Chang,B.K.Wang,N.Alidoust,G.Bian,M.Neupane,C.Zhang,S.Jia,A.Bansil,H.Lin,and M.Z.Hasan,Nat.Commun.6,7373(2015).
23 B.Q.Lv,N.Xu,H.M.Weng,J.Z.Ma,P.Richard,X.C.Huang,L.X.Zhao,G.F.Chen,C.E.Matt,F.Bisti,V.N.Strocov,J.Mesot,Z.Fang,X.Dai,T.Qian,M.Shi,and H.Ding,Nat.Phys.11,724(2015),arXiv:1503.09188.
24 N.Xu,H.M.Weng,B.Q.Lv,C.E.Matt,J.Park,F.Bisti,V.N.Strocov,D.Gawryluk,E.Pomjakushina,K.Conder,N.C.Plumb,M.Radovic,G.Autès,O.V.Yazyev,Z.Fang,X.Dai,T.Qian,J.Mesot,H.Ding,and M.Shi,Nat.Commun.7,11006(2016),arXiv:1507.03983.
25 Z.K.Liu,L.X.Yang,Y.Sun,T.Zhang,H.Peng,H.F.Yang,C.Chen,Y.Zhang,Y.F.Guo,D.Prabhakaran,M.Schmidt,Z.Hussain,S.K.Mo,C.Felser,B.Yan,and Y.L.Chen,Nat.Mater.15,27(2016).
26 S.Y.Xu,I.Belopolski,D.S.Sanchez,C.Zhang,G.Chang,C.Guo,G.Bian,Z.Yuan,H.Lu,T.R.Chang,P.P.Shibayev,M.L.Prokopovych,N.Alidoust,H.Zheng,C.C.Lee,S.M.Huang,R.Sankar,F.Chou,C.H.Hsu,H.T.Jeng,A.Bansil,T.Neupert,V.N.Strocov,H.Lin,S.Jia,and M.Z.Hasan,Sci.Adv.1,e1501092(2015),arXiv:1508.03102.
27 S.Y.Xu,N.Alidoust,I.Belopolski,Z.Yuan,G.Bian,T.R.Chang,H.Zheng,V.N.Strocov,D.S.Sanchez,G.Chang,C.Zhang,D.Mou,Y.Wu,L.Huang,C.C.Lee,S.M.Huang,B.K.Wang,A.Bansil,H.T.Jeng,T.Neupert,A.Kaminski,H.Lin,S.Jia,and M.Zahid Hasan,Nat.Phys.11,748(2015).
28 F.Arnold,C.Shekhar,S.C.Wu,Y.Sun,R.D.Dos Reis,N.Kumar,M.Naumann,M.O.Ajeesh,M.Schmidt,A.G.Grushin,J.H.Bardarson,M.Baenitz,D.Sokolov,H.Borrmann,M.Nicklas,C.Felser,E.Hassinger,and B.Yan,Nat.Commun.7,11615(2016),arXiv:1506.06577.
29 C.L.Zhang,S.Y.Xu,I.Belopolski,Z.Yuan,Z.Lin,B.Tong,G.Bian,N.Alidoust,C.C.Lee,S.M.Huang,T.R.Chang,G.Chang,C.H.Hsu,H.T.Jeng,M.Neupane,D.S.Sanchez,H.Zheng,J.Wang,H.Lin,C.Zhang,H.Z.Lu,S.Q.Shen,T.Neupert,M.Zahid Hasan,and S.Jia,Nat.Commun.7,10735(2016),arXiv:1601.04208.
30 C.Shekhar,A.K.Nayak,Y.Sun,M.Schmidt,M.Nicklas,I.Leermakers,U.Zeitler,Y.Skourski,J.Wosnitza,Z.Liu,Y.Chen,W.Schnelle,H.Borrmann,Y.Grin,C.Felser,and B.Yan,Nat.Phys.11,645 (2015),arXiv:1502.04361.
31 H.Wang,H.Wang,Y.Chen,J.Luo,Z.Yuan,J.Liu,Y.Wang,S.Jia,X.J.Liu,J.Wei,and J.Wang,Sci.Bull.62,425(2017).
32 A.Furusaki,Sci.Bull.62,788(2017).
33 A.A.Burkov,M.D.Hook,and L.Balents,Phys.Rev.B 84,235126(2011),arXiv:1110.1089.
34 H.Weng,Y.Liang,Q.Xu,R.Yu,Z.Fang,X.Dai,and Y.Kawazoe,Phys.Rev.B 92,045108(2015),arXiv:1411.2175.
35 R.Yu,H.Weng,Z.Fang,X.Dai,and X.Hu,Phys.Rev.Lett.115,036807(2015),arXiv:1504.04577.
36 Y.Kim,B.J.Wieder,C.L.Kane,and A.M.Rappe,Phys.Rev.Lett.115 ,036806(2015),arXiv:1504.03807.
37 C.Fang,Y.Chen,H.Y.Kee,and L.Fu,Phys.Rev.B 92,081201(2015),arXiv:1506.03449.
38 Z.Li,S.Y.Ning,H.B.Su,T.Iitaka,X.Y.Yang,J.X.Zhang,and T.Takami,Sci.China-Phys.Mech.Astron.60,017221(2017).
39 B.Bradlyn,J.Cano,Z.Wang,M.G.Vergniory,C.Felser,R.J.Cava,and B.A.Bernevig,Science 353,aaf5037(2016).
40 Z.Zhu,G.W.Winkler,Q.S.Wu,J.Li,and A.A.Soluyanov,Phys.Rev.X 6,031003(2016),arXiv:1605.04653.
41 H.Weng,C.Fang,Z.Fang,and X.Dai,Phys.Rev.B 94,165201(2016),arXiv:1605.05186.
42 H.Weng,C.Fang,Z.Fang,and X.Dai,Phys.Rev.B 93,241202(2016),arXiv:1604.08467.
43 G.Chang,S.Y.Xu,S.M.Huang,D.S.Sanchez,C.H.Hsu,G.Bian,Z.M.Yu,I.Belopolski,N.Alidoust,H.Zheng,T.R.Chang,H.T.Jeng,S.A.Yang,T.Neupert,H.Lin,and M.Z.Hasan,Sci.Rep.7,1688(2017).
44 J.P.Sun,D.Zhang,and K.Chang,Chin.Phys.Lett.34,027102(2017).
45 X.Zhang,Z.M.Yu,X.L.Sheng,H.Y.Yang,and S.A.Yang,Phys.Rev.B 95,235116(2017),arXiv:1704.03703.
46 I.C.Fulga,and A.Stern,Phys.Rev.B 95,241116(2017),arXiv:1702.03939.
47 M.Ezawa,Phys.Rev.B 95,205201(2017),arXiv:1612.05857.
48 J.B.He,D.Chen,W.L.Zhu,S.Zhang,L.X.Zhao,Z.A.Ren,and G.F.Chen,Phys.Rev.B 95,195165(2017),arXiv:1703.03211.
49 B.Q.Lv,Z.L.Feng,Q.N.Xu,X.Gao,J.Z.Ma,L.Y.Kong,P.Richard,Y.B.Huang,V.N.Strocov,C.Fang,H.M.Weng,Y.G.Shi,T.Qian,and H.Ding,Nature 546,627(2017).
50 A.A.Soluyanov,D.Gresch,Z.Wang,Q.S.Wu,M.Troyer,X.Dai,and B.A.Bernevig,Nature 527,495(2015),arXiv:1507.01603.
51 Z.Wang,D.Gresch,A.A.Soluyanov,W.Xie,S.Kushwaha,X.Dai,M.Troyer,R.J.Cava,and B.A.Bernevig,Phys.Rev.Lett.117,056805(2016),arXiv:1511.07440.
52 J.L.Zhang,S.J.Zhang,H.M.Weng,W.Zhang,L.X.Yang,Q.Q.Liu,S.M.Feng,X.C.Wang,R.C.Yu,L.Z.Cao,L.Wang,W.G.Yang,H.Z.Liu,W.Y.Zhao,S.C.Zhang,X.Dai,Z.Fang,and C.Q.Jin,Proc.Natl.Acad.Sci.USA 108,24(2011),arXiv:1009.3691.
53 K.Kirshenbaum,P.S.Syers,A.P.Hope,N.P.Butch,J.R.Jeffries,S.T.Weir,J.J.Hamlin,M.B.Maple,Y.K.Vohra,and J.Paglione,Phys.Rev.Lett.111,087001(2013),arXiv:1302.6488.
54 X.C.Pan,X.Chen,H.Liu,Y.Feng,Z.Wei,Y.Zhou,Z.Chi,L.Pi,F.Yen,F.Song,X.Wan,Z.Yang,B.Wang,G.Wang,and Y.Zhang,Nat.Commun.6,7805(2015),arXiv:1501.07394.
55 D.Kang,Y.Zhou,W.Yi,C.Yang,J.Guo,Y.Shi,S.Zhang,Z.Wang,C.Zhang,S.Jiang,A.Li,K.Yang,Q.Wu,G.Zhang,L.Sun,and Z.Zhao,Nat.Commun.6,7804(2015),arXiv:1502.00493.
56 P.Lu,J.S.Kim,J.Yang,H.Gao,J.Wu,D.Shao,B.Li,D.Zhou,J.Sun,D.Akinwande,D.Xing,and J.F.Lin,Phys.Rev.B 94,224512(2016).
57 Y.Li,Y.Zhou,Z.Guo,X.Chen,P.Lu,X.Wang,C.An,Y.Zhou,J.Xing,G.Du,X.Zhu,H.Yang,J.Sun,Z.Yang,Y.Zhang,and H.-H.Wen,npj Quantum Mater.2,66(2017),.arXiv:1611.02548.
58 Y.Zhou,P.Lu,Y.Du,X.Zhu,G.Zhang,R.Zhang,D.Shao,X.Chen,X.Wang,M.Tian,J.Sun,X.Wan,Z.Yang,W.Yang,Y.Zhang,and D.Xing,Phys.Rev.Lett.117,146402(2016).
59 M.Lu,Y.Guo,M.Zhang,H.Liu,and J.S.Tse,Solid State Commun.240,37(2016).
60 J.Zhang,F.L.Liu,J.K.Dong,Y.Xu,N.N.Li,W.G.Yang,and S.Y.Li,Chin.Phys.Lett.32,097102(2015).
61 C.J.Pickard,and R.J.Needs,J.Phys.-Condens.Matter 23,053201(2011),arXiv:1101.3987.
62 C.J.Pickard,and R.J.Needs,Phys.Rev.Lett.97,045504(2006).
63 G.Kresse,and J.Furthmüller,Comp.Mater.Sci.6,15(1996).
64 J.P.Perdew,K.Burke,and M.Ernzerhof,Phys.Rev.Lett.77,3865(1996).
65 E.Sjtedt,L.Nordstr,and D.J.Singh,Solid State Commun.114,15(2000).
66 G.K.H.Madsen,P.Blaha,K.Schwarz,E.Sjtedt,and L.Nordstr,Phys.Rev.B 64,195134(2001).
67 P.Blaha,K.Schwarz,G.Madsen,D.Kvasnicka,and J.Luitz,WIEN2k,An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties(Technische Universit鋞,Wien,2001).
68 J.KuneP.Novák,R.Schmid,P.Blaha,and K.Schwarz,Phys.Rev.B 64,153102(2001).
69 A.A.Mostofi,J.R.Yates,Y.S.Lee,I.Souza,D.Vanderbilt,and N.Marzari,Comp.Phys.Commun.178,685(2008),arXiv:0708.0650.
70 M.P.L.Sancho,J.M.Lopez Sancho,and J.Rubio,J.Phys.F-Met.Phys.14,1205(1984).
71 M.P.L.Sancho,J.M.Lopez Sancho,J.M.L.Sancho,and J.Rubio,J.Phys.F-Met.Phys.15,851(1985).
72 J.Xu,M.Greenblatt,T.Emge,P.Hhn,T.Hughbanks,and Y.Tian,Inorg.Chem.35,845(1996).
73 N.Schberg,W.G.Overend,A.Munthe-Kaas,and N.A.Sensen,Acta Chem.Scand.8,226(1954).
74 S.Furuseth,and A.Kjekshus,Acta Cryst.17,1077(1964).
75 J.J.Murray,J.B.Taylor,L.D.Calvert,Y.Wang,E.J.Gabe,and J.G.Despault,J.Less Common Met.46,311(1976).
76 Q.S.Wu,S.N.Zhang,H.F.Song,M.Troyer,and A.A.Soluyanov,Comp.Phys.Commun.https://doi.org/10.1016/j.cpc.2017.09.033(2017),arXiv:1703.37789.
77 R.Yu,X.L.Qi,A.Bernevig,Z.Fang,and X.Dai,Phys.Rev.B 84,075119(2011),arXiv:1101.2011.