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Chin. Phys. B, 2022, Vol. 31(11): 117303    DOI: 10.1088/1674-1056/ac6b2d

Anisotropic plasmon dispersion and damping in multilayer 8-Pmmn borophene structures

Kejian Liu(刘可鉴)1, Jian Li(李健)1,2,3, Qing-Xu Li(李清旭)1,2, and Jia-Ji Zhu(朱家骥)1,2,3,†
1 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2 Institute for Advanced Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
3 Southwest Center for Theoretical Physics, Chongqing University, Chongqing 401331, China
Abstract  We investigate the collective plasma oscillations theoretically in multilayer 8-Pmmn borophene structures, where the tilted Dirac electrons in spatially separated layers are coupled via the Coulomb interaction. We calculate the energy dispersions and Landau dampings of the multilayer plasmon excitations as a function of the total number of layers, the interlayer separation, and the different orientations. Like multilayer graphene, the plasmon spectrum in multilayer borophene consists of one in-phase optical mode and N - 1 out-of-phase acoustical modes. We show that the plasmon modes possess kinks at the boundary of the interband single-particle continuum and the apparent anisotropic behavior. All the plasmon modes approach the same dispersion at a sufficiently large interlayer spacing in the short-wavelength limit. Especially along specific orientations, the optical mode could touch an energy maximum in the nondamping region, which shows non-monotonous behavior. Our work provides an understanding of the multilayer borophene plasmon and may pave the way for multilayer borophene-based plasmonic devices.
Keywords:  plasmon      8-Pmmn borophene      multilayer      two-dimensional materials  
Received:  02 April 2022      Accepted manuscript online:  28 April 2022
PACS:  73.20.Mf (Collective excitations (including excitons, polarons, plasmons and other charge-density excitations))  
  78.67.Pt (Multilayers; superlattices; photonic structures; metamaterials)  
  73.21.Ac (Multilayers)  
  68.65.-k (Low-dimensional, mesoscopic, nanoscale and other related systems: structure and nonelectronic properties)  
Fund: This work was supported by the Scientific Research Program from Science and Technology Bureau of Chongqing City (Grant No. cstc2020jcyj-msxmX0684), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202000639), and in part by the National Natural Science Foundation of China (Grant No. 12147102).
Corresponding Authors:  Jia-Ji Zhu     E-mail:

Cite this article: 

Kejian Liu(刘可鉴), Jian Li(李健), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥) Anisotropic plasmon dispersion and damping in multilayer 8-Pmmn borophene structures 2022 Chin. Phys. B 31 117303

[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y S, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[2] Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N and Strano M S 2012 Nat. Nanotechnol. 7 699
[3] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805
[4] Chhowalla M, Shin H S, Eda G, Li L J, Loh K P and Zhang H 2013 Nat. Chem. 5 263
[5] Cao T, Wang G, Han W P, Ye H Q, Zhu C R, Shi J R, Niu Q, Tan P H, Wang E G, Liu B L and Feng J 2012 Nat. Commun. 3 887
[6] Coleman J N, Lotya M, O’Neill A, Bergin S D, King P J, Khan U, Young K, Gaucher A, De S, Smith R J, et al. 2011 Science 331 568
[7] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147
[8] Li L K, Yu Y J, Ye G J, Ge Q Q, Ou X D, Wu H, Feng D L, Chen X H and Zhang Y 2014 Nat. Nanotechnol. 9 372
[9] Qiao J S, Kong X H, Hu Z X, Yang F and Ji W 2014 Nat. Commun. 5 4475
[10] Xia F N, Wang H and Jia Y C 2014 Nat. Commun. 5 4458
[11] Tran V, Soklaski R, Liang Y F and Yang L 2014 Phys. Rev. B 89 235319
[12] Rodin A S, Carvalho A and Castro Neto A H 2014 Phys. Rev. Lett. 112 176801
[13] Ding W J, Zhu J B, Wang Z, Gao Y F, Xiao D, Gu Y, Zhang Z Y and Zhu W G 2017 Nat. Commun. 8 14956
[14] Zhu F F, Chen W J, Xu Y, Gao C L, Guan D D, Liu C H, Qian D, Zhang S C and Jia J F 2015 Nat. Mater. 14 1020
[15] Deng J L, Xia B Y, Ma X C, Chen H Q, Shan H, Zhai X F, Li B, Zhao A D, Xu Y, Duan W H, Zhang S C, Wang B and Hou J G 2018 Nat. Mater. 17 1081
[16] Liao M H, Zang Y Y, Guan Z Y, Li H W, Gong Y, Zhu K J, Hu X P, Zhang D, Xu Y, Wang Y Y, He K, Ma X C, Zhang S C and Xue Q K 2018 Nat. Phys. 14 344
[17] Rachel S and Ezawa M 2014 Phys. Rev. B 89 195303
[18] Reis F, Li G, Dudy L, Bauernfeind M, Glass S, Hanke W, Thomale R, Sch?fer J and Claessen R 2017 Science 357 287
[19] Aktürk E, Aktürk O ü and Ciraci S 2016 Phys. Rev. B 94 014115
[20] Feng B J, Sugino O, Liu R Y, Zhang J, Yukawa R, Kawamura M, Iimori T, Kim H, Hasegawa Y, Li H, et al. 2017 Phys. Rev. Lett. 118 096401
[21] Li W B, Kong L L, Chen C Y, Gou J, Sheng S X, Zhang W F, Li H, Chen L, Cheng P and Wu K H 2018 Sci. Bull. 63 282
[22] Wang Y X, Qiu G, Wang R X, Huang S Y, Wang Q X, Liu Y Y, Du Y C, Goddard III W A, Kim M J, Xu X F, Ye P D and Wu W Z 2018 Nat. Electron. 1 228
[23] Ci L J, Song L, Jin C H, Jariwala D, Wu D X, Li Y J, Srivastava A, Wang Z F, Storr K, Balicas L, Liu F and Ajayan P M 2010 Nat. Mater. 9 430
[24] Huang P, Riccardi E, Messelot S, Graef H, Valmorra F, Tignon J, Taniguchi T, Watanabe K, Dhillon S, Pla?ais B, Ferreira R and Mangeney J 2020 Nat. Commun. 11 863
[25] Zhang Y B, Tang T T, Girit C, Hao Z, Martin M C, Zettl A, Crommie M F, Shen Y R and Wang F 2009 Nature 459 820
[26] Wang F, Zhang Y B, Tian C S, Girit C, Zettl A, Crommie M and Shen Y R 2008 Science 320 206
[27] Bonaccorso F, Sun Z P, Hasan T and Ferrari A C 2010 Nat. Photon. 4 611
[28] Baugher B W H, Churchill H O H, Yang Y F and Jarillo-Herrero P 2014 Nat. Nanotechnol. 9 262
[29] Yu W J, Liu Y, Zhou H L, Yin A X, Li Z, Huang Y and Duan X F 2013 Nat. Nanotechnol. 8 952
[30] Zanella I, Guerini S, Fagan S B, Mendes Filho J and Souza Filho A G 2008 Phys. Rev. B 77 073404
[31] Ogawa S, Fukushima S and Shimatani M 2020 Sensors 20 3563
[32] Fang Z Y, Liu Z, Wang Y M, Ajayan P M, Nordlander P and Halas N J 2012 Nano Lett. 12 3808
[33] Luo L B, Zeng L H, Xie C, Yu Y Q, Liang F X, Wu C Y, Wang L and Hu J G 2014 Sci. Rep. 4 3914
[34] Popov V V, Polischuk O V, Davoyan A R, Ryzhii V, Otsuji T and Shur M S 2012 Phys. Rev. B 86 195437
[35] Nikitin A Y, Alonso-Gonzalez P, Vélez S, Mastel S, Centeno A, Pesquera A, Zurutuza A, Casanova F, Hueso L E, Koppens F H L and Hillenbrand R 2016 Nat. Photon. 10 239
[36] Rodrigo D, Limaj O, Janner D, Etezadi D, De Abajo F J G, Pruneri V and Altug H 2015 Science 349 165
[37] Wu L, Chu H S, Koh W S and Li E P 2010 Opt. Express 18 14395
[38] Anker J N, Hall W P, Lyandres O, Shah N C, Zhao J and Van D Richard P 2008 Nat. Mater. 7 442
[39] Ouyang Q L, Zeng S W, Jiang L, Hong L Y, Xu G X, Dinh X Q, Qian J, He S, Qu J, Coquet P and Yong K T 2016 Sci. Rep. 6 28190
[40] Wang C, Huang S Y, Xing Q X, Xie Y G, Song C Y, Wang F J and Yan H G 2020 Nat. Commun. 11 1158
[41] Song C Y, Yuan X, Huang C, Huang S Y, Xing Q X, Wang C, Zhang C, Xie Y G, Lei Y C, Wang F J, Mu L, Zhang J S, Xiu F X and Yan H G 2021 Nat. Commun. 12 386
[42] Jin F P, Roldan R, Katsnelson M I and Yuan S J ′ 2015 Phys. Rev. B 92 115440
[43] Ghosh B, Kumar P, Thakur A, Chauhan Y S, Bhowmick S and Agarwal A 2017 Phys. Rev. B 96 035422
[44] Mannix A J, Zhou X F, Kiraly B, Wood J D, Alducin D, Myers B D, Liu X L, Fisher B L, Santiago U, Guest J R, et al. 2015 Science 350 1513
[45] Feng B J, Zhang J, Zhong Q, Li W B, Li S, Li H, Cheng P, Meng S, Chen L and Wu K H 2016 Nat. Chem. 8 563
[46] Zhou X F, Dong X, Oganov A R, Zhu Q, Tian Y J and Wang H T 2014 Phys. Rev. Lett. 112 085502
[47] Dresselhaus M S, Dresselhaus G and Jorio A 2008 Group theory: application to the physics of condensed matter (Berlin: Springer Press)
[48] Hahn T 2005 International Tables for Crystallography, Volume A (Berlin: Springer Press)
[49] Lopez-Bezanilla A and Littlewood P B 2016 Phys. Rev. B 93 241405
[50] Yuan J H, Yu N N, Xue K H and Miao X S 2017 Rsc. Adv. 7 8654
[51] Sadhukhan K and Agarwal A 2017 Phys. Rev. B 96 035410
[52] Jalali-Mola Z and Jafari S A 2018 Phys. Rev. B 98 195415
[53] Jalali-Mola Z and Jafari S A 2018 Phys. Rev. B 98 235430
[54] Zabolotskiy A D and Lozovik Y E 2016 Phys. Rev. B 94 165403
[55] Zhang S H, Shao D F and Yang W 2019 J. Magn. Magn. Mater. 491 165631
[56] Kong Z, Li J, Zhang Y, Zhang S H and Zhu J J 2021 Nanomaterials 11 1462
[57] Zhu J J, Badalyan S M and Peeters F M 2013 Phys. Rev. B 87 085401
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