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Abstract

The transition metal dichalcogenides MX ₂/Chromium Trihalides Cr X ₃van der Waals heterostructures can control the valley polarization of of MX ₂effectively, which makes them possess promising potential applications in valleytronics. In the present work, the stacking order and electronic structure of MoSe ₂/CrI ₃, MoSe ₂/CrBr ₃and WS ₂/CrBr ₃are 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 MX ₂directly. Through the unfolding energy band, the electronic structure change of MX ₂induced by Cr X ₃is revealed clearly, and the valley splitting of MX ₂is 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 MoSe ₂/CrI ₃is enhanced to 10.713 meV with the increase of ABstacking, 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.

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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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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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Vol. 71, Issue 14 - 2022-07-20

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