General principles to high-throughput constructing two-dimensional carbon allotropes

doi:10.1088/1674-1056/ab6c4b

Abstract We propose general principles to construct two-dimensional (2D) single-atom-thick carbon allotropes. They can be viewed as the generalization of patterning Stone-Walse defects (SWDs) by manipulating bond rotation and of patterning inverse SWDs by adding (or removing) carbon pairs on the pristine graphene, respectively. With these principles, numerous 2D allotropes of carbon can be systematically constructed. Using 20 constructed 2D allotropes as prototypical and benchmark examples, besides nicely reproducing all well-known ones, such as pentaheptites, T-graphene, OPGs, etc, we still discover 13 new allotropes. Their structural, thermodynamic, dynamical, and electronic properties are calculated by means of first-principles calculations. All these allotropes are metastable in energy compared with that of graphene and, except for OPG-A and C3-10-H allotropes, the other phonon spectra of 18 selected allotropes are dynamically stable. In particular, the proposed C3-11 allotrope is energetically favorable than graphene when the temperature is increased up to 1043 K according to the derived free energies. The electronic band structures demonstrate that (i) the C3-8 allotrope is a semiconductor with an indirect DFT band gap of 1.04 eV, (ii) another unusual allotrope is C3-12 which exhibits a highly flat band just crossing the Fermi level, (iii) four allotropes are Dirac semimetals with the appearance of Dirac cones at the Fermi level in the lattices without hexagonal symmetry, and (vi) without the spin-orbit coupling (SOC) effect, the hexagonal C3-11 allotrope exhibits two Dirac cones at K and K' points in its Brillouin zone in similarity with graphene.

Keywords: graphene allotropes phonon spectra semimetal dirac Fermions modeling

Received: 11 December 2019
Revised: 12 January 2020
Accepted manuscript online:

PACS:	73.20.At	(Surface states, band structure, electron density of states)
	63.22.Np	(Layered systems)
	73.22.Pr	(Electronic structure of graphene)

Fund: Project supported by the National Science Fund for Distinguished Young Scholars, China (Grant No. 51725103) and the National Natural Science Foundation of China (Grant No. 51671193). All calculations have been performed on the high-performance computational cluster in the Shenyang National University Science and Technology Park.

Corresponding Authors: Xing-Qiu Chen
E-mail: xingqiu.chen@imr.ac.cn

Cite this article:

Qing Xie(谢庆), Lei Wang(王磊), Jiangxu Li(李江旭), Ronghan Li(李荣汉), Xing-Qiu Chen(陈星秋) General principles to high-throughput constructing two-dimensional carbon allotropes 2020 Chin. Phys. B 29 037306

[1]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[2]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A 2005 Nature 438 197
[3]	Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
[4]	Neto A H C, Guinea F, Peres N M R, Novoselov K S and Geim A K 2005 Rev. Mod. Phys. 81 109
[5]	Grüneis A, Attaccalite C, Rubio A, Vyalikh D V, Molodtsov S L, Fink J, Follath R, Eberhardt W, Büchner B and Pichler T 2009 Phys. Rev. B 80 075431
[6]	Yu H L and Zhai Z Y 2016 Chin. Phys. Lett. 33 117305
[7]	Yin Y H and Niu Y X 2016 Chin. Phys. Lett. 33 57202
[8]	An Y F and Dai Z H 2016 Chin. Phys. Lett. 34 17302
[9]	Song L L, Zhang L Z, Guan Y R, Lu J C, Yan C X and Cai J M 2019 Chin. Phys. B 28 37101
[10]	Zhang X F, Liu Z H, Liu W L, Lu X L, Li Z J, Yu Q K, Shen D W and Xie X M 2019 Chin. Phys. B 28 86103
[11]	Zhang W, Chen K B and Chen Z D 2018 Acta Phys. Sin. 67 237301 (in Chinese)
[12]	Yang Y, Chen S and Li X B 2018 Acta Phys. Sin. 67 237101 (in Chinese)
[13]	Chen R K, Yang C, Jia Y P, Gup L W and Chen J N 2019 Chin. Phys. B 28 117302
[14]	Bolotin K I, Ghahari F, Shulman M D, Stormer H L and Kim P 2009 Nature 462 196
[15]	Bonaccorso F, Colombo L, Yu G, Stoller M, Tozzini V, Ferrari A C, Ruoff R S and Pellegrini V 2015 Science 347 1246501
[16]	Zhu J, Yang D, Yin Z, Yan Q and Zhang H 2015 Small 10 3480
[17]	Raccichini R, Varzi A, Passerini S and Scrosati B 2015 Nat. Mater. 14 271
[18]	Zhong S Y, Shi J, Luo W W and Lei X L 2019 Chin. Phys. B 28 78201
[19]	Lin X F, Zhang Z Y, Yuan Z K, Li J, Xiao X F, Hong W, Chena X D and Yua D S 2016 Chin. Chem. Lett. 27 1259
[20]	Yoon J, Sung H, Lee G, Cho W, Ahn N, Jung H S and Choi M 2017 Energy Environ. Sci. 10 337
[21]	Akinwande D, Petrone N and Hone J 2014 Nat. Commum. 5 5678
[22]	Sato S 2015 Jpn. J. Appl. Phys. 54 040102
[23]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Efthimios K, Ashoori R C, and Jarillo-Herrero P 2018 Nature 556 80
[24]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Efthimios K and Jarillo-Herrero P 2018 Nature 556 43
[25]	Xu F and Zhang L 2019 Chin. Phys. B 28 117403
[26]	Baughman R H and Eckhardt H 1987 J. Chem. Phys. 87 6687
[27]	Malko D, Neiss C, Viñes F and Görling A 2012 Phys. Rev. Lett. 108 086804
[28]	Kim B G and Choi H J 2012 Phys. Rev. B 86 115435
[29]	Ivanovskii A L 2013 Prog. Solid State Chem. 4 1
[30]	Narita N, Nagai S, Suzuki S and Nakao K 1998 Phys. Rev. B 58 11009
[31]	Zhu H Y, Balaban A T, Klein D J and Zivkovic T P 1994 J. Chem. Phys. 101 5281
[32]	Crespi V H, Benedict L X, Cohen M L and Louie S G 1996 Phys. Rev. B 53 R13303
[33]	Tyutyulkov N, Dietz F, Müllen K and Baumgarten M 1997 Chem. Phys. Lett. 272 111
[34]	Terrones H, Terrones M, Hernandez E, Grobert N, Charlier J C and Ajayan P M 2000 Phys. Rev. Lett. 84 1716
[35]	Wang Z, Zhou X F, Zhang X, Zhu Q, Dong H, Zhao M and Oganov A R 2015 Nano Lett. 15 6182
[36]	Lusk M T and Carr L D 2008 Phys. Rev. Lett. 100 175503
[37]	Stone A J and Wales D J 1986 Chem. Phys. Lett. 128 501
[38]	Lusk M T and Carr L D 2009 Carbon 47 2226
[39]	Enyashin A N and Ivanovskii A L 2011 Phys. Status Solodi B 248 1879
[40]	Appelhans D J, Lin Z and Lusk M T 2010 Phys. Rev. B 82 073410
[41]	Hu M, Tian F, Zhao Z, Huang Q, Xu B, Wang L M, Wang H T, Tian Y and He J 2012 Phys. Rev. Lett. 108 225505
[42]	Sharma B R, Manjanath A and Singh A K 2014 Sci. Rep. 4 7164
[43]	Lu H and Li S D 2013 J. Mater. Chem. C 1 3677
[44]	Su C, Jiang H and Feng J 2013 Phys. Rev. B 87 075453
[45]	Wang X Q, Li H D and Wang J T 2013 Phys. Chem. Chem. Phys. 15 2024
[46]	Wang Y, Lv J, Zhu L and Ma Y 2010 Phys. Rev. B 82 094116.
[47]	Glass C W, Oganov A R and Hansen N 2006 Comp. Phys. Comm. 175 713
[48]	Xu L C, Wang R Z, Miao M S, Wei X L, Chen Y P, Yan H, Lau W M, Liu L M and Ma Y M 2014 Nanoscale 6 1113
[49]	Zhang S, Zhou J, Wang Q, Chen X, Kawazoe Y and Jena P 2015 Proc. Natl. Acad. Sci. USA 112 2372
[50]	Ewels C P, Rocquefelte X, Kroto H W, Rayson M J, Briddon P R and Heggie M I 2015 Proc. Natl. Acad. Sci. USA 112 15609
[51]	Bolotin K, Sikes K, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H 2008 Solid State Commun. 146 351
[52]	Wang Z J, Sun Y, Chen X Q, Franchini C, Xu G, Weng H M, Dai X and Fang Z 2012 Phys. Rev. B 85 195320
[53]	Cheng X, Li R, Sun Y, Chen X Q, Li D and Li Y 2014 Phys. Rev. B 89 245201
[54]	Wang Z J, Weng H M, Wu Q S, Dai X and Fang Z 2013 Phys. Rev. B 88 125427
[55]	Li R H, Ma H, Cheng X Y, Wang S L, Li D Z, Zhang Z Y, Li Y Y and Chen X Q 2016 Phys. Rev. Lett. 117 096401
[56]	Takane D, Souma S, Nakayama K, Nakamura T, Oinuma H, Hori K, Horiba K, Kumigashira H, Kimura N, Takahashi T and Sato T 2018 Phys. Rev. B 98 041105
[57]	Li S, Guo Z, Fu D, Pan X C, Wang J, Ran K, Bao S, Ma Z, Cai Z, Wang R, Yu R, Sun J, Song F and Wen J 2018 Science Bulletin 63 535
[58]	Li J, Ullah S, Li R, Liu M, Cao H, Li D, Li Y and Chen X Q 2019 Phys. Rev. B 99 165110
[59]	Li J, Xie Q, Ullah S, Li R, Ma H, Li D, Li Y and Chen X Q 2018 Phys. Rev. B 97 054305
[60]	Li J, Ma H, Xie Q, Feng S, Ullah S, Li R, Dong J, Li D, Li Y and Chen X Q 2018 Sci. China Mater. 61 23
[61]	Xie Q, Li J, Ullah S, Li R, Wang L, Li D, Li Y, Yunoki S and Chen X Q 2019 Phys. Rev. B 99 174306
[62]	Feng B, Fu B, Kasamatsu S, Ito S, Cheng P, Liu C C, Feng Y, Wu S, Mahatha S K, Sheverdyaeva P, Moras P, Arita M, Sugino O, Chiang T C, Shimada K, Miyamoto K, Okuda T, Wu K, Chen L, Yao Y and Matsuda I 2017 Nat. Commun. 8 1007
[63]	Gao L, Sun J T, Lu J C, Li H, Qian K, Zhang S, Zhang Y Y, Qian T, Ding H, Lin X, Du S and Gao H J 2018 Adv. Mater. 30 1707055
[64]	Li J, Xie Q, Liu J, Li R, Liu M, Wang L, Li D, Li Y and Chen X Q 2020 Phys. Rev. B 101 024301
[65]	Li J, Wang L, Liu J, Li R, Zhang Z and Chen X Q 2020 Phys. Rev. B 101 081403(R)
[66]	Ullah S, Wang L, Li J, Li R and Chen X Q 2019 Chin. Phys. B 28 077105
[67]	Liu Z, Lou R, Guo P, Wang Q, Sun S, Li C, Thirupathaiah S, Fedorov A, Shen D, Liu K, Lei H and Wang S 2018 Phys. Rev. X 8 031044
[68]	Chan Y H, Chiu C K, Chou M Y and Schnyder A P 2016 Phys. Rev. B 93 205132
[69]	Xu Q, Yu R, Fang Z, Dai X and Weng H 2017 Phys. Rev. B 95 045136
[70]	Schoop L M, Ali M N, Straßer C, Topp A, Varykhalov A, Marchenko D, Duppel V, Parkin S S P, Lotsch B V and Ast C R 2016 Nat. Commun. 7 11696
[71]	Hu J, Tang Z, Liu J, Zhu Y, Wei J and Mao Z 2017 Phys. Rev. B 96 045127
[72]	Schilling M B, Schoop L M, Lotsch B V, Dressel M and Pronin A V 2017 Phys. Rev. Lett. 119 187401
[73]	Pezzini S, van Delft M R, Schoop L M, Lotsch B V, Carrington A, Katsnelson M I, Hussey N E and Wiedmann S 2018 Nat. Phys. 14 178
[74]	Li R, Li J, Wang L, Liu J, Ma H, Song H F, Li D, Li Y and Chen X Q 2019 Phys. Rev. Lett. 123 136802
[75]	Yan Z, Huang P W and Wang Z 2016 Phys. Rev. B 93 085138
[76]	Rhim J W and Kim Y B 2015 Phys. Rev. B 92 045126
[77]	Huh Y, Moon E G and Kim Y B 2016 Phys. Rev. B 93 035138
[78]	Sankar R, Peramaiyan G, Muthuselvam I P, Butler C J, Dimitri K, Neupane M, Rao G N, Lin M T and Chou F C 2017 Sci. Rep. 7 40603
[79]	Wang J, Deng S, Liu Z and Liu Z 2015 Natl. Sci. Rev. 2 22
[80]	Meille S and Garboczi E J 2001 Modelling Simul. Mater. Sci. Eng. 9 371
[81]	Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[82]	Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[83]	Kresse G and Joubert D 1999 Phys. Rev. B 59 1758
[84]	Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188
[85]	Togo A and Tanaka I 2015 Scr. Mater. 108 1
[86]	Sobhit S, Irais V J, Olivia P and Aldo H R 2018 Phys. Rev. B 97 054108
[87]	Kumar S and Parks D M 2016 Journal of the Mechanics and Physics of Solids 86 19
[88]	Marchenko D, Varykhalov A, Scholz M, Bihlmayer G, Rashba E, Rybkin A, Shikin A and Rader O 2012 Nat. Commum. 3 1232
[89]	Li X, Cai W, An J, Kim S, Nah J, Yang D, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee S K, Colombo L and Ruoff R S 2009 Science 324 1312
[90]	Li G X, Li Y L, Liu H B, Guo Y B, Li Y J and Zhu D B 2010 Chem. Commun. 46 3256
[91]	Maździarz M, Mrozek A, Kuś W and Burczyński T 2018 Materials 11 432
[92]	Babu R and Hiroshi M 2018 Carbon 137 266
[93]	Gaikwad P V 2019 ACS Omega 4 5002
[94]	Dai Z, Jin W, Grady M, Sadowski J T, Dadap J I, Osgood R M and Pohl K 2017 Surface Science 660 16
[95]	Pop E, Varshney V and Roy A K 2012 MRS Bull. 37 1273

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