-
二维拓扑材料因其无耗散的边界态成为低功耗电子器件的理想候选材料.作为典型的二维体系，理论预言石墨烯在自旋-轨道耦合相互作用下存在量子自旋霍尔效应，但其能隙仅为微电子伏量级，这严重制约了其在实际器件中的应用.本文基于第一性原理计算，研究了ⅣB族4d过渡金属元素Zr晶格掺杂石墨烯形成的Zr2C12体系在应变调控下的电子结构和拓扑性质.声子谱计算表明，处于自由状态的Zr2C12具有良好的动力学稳定性.电子结构研究表明，在不考虑自旋-轨道耦合相互作用时，处于自由状态的Zr2C12呈现出狄拉克半金属相，其狄拉克点处的费米速度比石墨烯的略低.考虑自旋-轨道耦合相互作用后，狄拉克点打开了4.09 meV的能隙，该能隙比未掺杂的石墨烯大三个数量级.通过宇称计算确认Z2拓扑不变量为1，体系转变为二维拓扑绝缘体.在-5%至6%的大范围应变内，体系始终保持动力学稳定，且仍为Z2=1的拓扑绝缘体相，展现出鲁棒的拓扑性质.其能隙大小随拉伸应变的增加而增加，当施加6%拉伸应变时，能隙达到最大值8.41 meV.计算发现在6%拉伸应变下体系有非平庸的拓扑边界态，这进一步验证了应变调控下体系的非平庸拓扑性质.本研究拓展了过渡金属掺杂石墨烯体系的研究范畴，为低能耗电子器件以及量子计算和通信等领域的进一步研究提供了良好的材料平台.Two-dimensional topological materials are ideal candidates for low-dissipation electronic devices due to their non-dissipative edge states. As a typical two-dimensional system, graphene is theoretically predicted to exhibit the quantum spin Hall effect under the spin-orbit coupling interaction. However, the band gap in graphene is only in the order of micro-electron volt, which seriously restricts its practical applications. In this work, based on the first-principles calculations, we investigate the electronic structures and topological properties of strained Zr2C12, which is formed by substitutional doping graphene with the group ⅣB 4d transition metal Zr. The phonon spectrum calculation confirms that the freestanding Zr2C12 exhibits excellent dynamic stability. When the spin-orbit coupling is excluded, the bands cross linearly at the K point near the Fermi level, indicating the Dirac semimetal phase of freestanding Zr2C12. The Fermi velocity of the Dirac point is 0.677 × 106 m/s, which is approximately two-thirds of that in graphene (~ 1.00 × 106 m/s). When the spin-orbit coupling is considered, the Dirac point opens a gap of 4.09 meV, which is three orders of magnitude higher than that of undoped graphene. The parity analysis reveals that the Z2 topological invariant of the freestanding Zr2C12 is 1, indicating the system transits into a two-dimensional topological insulator. We also study the properties of Zr2C12 under strain regulation. The calculation results show that the system remains dynamically stable over a wide strain range of -5% to 6%. When the spin-orbit coupling is absent, the conduction band energy at the Γ point continuously rises with increasing strain, and the system maintains the Dirac semimetal phase. After including the spin-orbit coupling, the system remains the nontrivial topological insulator phase over a wide strain range of -5% to 6%, showing robust topological properties. The band gap at the Dirac point first decreases and then increases with increasing strain. When applying -1.6% compression strain, this band gap decreases to the minimum value of 0.059 meV. When the strain further increases to 6%, this gap increases to the maximum value of 8.41 meV. The edge states calculations of Zr2C12 under 6% expansion strain show that the gapless edge states connect the conduction bands and the valence bands, which further verify the non-trivial topological properties of this system under strain regulation. This study expands the research on transition-metal-doped graphene systems, providing a good material platform for further study of low-dissipation electronic devices and quantum computing and communication.
-
Keywords:
- graphene /
- doping /
- strain /
- Dirac semimetal /
- quantum spin Hall insulator
-
[1] Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett.107 076802
[2] Yuan D W, Hu Y F, Yang Y M, Zhang W 2021 Chin. Phys. Lett. 38 117301
[3] Weng H M, Ranjbar A, Liang Y Y, et al. 2015 Phys. Rev. B 92 075436
[4] Zhang W, Wu Q S, Yazyev O V, Weng H M, Guo Z X, Cheng W D, Chai G L 2018 Phys. Rev. B 98 115411
[5] Yuan D W, Yue C M, Hu Y F, Zhang W 2024 Chin. Phys. Lett. 41 037304
[6] Chen J, Qin H J, Yang F, et al. 2010 Phys. Rev. Lett. 105 176602
[7] Li Z G, Zhang S, Song F L 2015 Acta. Phys. Sin. 64 097202 (in Chinese) [李兆国，张帅，宋凤麒 2015 物理学报 64 097202]
[8] Qu D X, Hor Y S, Xiong J, Cava R J, Ong N P 2010 Science 329 821
[9] Yuan D W, Pi H Q, Jiang Y, et al. 2023 Sci. China-Phys. Mech. Astron. 66 247211
[10] Weng H M, Ranjbar A, Liang Y Y, et al. 2015 Phys. Rev. B 92 075436
[11] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[12] Novoselov K S, Geim A K, Morozov S V, et al. 2005 Nature 438 197
[13] Zhang Y, Tan Y, Stormer H L, Kim P 2005 Nature 438 201
[14] Kane C L, Mele E J 2005 Phys. Rev. Lett 95 226801
[15] Kane C L, Mele E J 2005 Phys. Rev. Lett 95 146802
[16] Yao Y G, Ye F, Qi X L, Zhang S C, Fang Z 2007 Phys. Rev. B 75 041401(R)
[17] Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J 2009 Phys. Rev. B 80 235431
[18] Sichau J, Prada M, Anlauf T, et al. 2019 Phys. Rev. Lett. 122 046403
[19] Zhang Y Q, Liang Y M, Zhou J X 2014 Acta Chim. Sinica 72 367 (in Chinese) [张芸秋，梁勇明，周建新 2014 化学学报 72 367]
[20] Chan K T, Neaton J B, Cohen M L 2008 Phys. Rev. B 77 235430
[21] Katsnelson M I, Guinea F, Geim A K 2009 Phys. Rev. B 79 195426
[22] Uchoa B, Kotov V N, Peres N M R, Castro Neto A H 2008 Phys. Rev. Lett. 101 026805
[23] Uchoa B, Castro Neto A H 2007 Phys. Rev. Lett. 98 146801
[24] Hu Y F, Yue C M, Yuan D W, et al. 2022 Sci. China-Phys. Mech. Astron. 65 297211
[25] Yuan D W, Zhang S, Chen J, Weng H M, Zhang W 2025 Phys. Rev. B 112 085122
[26] Martins T B, Miwa R H, da Silva A J R, Fazzio A 2007 Phys. Rev. Lett. 98 196803
[27] Wu M, Cao C, Jiang J Z 2010 Nanotechnology 21 505202
[28] Hu Y F, Shao D X, Yuan D W, Zhang W 2025 Phys. Scr. 100 035913
[29] Panchakarla L S, Subrahmanyam K S, Saha S K, et al. 2009 Adv. Mater. 21 4726
[30] Wang H, Zhou Y, Wu D, Liao L, Zhao S L, Peng H L, Liu Z F 2013 Small 9 1316
[31] Jin Z, Yao J, Kittrell C, Tour J M 2011 ACS Nano 5 4112
[32] Some S, Kim J, Lee K, Kulkarni A, Yoon Y, Lee S M, Kim T, Lee H 2012 Adv. Mater. 24 5481
[33] Zhou L, Zhou L S, Yang M M, et al. 2013 Small 9 1388
[34] Duplock E J, Scheffler M, Lindan P J D 2004 Phys. Rev. Lett. 92 225502
[35] Balog R, Jørgensen B, Nilsson L, et al. 2010 Nat. Mater. 9 315
[36] Son J, Lee S, Kim S J, et al. 2016 Nat. Commun. 7 13261
[37] Weeks C, Hu J, Alicea J, Franz M, Wu R 2011 Phys. Rev. X 1 021001
[38] Calleja F, Ochoa H, Garnic M, et al. 2015 Nat. Phys. 11 43
[39] Dyck O, Zhang L Z, Yoon M, et al. 2021 Carbon 173 205
[40] Villarreal R, Zarkua Z, Kretschmer S, et al. 2024 ACS Nano 18 17815
[41] Li W Q, Amiinu I S, Zhang B W, et al. 2018 Carbon 139, 1144
[42] Chen Z D, Hu Y F, Zhu Z M, Zhang W 2020 New J. Phys. 22 093055
[43] Zhang W, Luo K F, Chen Z D, Zhu Z M, Yu R, Fang C, Weng H M 2019 npj Comput. Mater. 5 105
[44] Wu M S, Xu B, Liu G, Ou Yang C Y 2012 Acta. Phys. Sin. 61 227102 (in Chinese) [吴木生，徐波，刘刚，欧阳楚英 2012 物理学报 61 227102]
[45] Xu S L, Hu Y F, Yuan D W, Chen W, Zhang W 2023 Acta. Phys. Sin. 72 127102 (in Chinese) [徐诗琳，胡岳芳，袁丹文，陈巍，张薇 2023 物理学报 72 127102]
[46] Bonaccorso F, Sun Z, Hasan T, Ferrari A C 2010 Nat. Photon. 4 611
[47] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
[48] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
[49] Blöchl P E 1994 Phys. Rev. B 50 17953
[50] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[51] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[52] Togo A, Tanaka I 2015 Scr. Mater. 108 1
[53] Marzari N, Vanderbilt D 1997 Phys. Rev. B 56 12847
[54] Souza I, Marzari N, Vanderbilt D 2001 Phys. Rev. B 65 035109
[55] Wu Q S, Zhang S N, Song H F, Troyer M, Soluyano A A 2018 Comput. Phys. Commun. 224 405
[56] Pauling L 1947 J. Am. Chem. Soc. 69 3
[57] Yu R, Qi X L, Bernevig A, Fang Z, Dai X 2011 Phys. Rev. B 84 075119
[58] Grusdt F, Abanin D, Demler E 2014 Phys. Rev. A 89 043621
计量
- 文章访问数: 39
- PDF下载量: 2
- 被引次数: 0
下载:
