Study of transition metal dichalcogenides/chromium trihalides van der Waals heterostructure by band unfolding method

Deng Lin-Mei; Si Jun-Shan; Wu Xu-Cai; Zhang Wei-Bing

doi:10.7498/aps.71.20220326

Abstract

The transition metal dichalcogenides MX₂/Chromium Trihalides CrX₃ van der Waals heterostructures can control the valley polarization of of MX₂ effectively, which makes them possess promising potential applications in valleytronics. In the present work, the stacking order and electronic structure of MoSe₂/CrI₃, MoSe₂/CrBr₃ and WS₂/CrBr₃ are investigated based on the first-principle calculation and k-projection band unfolding method. The underlying mechanism of valley splitting is also explored. The stacking energy surfaces are calculated and the stable stacking configurations are determined. The effects of the breaking of time-symmetry and spatial-symmetry on electronic structure are also revealed. Because of the orbital hybridization, the conduction band of heterostructure becomes complicated and the valence band maximum changes drastically. It is thus difficult to compare the electronic structure of vdW heterostructure with that of free-standing MX₂ directly. Through the unfolding energy band, the electronic structure change of MX₂ induced by CrX₃ is revealed clearly, and the valley splitting of MX₂ is obtained quantitatively. Moreover, the interlayer distance and strain are found to be able to tune the valley splitting effectively. When the interlayer distance reduces to 2.6 Å, the valley splitting of MoSe₂/CrI₃ is enhanced to 10.713 meV with the increase of AB stacking, which is 8.8 times as large as the value of equilibrium structure. This work breaks through the limit of the complex electronic structure in supercell, providing an important reference for studying other magnetic vdW heterostructure.

Keywords:

Authors and contacts

Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, School of Physics and Electronic Sciences, Changsha University of Science and Technology, Changsha 410114, China

Corresponding author: Zhang Wei-Bing, zhangwb@csust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874092), the Fok Ying-Tong Education Foundation, China (Grant No. 161005), and the Science Fund for Distinguished Young Scholars of Hunan Province, China (Grant No. 2021JJ10039)

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References

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Cited By

图 1 MoSe₂/CrI₃异质结的结构和布里渊区　(a), (b)对应于AB和AB' 堆垛的MoSe₂/CrI₃结构; (c)大六边形和小六边形分别对应MoSe₂原胞布里渊区和异质结布里渊区

Figure 1. Structure and Brillouin zone of MoSe₂/CrI₃ heterostructure: (a), (b) MoSe₂/CrI₃ heterostructure with the AB and AB' stacking, respectively; (c) the large and small hexagon correspond to the MoSe₂ protocell Brillouin region and the heterojunction Brillouin region, respectively

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图 2 (a) MoSe₂/CrI_3, (b) MoSe₂/CrBr₃和(c) WS₂/CrBr₃体系的堆垛势能面图

Figure 2. Stacking potential energy surfaces of (a) MoSe₂/CrI₃, (b) MoSe₂/CrBr₃ and (c) WS₂/CrBr₃

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图 3 MoSe₂/CrI₃的自旋电荷密度分布 ((a)和(b))以及层间${1}/{d} $随堆垛的变化图(c)

Figure 3. The spin density distribution ((a) and (b)) of MoSe₂/CrI₃, and the variation of $ {1}/{d} $ with different stacking (c)

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图 4 MoSe₂, CrI₃和AB堆垛 MoSe₂/CrI₃的能带图　(a)—(c)分别对应单层MoSe₂不考虑自旋极化且不考虑自旋轨道耦合时、考虑自旋极化以及考虑自旋极化和自旋轨道耦合时的能带; (d)—(f)对应CrI₃的情况; (g)—(i)对应 AB堆垛 MoSe₂/CrI₃

Figure 4. Band structure of MoSe₂, CrI₃ and AB-stacking MoSe₂/CrI₃ vdW heterostructure: (a)–(c) The energy band obtained without spin polarization and spin orbital coupling, with spin polarization and with spin polarization and spin orbital coupling; (d)–(f) the case of CrI₃; (g)–(i) the corresponding energy band of AB-stacking MoSe₂/CrI₃

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图 5 磁性异质结轨道分辨的能带图　(a)—(d)分别是MoSe₂/CrI₃中Mo-d, Se-p, Cr-d, I-p的轨道投影能带图; (e)—(h)分别是MoSe₂/CrBr₃中Mo-d, Se-p, Cr-d, Br-p的轨道投影能带图; (i)—(l)对应于WS₂/CrBr₃体系

Figure 5. Orbital resolved energy band of magnetic heterostructure: (a)–(d) The Mo-d, Se-p, Cr-d, I-p resolved energy band of MoSe₂/CrI₃; (e)–(h) the correspongding energy band of MoSe₂/CrBr₃; (i)–(l) the correspongding energy band of WS₂/CrBr₃

DownLoad: Full-Size Img PowerPoint

图 6 (a)自旋劈裂和谷劈裂的定义; (b), (c) AB堆垛的MoSe₂/CrI₃中MoSe₂在$1 \times1 $的布里渊区反折叠能带与单独存在的MoSe₂比较图, 其中子图为K₊/K_–附近的价带和导带情况; (d)—(f)${{AB}}'$堆垛 MoSe₂/CrI₃, AB堆垛 MoSe₂/CrBr₃ 和WS₂/CrBr₃的反折叠能带图

Figure 6. (a) The definition of spin splitting and valley splitting; (b), (c) the comparison between the unfolding band of MoSe₂ in AB-stacking MoSe₂/CrI₃ heterostructure and free-standing MoSe₂, the VBM (b) and CBM (c); (d)–(f) the unfolding energy band of ${{AB}}'$ stacking MoSe₂/CrI₃, AB stacking MoSe₂/CrBr₃ and WS₂/${\rm{CrBr}}_3 $, respectively

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图 7 AB堆垛 MoSe₂/CrI₃能谷劈裂和能量随层间距和应力的变化　(a), (b)能谷劈裂和能量随层间距的变化关系; (c), (d) AB堆垛MoSe₂/CrI₃的能谷劈裂和能量随应变的变化关系

Figure 7. The change of valley splitting and energy with interlayer distance and strain of MoSe₂/CrI₃: (a), (b) The change of valley splitting and energy with interlayer distance; (c), (d) change with strain

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表 1 三种异质结不同堆垛的自旋和能谷劈裂(单位: meV)

Table 1. The spin splitting and valley splitting in unit of meV of three vdW heterostructure with different stacking order.

异质结	堆垛	a/Å	失配率/%	$\varDelta_{{\rm{spin}}}^{{\rm{VBM}}/K_+}$	$\varDelta_{{\rm{spin}}}^{{\rm{VBM}}/K_-}$	$\varDelta_{{\rm{spin}}}^{{\rm{CBM}}/K_+}$	$\varDelta_{{\rm{spin}}}^{{\rm{CBM}}/K_-}$	$\varDelta_{{\rm{val}}}^{{\rm{VBM}}}$	$\varDelta_{{\rm{val}}}^{{\rm{CBM}}}$
MoSe₂/CrI₃	AB	6.65	4.9%	184.64	187.057	22.629	19.14	1.215	1.756
MoSe₂/CrI₃	AB'	6.65		186.02	184.8	29.598	25.192	0.596	0.94
MoSe₂/CrBr₃	AB	6.65	3.1%	183.756	187.815	26.08	18.043	1.852	3.887
MoSe₂/CrBr₃	AB'	6.65		185.474	184.022	25.11	18.237	2.028	3.096
WS₂/CrBr₃	AB	6.4	0.7%	434.922	436.345	24.459	27.308	0.666	0.756
WS₂/CrBr₃	AB'	6.4		435.474	435.392	25.019	24.823	0.27	0.439

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[1]	Xu X, Yao W, Xiao D, Heinz T F 2014 Nat. Phys. 10 343 Google Scholar
[2]	Schaibley J R, Yu H, Clark G, Rivera P, Ross J S, Seyler K L, Yao W, Xu X 2016 Nat. Rev. Mater. 1 16055 Google Scholar
[3]	Liu G B, Xiao D, Yao Y, Xu X, Yao W 2015 Chem. Soc. Rev. 44 2643 Google Scholar
[4]	Chu J, Wang Y, Wang X, Hu K, Rao G, Gong C, Wu C, Hong H, Wang X, Liu K, Gao C, Xiong J 2021 Adv. Mater. 33 2004469 Google Scholar
[5]	Du L, Hasan T, Castellanos-Gomez A, Liu G B, Yao Y, Lau C N, Sun Z 2021 Nat. Rev. Phys. 3 193 Google Scholar
[6]	孙真昊, 管鸿明, 付雷, 沈波, 唐宁 2021 物理学报 70 027302 Google Scholar Sun Z H, Guan H M, Fu L, Shen B, Tang N 2021 Acta Phys. Sin. 70 027302 Google Scholar
[7]	Zhao S, Li X, Dong B, Wang H, Wang H, Zhang Y, Han Z, Zhang H 2021 Rep. Prog. Phys. 84 026401 Google Scholar
[8]	Vitale S A, Nezich D, Varghese J O, Kim P, Gedik N, Jarillo-Herrero P, Xiao D, Rothschild M 2018 Small 14 1801483 Google Scholar
[9]	Lu H Z, Yao W, Xiao D, Shen S Q 2013 Phys. Rev. Lett. 110 016806 Google Scholar
[10]	Xiao D, Yao W, Niu Q 2007 Phys. Rev. Lett. 99 236809 Google Scholar
[11]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[12]	Yao W, Xiao D, Niu Q 2008 Phys. Rev. B 77 235406 Google Scholar
[13]	Zeng H, Dai J, Yao W, Xiao D, Cui X 2012 Nat. Nanotechnol. 7 490 Google Scholar
[14]	Cao T, Wang G, Han W, Ye H, Zhu C, Shi J, Niu Q, Tan P, Wang E, Liu B, Feng J 2012 Nat. Commun. 3 887 Google Scholar
[15]	Cheng Y C, Zhang Q Y, Schwingenschlögl U 2014 Phys. Rev. B 89 155429 Google Scholar
[16]	Li Y, Ludwig J, Low T, Chernikov A, Cui X, Arefe G, Kim Y D, van der Zande A M, Rigosi A, Hill H M, Kim S H, Hone J, Li Z, Smirnov D, Heinz T F 2014 Phys. Rev. Lett. 113 266804 Google Scholar
[17]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormányos A, Zólyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[18]	Aivazian G, Gong Z, Jones A M, Chu R L, Yan J, Mandrus D G, Zhang C, Cobden D, Yao W, Xu X 2015 Nat. Phys. 11 148 Google Scholar
[19]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[20]	Stier A V, McCreary K M, Jonker B T, Kono J, Crooker S A 2016 Nat. Commun. 7 10643 Google Scholar
[21]	Qi J, Li X, Niu Q, Feng J 2015 Phys. Rev. B 92 121403 Google Scholar
[22]	Norden T, Zhao C, Zhang P, Sabirianov R, Petrou A, Zeng H 2019 Nat. Commun. 10 4163 Google Scholar
[23]	Zhang W B, Qu Q, Zhu P, Lam C H 2015 J. Mater. Chem. C 3 12457 Google Scholar
[24]	Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P, Xu X 2017 Nature 546 270 Google Scholar
[25]	Gong C, Li L, Li Z, Ji H, Stern A, Xia Y, Cao T, Bao W, Wang C, Wang Y, Qiu Z Q, Cava R J, Louie S G, Xia J, Zhang X 2017 Nature 546 265 Google Scholar
[26]	Seyler K L, Zhong D, Huang B, Linpeng X, Wilson N P, Taniguchi T, Watanabe K, Yao W, Xiao D, McGuire M A, Fu K M C, Xu X 2018 Nano Lett. 18 3823 Google Scholar
[27]	Zhong D, Seyler K L, Linpeng X, Cheng R, Sivadas N, Huang B, Schmidgall E, Taniguchi T, Watanabe K, McGuire M A, Yao W, Xiao D, Fu K M C, Xu X 2017 Sci. Adv. 3 e1603113 Google Scholar
[28]	Hu T, Zhao G, Gao H, Wu Y, Hong J, Stroppa A, Ren W 2020 Phys. Rev. B 101 125401 Google Scholar
[29]	Zhang H, Yang W, Ning Y, Xu X 2020 Phys. Rev. B 101 205404 Google Scholar
[30]	Zhang Z, Ni X, Huang H, Hu L, Liu F 2019 Phys. Rev. B 99 115441 Google Scholar
[31]	Kresse G, Furthmüller J 1996 Comp. Mater. Sci. 6 15 Google Scholar
[32]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[33]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[34]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758 Google Scholar
[35]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[36]	Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505 Google Scholar
[37]	Grimme S 2006 J. Comp. Chem. 27 1787 Google Scholar
[38]	Chen M X, Weinert M 2014 Nano Lett. 14 5189 Google Scholar
[39]	Chen M, Weinert M 2018 Phys. Rev. B 98 245421 Google Scholar
[40]	Chen M X, Chen W, Zhang Z, Weinert M 2017 Phys. Rev. B 96 245111 Google Scholar
[41]	Si J S, Li H, He B G, Cheng Z P, Zhang W B 2021 J. Phys. Chem. C 125 7314 Google Scholar
[42]	Zollner K, Faria Junior P E, Fabian J 2019 Phys. Rev. B 100 085128 Google Scholar
[43]	Ciorciaro L, Kroner M, Watanabe K, Taniguchi T, Imamoglu A 2020 Phys. Rev. Lett. 124 197401 Google Scholar
[44]	Xie J, Jia L, Shi H, Yang D, Si M 2018 JPN J. Appl. Phys. 58 010906 Google Scholar
[45]	Ge M, Wang H, Wu J, Si C, Zhang J, Zhang S 2022 NPJ Comp. Mater. 8 32 Google Scholar

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