Theoretical study on regulatory mechanism of dielectric environmental screening effects on binding energy of two-dimensional In<i>X </i>(<i>X</i> = Se, Te) exciton

Duan Xiu-Ming; Yi Zhi-Jun

doi:10.7498/aps.72.20230528

Abstract

The calculations using GW method based on Green’s function show that two-dimensional monolayer InSe and InTe have desired electronic band gaps for absorbing visible light, high electron mobilities, and suitable electronic band structures for water splitting, and that the spin orbit coupling (SOC) leads to an indirect-to -direct band gap transition for monolayer InTe. On the basis of quasi-particle energy levels, the calculations via solving Bethe-Salpter equation (BSE) show that the exciton binding energy of isolated monolayer InSe and InTe are much higher than that of the dissociation energy of exciton at room temperature. On the other hand, two-dimensional semiconductors in laboratory are often supported by substrates for mechanical stability, and the atomic thickness values of two-dimensional semiconductors are also various in different experiments. These factors will change the dielectric environments of two-dimensional semiconductor, and the further calculations show that the exciton binding energy of InSe and InTe decrease with the increase of the thickness of InSe and InTe and also the thickness of their substrates, also revealing that the exciton binding energy can be accurately controlled by engineering the thickness of two-dimensional semiconductors and the substrates. Our results provide important theoretical basis for accurately controlling the binding energy of two-dimensional InSe and InTe.

Keywords:

Authors and contacts

School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China

Corresponding author: Yi Zhi-Jun, 5216@cumt.edu.cn

Funds: Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 2019XKQYMS15).

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References

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Cited By

图 1 (a) 孤立单层InX (X = Se/Te) 几何结构; (b) InX原胞的第一布里渊区以及高对称位置K点分布

Figure 1. (a) Geometric structure of isolated monolayer InX (X = Se/Te); (b) the first Brillouin zone and high-symmetry K point distributions of primitive unit cell for InX.

DownLoad: Full-Size Img PowerPoint

图 2 孤立单层InSe (a), (b) 和InTe (c), (d) 的能带结构(左)和原子投影分态密度(右)

Figure 2. The band structures (left) and atom projected density of states (right) of isolated monolayer InSe (a), (b) and InTe (c), (d).

DownLoad: Full-Size Img PowerPoint

图 3 (a) 基于PBE和GW方法得到的孤立单层InSe和InTe带边能级排列示意图; (b) 准粒子能级, 光学带隙以及激子结合能示意图

Figure 3. (a) The band edge alignments of isolated monolayer InSe and InTe based on PBE and GW method; (b) quasi-particle energy level, optical band gap and schematic diagram of exciton binding energy.

DownLoad: Full-Size Img PowerPoint

图 4 单层InSe (a), (b) 和单层InTe (c), (d)分别沿x和z方向的光学吸收谱

Figure 4. The absorption spectrum of monolayer InSe (a), (b) and monolayer InTe (c), (d) along x and z polarization directions.

DownLoad: Full-Size Img PowerPoint

图 5 InSe (a)和InTe (b)的激子结合能随自身原子层数量的变化关系

Figure 5. The relationship diagrams of exciton binding energies of InSe and InTe with the variation of their self-atomic layer numbers.

DownLoad: Full-Size Img PowerPoint

图 6 单层InSe/InTe和环境之间的结构示意图

Figure 6. The structural diagram between monolayer InSe/InTe and environment.

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图 7 单层InSe (a) 和InTe (b) 的激子结合能随h-BN原子层数量的变化关系

Figure 7. The relationship diagrams of exciton binding energies of monolayer InSe and InTe with the variation of number of h-BN atomic layers.

DownLoad: Full-Size Img PowerPoint

图 B1 InSe和InTe沿a (图中方向1)和b (图中方向2)两个方向导带边和价带边抛物线拟合

Figure B1. Fitted results of conduction band edge and valence band edge of InSe and InTe along both a (direction 1 in the figure) and b (direction 2 in the figure).

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表 1 InSe和InTe导带和价带带边电子和空穴的有效质量

Table 1. The effective masses of electrons and holes of conduction and valence band edges for InSe and InTe.

n (InSe/InTe) 1 5 10 20 30

E_b (InSe)/eV 0.419 0.350 0.342 0.338 0.337
E_b (InTe)/eV 0.294 0.244 0.237 0.235 0.234

DownLoad: CSV

表 2 不同原子层厚度InSe以及InTe放置在50个原子层厚度h-BN衬底上时的激子结合能

Table 2. The exciton binding energies for different atomic thicknesses of InSe and InTe on h-BN substrate with 50 atomic layer thickness.

n (InSe/InTe) 1 5 10 20 30

E_b (InSe)/eV 0.419 0.350 0.342 0.338 0.337
E_b (InTe)/eV 0.294 0.244 0.237 0.235 0.234

DownLoad: CSV

map

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[2]	Bandurin D A, Tyurnina A V, Yu G L, Mishchenko A, Zolyomi V, Morozov S V, Kumar R K, Gorbachev R V, Kudrynskyi Z R, Pezzini S, Kovalyuk Z D, Zeitler U, Novoselov K S, Patanè A, Eaves L, Grigorieva I V, Fal’ko V I, Geim A K, Cao Y 2017 Nat. Nanotechnol. 12 223 Google Scholar
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[4]	Feng W, Zhou X, Tian W Q, Zheng W, Hu P 2015 Phys. Chem. Chem. Phys. 17 3653 Google Scholar
[5]	Mudd G W, Svatek S A, Hague L, Makarovsky O, Kudrynskyi Z R, Mellor C J, Beton P H, Eaves L, Novoselov K S, Kovalyuk Z D, Vdovin E E, Marsden A J, Wilson N R, Patane A 2015 Adv. Mater. 27 3760 Google Scholar
[6]	张芳, 贾利群, 孙现亭, 戴宪起, 黄奇祥, 李伟 2020 69 157302 Google Scholar Zhang F, Jia L Q, Sun X T, Dai X Q, Huang Q X, Li W 2020 Acta Phys. Sin. 69 157302 Google Scholar
[7]	Mudd G W, Svatek S A, Ren T, Patanè A, Makarovsky O, Eaves L, Beton P H, Kovalyuk Z D, Lashkarev G V, Kudrynskyi Z R, Dmitriev A I 2013 Adv. Mater. 25 5714 Google Scholar
[8]	Henck H, Pierucci D, Zribi J, Bisti F, Papalazarou E, Girard J C, Chaste J., Bertran F, Fèvre P L, Sirotti F, Perfetti L, Giorgetti C, Shukla A, Rault J E, Ouerghi A 2019 Phys. Rev. Mater. 3 034004 Google Scholar
[9]	Lei S, Ge L, Najmaei S, George A, Kappera R, Lou J, Chhowalla M, Yamaguchi H, Gupta G, Vajtai R, Mohite A D, Ajayan P M 2014 ACS Nano 8 1263 Google Scholar
[10]	Zhou J, Shi J, Zeng Q, Chen Y, Niu L, Liu F, Yu T, Suenaga Kazu, Liu X, Lin J, Liu Z 2018 2D Mater. 5 025019 Google Scholar
[11]	Sucharitakul S, Goble N J, Kumar U R, Sankar R, Bogorad Z A, Chou F, Chen Y T, Gao Xuan P A 2015 Nano Lett. 156 3815 Google Scholar
[12]	Lauth J, Gorris F E S, Khoshkhoo M S, Chassé T, Friedrich W, Lebedeva V, Meyer A, Klinke C, Kornowski A, Scheele M, Weller H 2016 Chem. Mater. 28 1728 Google Scholar
[13]	范人杰, 江先燕, 陶奇睿, 梅期才, 唐颖菲, 陈志权, 苏贤礼, 唐新峰 2021 70 137102 Google Scholar Fan R J, Jiang X Y, Tao Q R, Mei Q C, Tang Y F, Chen Z Q, Su X L, Tang X F 2021 Acta Phys. Sin. 70 137102 Google Scholar
[14]	Pal S, Bose D N 1996 Solid State Commun. 97 725 Google Scholar
[15]	Zólyomi V, Drummond N D, Falko V I 2014 Phys. Rev. B 89 205416 Google Scholar
[16]	Jain M, Chelikowsky J R, Louie S, G, 2011 Phys. Rev. Lett. 107 216806 Google Scholar
[17]	Ma H, Feng J, Jin F, Wei M, Liu C, Ma Y 2018 Nanoscale 10 15624 Google Scholar
[18]	Yi Z, Wu M, Pang Y, Jia R, Xu R R 2021 Appl. Surf. Sci. 567 150842 Google Scholar
[19]	Klots A R, Newaz A K M, Wang B, Prasai D, Krzyzanowska H, Lin Junhao, Caudel D, Ghimire N J, Yan J, Ivanov B L, Velizhanin K A, Burger A, Mandrus D G, Tolk N H, Pantelides S T, Bolotin K I 2014 Sci. Rep. 4 6608 Google Scholar
[20]	Thygesen K S 2017 2D Mater. 4 022004 Google Scholar
[21]	Jiang Y, Chen S, Zheng W, Zheng B, Pan A 2021 Light-Sci. Appl. 10 72 Google Scholar
[22]	Qiu, D. Y. Jornada F da H, Louie S G 2013 Phys. Rev. Lett. 111 216805 Google Scholar
[23]	Komsa, H P, Krasheninnikov A V 2012 Phys. Rev. B 86 241201(R Google Scholar
[24]	Shi H L, Pan H, Zhang Y W, Yakobson B I 2013 Phys. Rev. B 87 155304 Google Scholar
[25]	Qiu D Y, Felipe H da J, Louie, S G 2017 Nano Lett. 17 4706 Google Scholar
[26]	Raja A, Chaves A, Yu J, Arefe G, Hill Heather M, Rigosi Albert F, Berkelbach Timothy C, Nagler P, Schüller C, Korn T, Nuckolls C, Hone J, Brus Louis E, Heinz Tony F, Reichman David R, Chernikov A 2017 Nat. Commun. 8 15251 Google Scholar
[27]	Ugeda Miguel M, Bradley Aaron J, Shi S F, Jornada Felipe H da, Zhang Y, Qiu Diana Y, Ruan W, Mo S K, Hussain Z, Shen Z X, Wang F, Louie Steven G, Crommie Michael F 2014 Nat. Mater. 13 1091 Google Scholar
[28]	Enkovaara J, Rostgaard C, Mortensen J J, Chen J, Dułak M, Ferrighi L, Gavnholt J, Glinsvad C, Haikola V, Hansen H A, Kristoffersen H H, Kuisma M, Larsen A H, Lehtovaara L, Ljungberg M, Lopez-Acevedo O, Moses P G, Ojanen J, Olsen T, Petzold V, Romero N A, Stausholm-Møller J, Strange M, Tritsaris G A, Vanin M, Walter M, Hammer B, Häkkinen H, Madsen G K H, Nieminen R M, Nørskov J K, Puska M, Rantala T T, Schiøtz J, Thygesen K S, Jacobsen K W 2010 J. Phys. Condens. Mater. 22 253202 Google Scholar
[29]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[30]	Perdew J P, Burke K 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[31]	Babaie-Kafaki S, Aminifard Z 2019 Numer. Algorithms 82 1345 Google Scholar
[32]	Hüser F, Olsen T, Thygesen K S 2013 Phys. Rev. B 87 235132 Google Scholar
[33]	Yan J, Mortensen J J, Jacobsen K W, Thygesen K S 2011 Phys. Rev. B 83 245122 Google Scholar
[34]	Yi Z, Ma Y, Zheng Y, Duan Y, Li H 2019 Adv. Mater. Interfaces 6 1801175 Google Scholar
[35]	Rozzi C A, Varsano D, Marini A, Gross E K U, Rubio A 2006 Phys. Rev. B 73 205119 Google Scholar
[36]	Smail-Beigi S 2006 Phys. Rev. B 73 233103 Google Scholar
[37]	Rasmussen F A, Schmidt P S, Winther K T, Thygesen K S 2016 Phys. Rev. B 94 155406 Google Scholar
[38]	Olsen T 2016 Phys. Rev. B 94 235106 Google Scholar
[39]	Tiago M L, Ismail-Beigi S, Louie S G 2004 Phys. Rev. B 69 125212 Google Scholar
[40]	Klimeš J, Kaltak M, Kresse G 2014 Phys. Rev. B 90 075125 Google Scholar
[41]	Haastrup S, Strange Mikke, Pandey M, Deilmann T, Schmidt Per S, Hinsche Nicki F, Gjerding Morten N, Torelli D, Larsen Peter M, Riis-Jensen Anders C 2018 2D Mater. 5 042002 Google Scholar
[42]	Onida G, Reining L and Rubio A 2002 Rev. Mod. Phys. 74 601 Google Scholar
[43]	隋国民, 严桂俊, 杨光, 张宝, 冯亚青 2022 71 208801 Google Scholar Sui G M, Yan G J, Yang G, Zhang B, Feng Y Q 2022 Acta Phys. Sin. 71 208801 Google Scholar
[44]	Andersen K, Latini S, Thygesen K S 2015 Nano Lett. 15 4616 Google Scholar
[45]	Pandey T, Parker David S, Lindsay L 2017 Nanotechnology 28 455706 Google Scholar
[46]	Pang Y, Wu M, Zhang J, Yi Z 2021 J. Phys. Chem. C 125 3027 Google Scholar

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Theoretical study on regulatory mechanism of dielectric environmental screening effects on binding energy of two-dimensional InX (X = Se, Te) exciton

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n (InSe/InTe)	1	5	10	20	30
E_b (InSe)/eV	0.419	0.350	0.342	0.338	0.337
E_b (InTe)/eV	0.294	0.244	0.237	0.235	0.234

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Theoretical study on regulatory mechanism of dielectric environmental screening effects on binding energy of two-dimensional InX (X = Se, Te) exciton

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Corresponding author: Yi Zhi-Jun, 5216@cumt.edu.cn

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