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The controllable band gap of single-walled carbon nanotube (SWCNT) has become a research hotspot. This study introduces a torsional model that involves each rotating carbon atom along the axial direction of SWCNT, and a detailed description of the model creation process. Two guidelines for constructing the model are proposed, and the self-consistency of the torsion model is established through first-principles density functional theory. Initially, the band gap map of SWCNTs under torsion is present. As the twist strength increases, the band gap of SWCNT undergoes several phase transitions, including semiconductor-metal transition and metal-semiconductor transition. Moreover, we investigate the variations in the average bond length, average bond angle, and diameter of SWCNT under torsion. Furthermore, this work turns to the analysis of carbon atomic energy statistics, revealing distinct energy changes for different types of single-walled carbon nanotubes under identical torsion intensity. The findings shed light on the controllable band gap of SWCNTs, offering a theoretical foundation for the development of nanoelectronic devices and microintegrated circuits utilizing single-walled carbon nanotubes. In conclusion, this research presents a novel approach for exploring the controllable band gap of single-walled carbon nanotube through torsional manipulation. Theoretical insights into the behavior of SWCNTs under torsion provide valuable contributions to the field and pave the way for potential applications in nanoelectronics and microintegrated circuits.
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Keywords:
- single-walled carbon nanotubes /
- first principles /
- torsional deformation /
- band gap
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图 1 碳纳米管结构示意图
Figure 1. Schematic diagram of carbon nanotube structure.
图 2 6种单壁碳纳米管的最小扭转周期角示意图 (a) 90°; (b) 72°; (c) 60°; (d) 45°; (e) 36°; (f) 30°
Figure 2. Schematic diagram of the minimum torsional period angle of the six SWCNTs: (a) 90°; (b) 72°; (c) 60°; (d) 45°; (e) 36°; (f) 30°.
图 3 (8, 0) 单壁碳纳米管扭转后模型图 (扭转强度 = 3.52 (°)/Å)
Figure 3. The (8, 0) SWCNT model diagram after torsion (Torsional strength = 3.52 (°)/Å).
图 4 扭转 (8, 0) 单壁碳纳米管过程示意图
Figure 4. Schematic diagram of the torsional process for (8, 0) SWCNT.
图 5 扭转 (5, 5) 单壁碳纳米管后能带图与电荷局域密度图
Figure 5. Change in the band structure and electron localization function of (5, 5) SWCNT.
图 6 单壁碳纳米管带隙变化图 (a) 扶手椅型单壁碳纳米管; (b) 3类碳纳米带中本征单壁碳纳米管; (c) 锯齿型单壁碳纳米管
Figure 6. Band gap variation chart of SWCNTs: (a) Armchair SWCNTs; (b) SWCNTs in three types of carbon nanoribbons; (c) zigzag SWCNTs.
图 7 单壁碳纳米管直径变化图 (a) 扶手椅型单壁碳纳米管直径随扭转强度的变化; (b) 3类碳纳米带中本征单壁碳纳米管直径变化; (c)锯齿型单壁碳纳米管直径随扭转强度的变化
Figure 7. Diameter variation chart of SWCNTs: (a) Relationship between diameter and torsional strength for armchair SWCNTs; (b) diameter of SWCNTs in three types of carbon nanoribbons; (c) relationship between diameter and torsional strength for zigzag SWCNTs.
图 8 单壁碳纳米管键长与键角随扭转强度的变化 (a)键长; (b)键角
Figure 8. Variation of carbon bond length and carbon bond angle in SWCNTs: (a) Bond length; (b) bond angle.
图 9 扭转单壁碳纳米管的能量变化图
Figure 9. Relationship between energy and torsional strength for SWCNTs.
图 A1 扭转SWCNTs后能带图
Figure A1. Change in the band structure of SWCNTs.
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[1] Iijima S 1991 Nature 354 56
Google Scholar
[2] Iijima S, Ichihashi T 1993 Nature 364 737
Google Scholar
[3] Treacy M, Ebbesen T W, Gibson J M 1996 Nature 381 680
Google Scholar
[4] Krishnan A, Dujardin E, Ebbesen T W, Yianilos P N, Treacy M M J 1998 Phys. Rev. B 58 14013
Google Scholar
[5] Hernandez E, Goze C, Bernier P, Rubio A 1999 Appl. Phys. A Mater. 68 287
Google Scholar
[6] Takakura A, Beppu K, Nishihara T, Fukui A, Kozeki T, Namazu T, Miyauchi Y, Itami K 2019 Nat. Commun. 10 3040
Google Scholar
[7] Fischer J E, Johnson A T 1999 Curr. Opin. Solid St. M. 4 28
Google Scholar
[8] Jia J, Shi D, Feng X, Chen G 2014 Carbon 76 54
Google Scholar
[9] Ezawa M 2006 Phys. Rev. B 73 045432
Google Scholar
[10] Karimkhani H, Vahed H 2022 Optik 254 168633
Google Scholar
[11] Tombler T W, Zhou C W, Alexseyev L, Kong J, Dai H J, Lei L, Jayanthi C S, Tang M J, Wu S Y 2000 Nature 405 769
Google Scholar
[12] Jia J M, Ju S P, Shi D N, Lin K F 2012 J. Appl. Phys. 111 013704
Google Scholar
[13] Yang L, Han J 2000 Phys. Rev. Lett. 85 154
Google Scholar
[14] Moon S, Song W, Kim N, Lee J S, Na P S, Lee S G, Park J, Jung M H, Lee H W, Kang K H, Lee C J, Kim J 2007 Nanotechnology 18 235201
Google Scholar
[15] Mazzoni M, Chacham H 2000 Appl. Phys. Lett. 76 1561
Google Scholar
[16] Peng S, Cho K 2002 J. Appl. Mech T. ASME 69 451
Google Scholar
[17] Shtogun Y V, Woods L M 2009 Carbon 47 3252
Google Scholar
[18] Shtogun Y V, Woods L M 2009 J. Phys. Chem. C 113 4792
Google Scholar
[19] Kang Y J, Kim Y H, Chang K J 2009 Curr. Appl. Phys. 9 S7
Google Scholar
[20] Berd M, Moussi K, Aouabdia Y, Benchallal L, Chahi G, Kahouadji B 2021 Chem. Phys. Lett. 781 138988
Google Scholar
[21] Kato K, Koretsune T, Saito S 2012 Phys. Rev. B 85 115448
Google Scholar
[22] Wang Q 2008 Carbon 46 1172
Google Scholar
[23] Wang Y, Wang X X, Ni X G 2004 Model. Simul. Mater. Sc. 12 1099
Google Scholar
[24] Kang J W, Kim K S, Park S Y, Kim H, Hwang H J, Choi Y G 2010 J. Comput. Theor. Nanos. 7 2317
Google Scholar
[25] Melker A I, Zhaldybin A I 2007 Nanomeeting (Minsk Byelarus: May 22–25) p233
[26] Dian R H, Lei Z, Ya F D, Cheng L L 2017 Mater. Res. Express 4 105004
Google Scholar
[27] Ansari R, Mirnezhad M, Rouhi H 2015 Acta. Mech. 226 2955
Google Scholar
[28] Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864
Google Scholar
[29] Kohn W, Sham L 1965 Phys. Rev. 140 A1133
Google Scholar
[30] Langreth D C, Mehl M J 1983 Phys. Rev. B 28 1809
Google Scholar
[31] Blochl P E 1994 Phys. Rev. B 50 17953
Google Scholar
[32] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[33] Kinoshita Y, Ohno N 2010 Phys. Rev. B 82 085433
Google Scholar
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