上海大学学报(自然科学版) ›› 2022, Vol. 28 ›› Issue (5): 768-779.doi: 10.12066/j.issn.1007-2861.2438
收稿日期:
2022-03-15
出版日期:
2022-10-30
发布日期:
2022-11-12
通讯作者:
任伟
E-mail:renwei@shu.edu.cn
作者简介:
任 伟(1979—), 男, 教授, 博士生导师, 博士, 研究方向为凝聚态物理、计算材料学等. E-mail: renwei@shu.edu.cn基金资助:
GAO Heng1,2, HU Shunbo1,2, REN Wei1,2()
Received:
2022-03-15
Online:
2022-10-30
Published:
2022-11-12
Contact:
REN Wei
E-mail:renwei@shu.edu.cn
摘要:
狄拉克半金属由于其新奇的电子结构和输运性质, 受到了实验和理论学者广泛的关注. 该拓扑材料在费米能级附近存在受对称性保护的狄拉克点, 是由于固体中导带和价带的能带反转导致的. 本综述介绍了中心对称拓扑狄拉克半金属, 并且引入了一种新的三维非中心对称拓扑狄拉克半金属. 通过晶体结构对称性和能带对称性分析可知, 具有C$_{\rm 4v}$或C$_{\rm 6v}$点群的晶体可以实现非中心对称拓扑狄拉克半金属. 具有C$_{\rm 4v}$点群对称性的BiPd$_{2}$O$_{4}$晶体被理论预测为非中心对称的狄拉克半金属, 并且在四重旋转轴上可以实现第二类型的拓扑狄拉克点. 此外, 具有C$_{\rm 6v}$点群对称性的SrHgPb晶体和LiZnSb$_{x}$Bi$_{1-x}$合金可以实现狄拉克点与外尔点共存的拓扑半金属, 并且在LiZnSb$_{x}$Bi$_{1-x}$合金中外尔点的出现和位置可以通过元素成分比例$x$调控. 与中心对称拓扑狄拉克半金属相比, 非中心对称拓扑狄拉克半金属由于中心反演对称性的破缺, 在非线性光学和非线性霍尔输运等方面有潜在的应用.
中图分类号:
高恒, 胡顺波, 任伟. 非中心对称拓扑狄拉克半金属的研究进展[J]. 上海大学学报(自然科学版), 2022, 28(5): 768-779.
GAO Heng, HU Shunbo, REN Wei. Research progress on noncentrosymmetric topological Dirac semimetals[J]. Journal of Shanghai University(Natural Science Edition), 2022, 28(5): 768-779.
[1] |
Wen X G. Topological orders and edge excitations in fractional quantum Hall states[J]. Advances in Physics, 1995, 44(5): 405-473.
doi: 10.1080/00018739500101566 |
[2] |
Thouless D J, Kohmoto M, Nightingale M P, et al. Quantized hall conductance in a two-dimensional periodic potential[J]. Physical Review Letters, 1982, 49(6): 405-408.
doi: 10.1103/PhysRevLett.49.405 |
[3] |
Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 2011, 83(4): 1057-1110.
doi: 10.1103/RevModPhys.83.1057 |
[4] |
Hasan M Z, Kane C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 2010, 82: 3045-3067.
doi: 10.1103/RevModPhys.82.3045 |
[5] |
Fu L. Topological crystalline insulators[J]. Physical Review Letters, 2011, 106: 106802.
doi: 10.1103/PhysRevLett.106.106802 |
[6] |
Armitage N P, Mele E J, Vishwanath A. Weyl and Dirac semimetals in three-dimensional solids[J]. Reviews of Modern Physics, 2018, 90: 015001.
doi: 10.1103/RevModPhys.90.015001 |
[7] | Gao H, Venderbos J W F, Kim Y, et al. Topological semimetals from first principles[J]. Annual Review of Materials Resarch, 2019, 49(1): 153-183. |
[8] | Weng H, Dai X, Fang Z. Topological semimetals predicted from first-principles calculations[J]. Journal of Physicals: Condensed Matter, 2016, 28(30): 303001. |
[9] |
Bernevig A, Weng H, Fang Z, et al. Recent progress in the study of topological semimetals[J]. Journal of the Physical Society of Japan, 2018, 87(4): 041001.
doi: 10.7566/JPSJ.87.041001 |
[10] |
Weng H, Fang C, Fang Z, et al. A new member of the topological semimetals family[J]. National Science Review, 2017, 4(6): 798-799.
doi: 10.1093/nsr/nwx066 |
[11] |
Young S M, Zaheer S, Teo J C Y, et al. Dirac semimetal in three dimensions[J]. Physical Review Letters, 2012, 108: 140405.
doi: 10.1103/PhysRevLett.108.140405 |
[12] |
Wang Z, Sun Y, Chen X Q, et al. Dirac semimetal and topological phase transitions in $A_3$Bi($A$=Na, K, Rb)[J]. Physical Review B, 2012, 85: 195320.
doi: 10.1103/PhysRevB.85.195320 |
[13] |
Wan X G, Turner A M, Vishwanath A, et al. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates[J]. Physical Review B, 2011, 83(20): 205101.
doi: 10.1103/PhysRevB.83.205101 |
[14] |
Weng H, Fang C, Fang Z, et al. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides[J]. Physical Review X, 2015, 5: 011029.
doi: 10.1103/PhysRevX.5.011029 |
[15] |
Lü B Q, Weng H M, Fu B B, et al. Experimental discovery of Weyl semimetal TaAs[J]. Physical Review X, 2015, 5: 031013.
doi: 10.1103/PhysRevX.5.031013 |
[16] |
Liu D F, Liang A J, Liu E K, et al. Magnetic Weyl semimetal phase in a Kagome crystal[J]. Science, 2019, 365(6459): 1282-1285.
doi: 10.1126/science.aav2873 pmid: 31604236 |
[17] |
Wieder B J, Kim Y, Rappe A M, et al. Double Dirac semimetals in three dimensions[J]. Physical Review Letters, 2016, 116: 186402.
doi: 10.1103/PhysRevLett.116.186402 |
[18] |
Kim Y, Wieder B J, Kane C L, et al. Dirac line nodes in inversion-symmetric crystals[J]. Physical Review Letters, 2015, 115: 036806.
doi: 10.1103/PhysRevLett.115.036806 |
[19] |
Yu R, Weng H, Fang Z, et al. Topological node-line semimetal and Dirac semimetal state in antiperovskite Cu$_3$PdN[J]. Physical Review Letters, 2015, 115: 036807.
doi: 10.1103/PhysRevLett.115.036807 |
[20] |
Fang C, Weng H, Dai X, et al. Topological nodal line semimetals[J]. Chin Phys B, 2016, 25(11): 117106.
doi: 10.1088/1674-1056/25/11/117106 |
[21] |
Wieder B J. Threes company[J]. Nature Physics, 2018, 14(4): 329-330.
doi: 10.1038/s41567-017-0032-5 |
[22] | Bradlyn B, Cano J, Wang Z, et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals[J]. Science, 2016, 353(6299): 558. |
[23] |
Jeon S, Zhou B B, Gyenis A, et al. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd$_3$As$_2$[J]. Nature Materials, 2014, 13(9): 851-856.
doi: 10.1038/nmat4023 |
[24] |
Feng J, Pang Y, Wu D, et al. Large linear magnetoresistance in Dirac semimetal Cd$_3$As$_2$ with Fermi surfaces close to the Dirac points[J]. Physical Review B, 2015, 92(8): 081306.
doi: 10.1103/PhysRevB.92.081306 |
[25] | Zhang C, Xu S Y, Belopolski I, et al. Observation of the Adler-Bell-Jackiw chiral anomaly in a Weyl semimetal[EB/OL]. (2015-03-09)[2022-03-15]. http//arxiv.org/abs/150302630v1. |
[26] |
Huang X, Zhao L, Long Y, et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs[J]. Physical Review X, 2015, 5(3): 031023.
doi: 10.1103/PhysRevX.5.031023 |
[27] |
Wang Y, Liu E, Liu H, et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-Ⅱ Weyl semimetal WTe$_2$[J]. Nature Communications, 2016, 7: 13142.
doi: 10.1038/ncomms13142 |
[28] |
Rajamathi C R, Gupta U, Kumar N, et al. Weyl semimetals as hydrogen evolution catalysts[J]. Advanced Materials, 2017, 29(19): 1606202.
doi: 10.1002/adma.201606202 |
[29] |
Li J, Ma H, Xie Q, et al. Topological quantum catalyst: Dirac nodal line states and a potential electrocatalyst of hydrogen evolution in the TiSi family[J]. Science China Materials, 2018, 61(1): 23-39.
doi: 10.1007/s40843-017-9178-4 |
[30] |
Nayak C, Simon S H, Stern A, et al. Non-Abelian anyons and topological quantum computation[J]. Reviews of Modern Physics, 2008, 80(3): 1083-1159.
doi: 10.1103/RevModPhys.80.1083 |
[31] |
Yang S A. Dirac and Weyl materials: fundamental aspects and some spintronics applications[J]. SPIN, 2016, 6(2): 1640003.
doi: 10.1142/S2010324716400038 |
[32] |
Xu G, Weng H, Wang Z, et al. Chern semimetal and the quantized anomalous Hall effect in HgCr$_2$Se$_4$[J]. Physical Review Letters, 2011, 107(18): 186806.
doi: 10.1103/PhysRevLett.107.186806 |
[33] |
Xu Q, Liu E, Shi W, et al. Topological surface Fermi arcs in the magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$[J]. Physical Review B, 2018, 97(23): 235416.
doi: 10.1103/PhysRevB.97.235416 |
[34] |
Huang S M, Xu S Y, Belopolski I, et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class[J]. Nature Communications, 2015, 6: 7373.
doi: 10.1038/ncomms8373 |
[35] |
Lü B Q, Muff S, Qian T, et al. Observation of Fermi-arc spin texture in TaAs[J]. Physical Review Letters, 2015, 115(21): 217601.
doi: 10.1103/PhysRevLett.115.217601 |
[36] |
Xu S Y, Belopolski I, Alidoust N, et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs[J]. Science, 2015, 349(6248): 613-617.
doi: 10.1126/science.aaa9297 |
[37] |
Yang L X, Liu Z K, Sun Y, et al. Weyl semimetal phase in the non-centrosymmetric compound TaAs[J]. Nature Physics, 2015, 11(9): 728-732.
doi: 10.1038/NPHYS3425 |
[38] |
Liu Q, Zunger A. Predicted realization of cubic Dirac Fermion in quasi-one-dimensional transition-metal mono-chalcogenides[J]. Physical Review X, 2017, 7: 021019.
doi: 10.1103/PhysRevX.7.021019 |
[39] |
Liu Z K, Zhou B, Zhang Y, et al. Discovery of a three-dimensional topological Dirac semimetal, Na$_3$Bi[J]. Science, 2014, 343(6173): 864-867.
doi: 10.1126/science.1245085 pmid: 24436183 |
[40] |
Liu Z K, Jiang J, Zhou B, et al. A stable three-dimensional topological Dirac semimetal Cd$_3$As$_2$[J]. Nature Materials, 2014, 13(7): 677-681.
doi: 10.1038/nmat3990 pmid: 24859642 |
[41] |
Wang Z, Weng H, Wu Q, et al. Three-dimensional Dirac semimetal and quantum transport in Cd$_3$As$_2$[J]. Physical Review B, 2013, 88: 125427.
doi: 10.1103/PhysRevB.88.125427 |
[42] |
Yang B J, Nagaosa N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology[J]. Nature Communications, 2014, 5: 4898.
doi: 10.1038/ncomms5898 |
[43] |
Gibson Q D, Schoop L M, Muechler L, et al. Three-dimensional Dirac semimetals: design principles and predictions of new materials[J]. Physical Review B, 2015, 91: 205128.
doi: 10.1103/PhysRevB.91.205128 |
[44] |
Du Y, Tang F, Wang D, et al. CaTe: a new topological node-line and Dirac semimetal[J]. npj Quantum Materials, 2017, 2(1): 3.
doi: 10.1038/s41535-016-0005-4 |
[45] |
Mutch J, Chen W C, Went P, et al. Evidence for a strain tuned topological phase transition in ZrTe$_5$[J]. Science Advances, 2019, 5(8): eaav9771.
doi: 10.1126/sciadv.aav9771 |
[46] |
Li G, Yan B, Wang Z, et al. Topological Dirac semimetal phase in Pd and Pt oxides[J]. Physical Review B, 2017, 95: 035102.
doi: 10.1103/PhysRevB.95.035102 |
[47] |
Wu Q, Piveteau C, Song Z, et al. MgTa$_2$N$_3$: a reference Dirac semimetal[J]. Physical Review B, 2018, 98: 081115.
doi: 10.1103/PhysRevB.98.081115 |
[48] |
Bradlyn B, Elcoro L, Cano J, et al. Topological quantum chemistry[J]. Nature, 2017, 547(7663): 298-305.
doi: 10.1038/nature23268 |
[49] |
Vergniory M G, Elcoro L, Felser C, et al. A complete catalogue of high-quality topological materials[J]. Nature, 2019, 566(7745): 480-485.
doi: 10.1038/s41586-019-0954-4 |
[50] |
Zhang T, Jiang Y, Song Z, et al. Catalogue of topological electronic materials[J]. Nature, 2019, 566(7745): 475-479.
doi: 10.1038/s41586-019-0944-6 |
[51] |
Tang F, Po H C, Vishwanath A, et al. Comprehensive search for topological materials using symmetry indicators[J]. Nature, 2019, 566(7745): 486-489.
doi: 10.1038/s41586-019-0937-5 |
[52] |
Gao Z, Hua M, Zhang H, et al. Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetr[J]. Physical Review B, 2016, 93: 205109.
doi: 10.1103/PhysRevB.93.205109 |
[53] |
Cao W, Tang P, Xu Y, et al. Dirac semimetal phase in hexagonal LiZnBi[J]. Physical Review B, 2017, 96(11): 115203.
doi: 10.1103/PhysRevB.96.115203 |
[54] |
Chen C, Wang S S, Liu L, et al. Ternary wurtzite CaAgBi materials family: a playground for essential and accidental, type-Ⅰ and type-Ⅱ Dirac fermions[J]. Phys Rev Materials, 2017, 1: 044201.
doi: 10.1103/PhysRevMaterials.1.044201 |
[55] |
Zyuzin A A, Zyuzin V A. Chiral electromagnetic waves in Weyl semimetals[J]. Physical Review B, 2015, 92(11): 115310.
doi: 10.1103/PhysRevB.92.115310 |
[56] |
Xia Y, Cai X, Li G. Multitype Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system[J]. Physical Review B, 2020, 102: 041201.
doi: 10.1103/PhysRevB.102.041201 |
[57] |
Fang C, Gilbert M J, Dai X, et al. Multi-Weyl topological semimetals stabilized by point group symmetry[J]. Physical Review Letters, 2012, 108: 266802.
doi: 10.1103/PhysRevLett.108.266802 |
[58] |
Gao H, Strockoz J, Frakulla M, et al. Noncentrosymmetric topological Dirac semimetals in three dimensions[J]. Physical Review B, 2021, 103(20): 205151.
doi: 10.1103/PhysRevB.103.205151 |
[59] |
Arpe R, Müller-Buschbaum H. Zur Kenntnis von Bi$_2$PdO$_4$/about Bi$_2$PdO$_4$[J]. Zeitschrift für Naturforschung B, 1976, 31(12): 1708-1709.
doi: 10.1515/znb-1976-1228 |
[60] |
He J, Hao S, Xia Y, et al. Bi$_2$PdO$_4$: a promising thermoelectric oxide with high power factor and low lattice thermal conductivity[J]. Chem Mater, 2017, 29(6): 2529-2534.
doi: 10.1021/acs.chemmater.6b04230 |
[61] |
Soluyanov A A, Gresch D, Wang Z, et al. Type-Ⅱ Weyl semimetals[J]. Nature, 2015, 527(7579): 495-498.
doi: 10.1038/nature15768 |
[62] |
Huang H, Zhou S, Duan W. Type-Ⅱ Dirac fermions in the PtSe$_2$ class of transition metal dichalcogenides[J]. Physical Review B, 2016, 94: 121117.
doi: 10.1103/PhysRevB.94.121117 |
[63] |
Chang T R, Xu S Y, Sanchez D S, et al. Type-Ⅱ aymmetry-protected topological Dirac semimetals[J]. Physical Review Letters, 2017, 119: 026404.
doi: 10.1103/PhysRevLett.119.026404 |
[64] |
Merlo F, Pani M, Fornasini M L. RMX compounds formed by alkaline earths, europium and ytterbium Ⅲ. Ternary phases with M$\equiv$Mg, Hg and X$\equiv$Si, Ge, Sn, Pb[J]. Journal of Alloys and Compounds, 1993, 196(1): 145-148.
doi: 10.1016/0925-8388(93)90585-B |
[65] |
Bennett J W, Garrity K F, Rabe K M, et al. Hexagonal $ABC$ semiconductors as ferroelectrics[J]. Physical Review Letters, 2012, 109(16): 167602.
doi: 10.1103/PhysRevLett.109.167602 |
[66] |
Narayan A. Class of Rashba ferroelectrics in hexagonal semiconductors[J]. Physical Review B, 2015, 92(22): 220101.
doi: 10.1103/PhysRevB.92.220101 |
[67] |
Monserrat B, Bennett J W, Rabe K M, et al. Antiferroelectric topological insulators in orthorhombic $A$MgBi compounds ($A$=Li, Na, K)[J]. Physical Review Letters, 2017, 119(3): 036802.
doi: 10.1103/PhysRevLett.119.036802 |
[68] |
Di Sante D, Barone P, Stroppa A, et al. Intertwined Rashba, Dirac, and Weyl fermions in hexagonal hyperferroelectrics[J]. Physical Review Letters, 2016, 117(7): 076401.
doi: 10.1103/PhysRevLett.117.076401 |
[69] |
Ruan J, Jian S K, Zhang D, et al. Ideal Weyl semimetals in the chalcopyrites CuTlSe$_2$, AgTlTe$_2$, AuTlTe$_2$, and ZnPbAs$_2$[J]. Physical Review Letters, 2016, 116(22): 226801.
doi: 10.1103/PhysRevLett.116.226801 |
[70] |
Gao H, Kim Y, Venderbos J W F, et al. Dirac-Weyl semimetal: coexistence of Dirac and Weyl fermions in polar hexagonal $ABC$ crystals[J]. Physical Review Letters, 2018, 121: 106404.
doi: 10.1103/PhysRevLett.121.106404 |
[71] |
Schroeder G, Schuster H U. LiZnSb, eine weitere ternare phase mit Wurtzitgerust/LiZnSb, an additional ternary phase with a wurtzit-type lattice[J]. Zeitschrift für Naturforschung B, 1975, 30(11/12): 978-979.
doi: 10.1515/znb-1975-11-1234 |
[72] |
Tiburtius C, Schuster H U. LiBeSb and LiZnBi, ternary compounds with a wurtzite-type lattice[J]. Z Naturforsch, 1978, 33(1): 35-38.
doi: 10.1515/znb-1978-0108 |
[73] |
Zhang H, Huang W, Mei J W, et al. Influences of spin-orbit coupling on Fermi surfaces and Dirac cones in ferroelectriclike polar metals[J]. Physical Review B, 2019, 99: 195154.
doi: 10.1103/PhysRevB.99.195154 |
[74] |
Huang H, Jin K H, Liu F. Alloy engineering of topological semimetal phase transition in MgTa$_{2-x}$Nb$_x$N$_3$[J]. Physical Review Letters, 2018, 120: 136403.
doi: 10.1103/PhysRevLett.120.136403 |
[75] |
Fang Z, Gao H, Venderbos J W F, et al. Ideal near-Dirac triple-point semimetal in Ⅲ-Ⅴ semiconductor alloys[J]. Physical Review B, 2020, 101: 125202.
doi: 10.1103/PhysRevB.101.125202 |
[76] | Zhang J, Chang C Z, Zhang Z, et al. Band structure engineering in (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ ternary topological insulators[J]. Nature Communications, 2011, 2(1): 1-6. |
[77] |
Sato T, Segawa K, Kosaka K, et al. Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator[J]. Nature Physics, 2011, 7(11): 840-844.
doi: 10.1038/nphys2058 |
[78] |
Mostofi A A, Yates J R, Lee Y S, et al. Wannier90: a tool for obtaining maximally-localised wannier functions[J]. Comput Phys Commun, 2008, 178(9): 685-699.
doi: 10.1016/j.cpc.2007.11.016 |
[79] | Wu L, Patankar S, Morimoto T, et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals[J]. Nat Phys, 2017, 13(4): 350-355. |
[80] |
Ma J, Gu Q, Liu Y, et al. Nonlinear photoresponse of type-Ⅱ Weyl semimetals[J]. Nature Materials, 2019, 18(5): 476-481.
doi: 10.1038/s41563-019-0296-5 |
[81] |
Sodemann I, Fu L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials[J]. Physical Review Letters, 2015, 115: 216806.
doi: 10.1103/PhysRevLett.115.216806 |
[82] |
Ma Q, Xu S Y, Shen H, et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions[J]. Nature, 2019, 565(7739): 337-342.
doi: 10.1038/s41586-018-0807-6 |
[1] | 李一航, 肖斌, 唐宇超, 刘馥, 王小梦, 刘轶. 尖晶石氧化物能量和结构的第一性原理计算和机器学习[J]. 上海大学学报(自然科学版), 2021, 27(4): 635-649. |
[2] | 袁莹, 李惟驹, 陈竞哲. 单分子二极管整流特性的第一性原理计算[J]. 上海大学学报(自然科学版), 2021, 27(2): 298-306. |
[3] | 游洋, 杜婉, 李惟驹, 陈竞哲. 基于机器学习方法的二维材料带隙预测[J]. 上海大学学报(自然科学版), 2020, 26(5): 824-833. |
[4] | 李晖, 辛子华. 硼氮掺杂C64-石墨炔材料几何及电子结构第一性原理[J]. 上海大学学报(自然科学版), 2020, 26(5): 816-823. |
[5] | 马帅, 李拥华, 高裕博. Ca 对氧化铝晶界处氧空位扩散的活化机理[J]. 上海大学学报(自然科学版), 2020, 26(4): 562-569. |
[6] | 钱利江, 李惟驹, 张义邴, 陈竞哲. STM 分子结中电流非对称性的定性分析[J]. 上海大学学报(自然科学版), 2020, 26(2): 197-206. |
[7] | 梁成功, 张云波. 自旋轨道耦合二维费米气体的热力学性质[J]. 上海大学学报(自然科学版), 2019, 25(6): 914-923. |
[8] | 杨凯, 裴宁, 王琦鑫, 蔡兰兰. 一种新型磁性生物贴片的性质[J]. 上海大学学报(自然科学版), 2019, 25(5): 767-775. |
[9] | 金山, 靳锡联, 焦正, 孟醒. Ca$_{\textbf{0.5}}$Ba$_{\textbf{0.5}}$MnO$_{\textbf{3}}$多铁性的第一性原理[J]. 上海大学学报(自然科学版), 2019, 25(4): 590-596. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||