本文采用第一性原理计算方法研究了锯齿型延伸对扶手椅边缘三角形石墨烯量子点磁性的物理影响。研究结果表明，当向三角形石墨烯量子点的扶手椅边缘添加两个或三个锯齿型延伸时，大部分修饰结构的基态都符合Lieb定理，但少部分修饰结构违背了Lieb定理，后者可以归因于最高占据分子轨道和最低未占据分子轨道之间较小的能量差。此外，我们还发现添加锯齿型延伸后，一部分修饰结构的基态仍然保持低自旋态，而另一部分结构的基态从低自旋态变成了高自旋态。我们的发现对于调控具有扶手椅边缘石墨烯量子点的磁学特性具有重要的意义。
Using first-principles calculations, we investigate the effect of zigzag extensions on the magnetic properties of triangular graphene quantum dot with armchair edges. The results show that when two or three zigzag extensions are added to the armchair edges of triangular graphene quantum dot, the ground states of most modified structures conform to the Lieb’s theorem, while some structures violate the Lieb’s theorem, which can be attributed to the small energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition, we find that the ground states of partial modified structures remain in the low-spin state, while the others change from a low-spin state to a high-spin state. Our findings have important im-plications for manipulating the magnetism of graphene quantum dot with armchair edges.
1Faculty of Physics and Electronic Technology, Hubei University, Wuhan Hubei
2School of Materials Science and Engineering, Hubei University, Wuhan Hubei
Received: Apr. 25th, 2022; accepted: May 23rd, 2022; published: May 31st, 2022
ABSTRACT
Using first-principles calculations, we investigate the effect of zigzag extensions on the magnetic properties of triangular graphene quantum dot with armchair edges. The results show that when two or three zigzag extensions are added to the armchair edges of triangular graphene quantum dot, the ground states of most modified structures conform to the Lieb’s theorem, while some structures violate the Lieb’s theorem, which can be attributed to the small energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition, we find that the ground states of partial modified structures remain in the low-spin state, while the others change from a low-spin state to a high-spin state. Our findings have important implications for manipulating the magnetism of graphene quantum dot with armchair edges.
The structure name, structure, energy difference between doublet and quartet states, the ground state and Lieb’s theorem state of eleven trimers with S = 3/
The structure name, structure, energy difference between doublet and quartet states, the ground state and Lieb’s theorem state of eleven trimers with S = 1/
刘希超,方世超,高 云,黄忠兵. 锯齿型延伸修饰扶手椅边缘三角形石墨烯量子点磁性的第一性原理研究First-Principles Study on the Magnetism of Triangular Graphene Quantum Dot with Armchair Edges Decorated by Zigzag Extensions[J]. 凝聚态物理学进展, 2022, 11(02): 38-48. https://doi.org/10.12677/CMP.2022.112005
ReferencesWeiss, N.O., Zhou, H., Liao, L., Liu, Y., Jiang, S., Huang, Y. and Duan, X. (2012) Graphene: An Emerging Electronic Material. Advanced Materials, 24, 5782-5825. <br>https://doi.org/10.1002/adma.201201482Katsnelson, M.I., Novoselov, K.S. and Geim, A.K. (2006) Chiral Tunnelling and the Klein Paradox in Graphene. Nature Physics, 2, 620-625. <br>https://doi.org/10.1038/nphys384Zhang, Y., Tan, Y.W., Stormer, H.L. and Kim, P. (2005) Experi-mental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene. Nature, 438, 201-204. <br>https://doi.org/10.1038/nature04235Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Elias, D.C., Jaszczak, J.A. and Geim, A.K. (2008) Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer. Physical Re-view Letters, 100, Article ID: 016602.
<br>https://doi.org/10.1103/PhysRevLett.100.016602Lee, C., Wei, X., Kysar, J.W. and Hone, J. (2008) Meas-urement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. Science, 321, 385-388. <br>https://doi.org/10.1126/science.1157996Hu, J., Ruan, X. and Chen, Y.P. (2009) Thermal Conductivity and Thermal Rectification in Graphene Nanoribbons: A Molecular Dynamics Study. Nano Letters, 9, 2730-2735. <br>https://doi.org/10.1021/nl901231sEvans, W.J., Hu, L. and Keblinski, P. (2010) Thermal Conductivity of Graphene Ribbons from Equilibrium Molecular Dynamics: Effect of Ribbon Width, Edge Roughness, and Hydrogen Termination. Applied Physics Letters, 96, Article ID: 203112. <br>https://doi.org/10.1063/1.3435465Cao, Y., Fatemi, V., Demir, A., Fang, S., Tomarken, S.L., Luo, J.Y., et al. (2018) Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices. Nature, 556, 80-84. <br>https://doi.org/10.1038/nature26154Cao, Y., Fatemi, V., Fang, S., Watanabe, K., Taniguchi, T., Kaxiras, E. and Jarillo-Herrero, P. (2018) Unconventional Supercon-ductivity in Magic-Angle Graphene Superlattices. Nature, 556, 43-50. <br>https://doi.org/10.1038/nature26160Cao, Y., Park, J.M., Watanabe, K., Taniguchi, T. and Jarillo-Herrero, P. (2021) Pauli-Limit Violation and Re-Entrant Superconductivity in Moiré Graphene. Nature, 595, 526-531. <br>https://doi.org/10.1038/s41586-021-03685-yBacon, M., Bradley, S.J. and Nann, T. (2014) Graphene Quan-tum Dots. Particle & Particle Systems Characterization, 31, 415-428. <br>https://doi.org/10.1002/ppsc.201300252Jiang, D.E., Sumpter, B.G. and Dai, S. (2007) First Principles Study of Magnetism in Nanographenes. The Journal of Chemical Physics, 127, Article ID: 124703. <br>https://doi.org/10.1063/1.2770722Ezawa, M. (2007) Metallic Graphene Nanodisks: Electronic and Magnetic Properties. Physical Review B, 76, Article ID: 245415. <br>https://doi.org/10.1103/PhysRevB.76.245415Fernán-dez-Rossier, J. and Palacios, J.J. (2007) Magnetism in Graphene Nanoislands. Physical Review Letters, 99, Article ID: 177204. <br>https://doi.org/10.1103/PhysRevLett.99.177204Osman, W., Abdelsalam, H., Ali, M., Teleb, N.H., Yahia, I.S., Ibrahim, M.A. and Zhang, Q. (2021) Electronic and Magnetic Properties of Graphene Quantum Dots Doped with Alkali Metals. Journal of Materials Research and Technology, 11, 1517-1533. <br>https://doi.org/10.1016/j.jmrt.2021.01.119Rizzo, D.J., Veber, G., Jiang, J., McCurdy, R., Cao, T., Bronner, C., et al. (2020) Inducing Metallicity in Graphene Nanoribbons via Zero-Mode Superlattices. Science, 369, 1597-1603. <br>https://doi.org/10.1126/science.aay3588Sun, Q., Yao, X., Groning, O., Eimre, K., Pignedoli, C.A., Müllen, K., et al. (2020) Coupled Spin States in Armchair Graphene Nanoribbons with Asymmetric zigzag Edge Extensions. Nano Letters, 20, 6429-6436.
<br>https://doi.org/10.1021/acs.nanolett.0c02077Lieb, E.H. (1989) Two Theorems on the Hubbard Model. Phys-ical Review Letters, 62, 1201-1204.
<br>https://doi.org/10.1103/PhysRevLett.62.1201Perdew, J.P., Burke, K. and Ernzerhof, M. (1996) Generalized Gradient Approximation Made Simple. Physical Review Letters, 77, 3865-3868. <br>https://doi.org/10.1103/PhysRevLett.77.3865Delley, B. (2000) From Molecules to Solids with the DMol 3 Approach. The Journal of Chemical Physics, 113, 7756-7764. <br>https://doi.org/10.1063/1.1316015Kimura, T., Goto, T., Shintani, H., Ishizaka, K., Arima, T.H. and Tokura, Y. (2003) Magnetic Control of Ferroelectric Polarization. Nature, 426, 55-58. <br>https://doi.org/10.1038/nature02018Blöchl, P.E. (1994) Projector Augmented-Wave Method. Physical Review B, 50, 17953-17979.
<br>https://doi.org/10.1103/PhysRevB.50.17953Qu, Z., Zhang, S., Liu, C. and Malrieu, J.P. (2011) Communica-tion: A Dramatic Transition from Nonferromagnet to Ferromagnet in Finite Fused-Azulene Chain. The Journal of Chem-ical Physics, 134, Article ID: 021101.
<br>https://doi.org/10.1063/1.3533363Yang, H., Huang, Z., Gao, Y. and Lin, H. (2017) Room Temperature Mul-tiferroicity in Hydrogenated Triapentafulvalene and Pentaheptafulvalene Oligomers. Journal of Chemical Physics, 146, Article ID: 084306.
<br>https://doi.org/10.1063/1.4976993
