Valley manipulation in WSeTe/CrI<sub>3</sub> van der Waals Heterostructures: A first-principles study

LIAO Yumin; CHEN Xumin; XU Huanglei; YI Shuisheng; WANG Hui; HUO Dexuan

doi:10.7498/aps.74.20241750

Abstract

The valley degree of freedom, besides charge and spin, can be used to process information and perform logic operations as well, with the advantage of low power consumption and high speed. The effective manipulation of valley degrees of freedom is essential for their practical applications in valleytronics and spintronics. In this work, the effective strategy is investigated for the valley manipulation of the WSeTe/CrI₃ van der Waals heterojunction with about 2% lattice mismatch by the first-principles calculations. The valley degree of freedom in WSeTe can be modulated by the magnetism of Cr atoms in the substrate via the magnetic proximity effect, including the vertical strain method and the rotation of the magnetic moments of Cr atoms. First-principles calculations are performed by using the VASP software package with the generalized gradient approximation functional in PerdewBurke-Ernzerhof (PBE) form. The spin-orbit coupling is considered when calculating the band structure to investigate the valley properties. The dependence of valley polarization on both vertical strain and the substrate’s magnetic moment direction has been systematically analyzed. There are two different stacking configurations for the WSeTe/CrI₃ heterojunction with Te/Se atoms at the interface, namely Te-stacking and Se-stacking. Although single-layer WSeTe does not have valley polarization, the Te-stacked and Se-stacked WSeTe/CrI₃ heterojunctions exhibit valley polarizations of 25 meV and 2 meV, respectively, which is influenced by spin-orbit coupling and the proximity effect of the magnetic substrate CrI₃, indicating the importance of the stack configuration. The Te-stacked configuration of the heterojunction has a larger valley polarization due to stronger orbital hybridization between W atoms in WSeTe layer and Cr atoms in CrI₃ layer. The application of vertical strain, which effectively tunes the interlayer distance, significantly regulates the valley polarization. Specifically, the valley polarization is increased to 59 meV when the interlayer distance decreases by 0.5 Å, while it decreases to 10 meV when the interlayer distance increases by 0.5 Å. Additionally, when the magnetic moment of the CrI₃ substrate rotates by 360°, the valley polarization changes between –25 meV and 25 meV. It reaches a maximum value when the magnetic moment is aligned along the out-of-plane direction. This study demonstrates that the valley degree of freedom in the WSeTe/CrI₃ van der Waals heterojunction can be effectively manipulated by adjusting the interlayer distance through vertical strain and by controlling the magnetic moment direction of the substrate. These findings provide valuable insights into the design and application of valleytronic and spintronic devices based on two-dimensional van der Waals heterostructures.

Keywords:

Authors and contacts

1.
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
2.
School of Materials and Environmental Engineering, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding author: CHEN Xumin, 41790@hdu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874011).

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References

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Cited By

图 1 T堆叠WSeTe/CrI₃异质结俯视图与侧视图　(a) Te构型; (b) Se构型

Figure 1. Top and side views of the T-stacked WSeTe/CrI₃ heterojunction: (a) Te model; (b) Se model.

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图 2 单层WSeTe的电子性质　(a)不考虑SOC的能带; (b)考虑SOC的能带; (c) Berry曲率; (d)能谷光学选择定则示意图

Figure 2. Electronic properties of monolayer WSeTe: (a) Band structures without SOC; (b) band structures with SOC; (c) Berry curvature; (d) schematic diagram of valley optical selection rules.

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图 3 WSeTe/CrI₃异质结能带图　(a)不考虑SOC的Se构型; (b)考虑SOC的Se构型; (c)不考虑SOC的Te构型; (d)考虑SOC的Te构型; 蓝色虚线代表自旋向下, 红色实线代表自旋向上; 插图为能谷放大视图

Figure 3. Band structures of WSeTe/CrI₃: (a) The band structures of Se model without SOC; (b) the band structures of Se model with SOC; (c) the band structures of Te model without SOC; (d) the band structures of Te model with SOC, the blue dashed lines represent spin-down, and the red lines represent spin-up. The insets are enlarged local views.

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图 4 WSeTe/CrI₃异质结Te构型的投影能带图　(a)原子投影能带; (b) CrI₃与WSeTe层投影能带; (c) W原子S_z方向自旋投影能带, 其中红色和蓝色代表自旋向上和向下的能带, ${E_\sigma }$代表导带谷到价带谷的能量差

Figure 4. Projected band structures of the Te-model WSeTe/CrI₃ heterojunction: (a) Atom projected band structures; (b) layer projected band structures of CrI₃ and WSeTe; (c) projected band structures of W along the S_z direction of spin, where the red and blue circles correspond to spin-up and spin-down bands, ${E_\sigma }$represents the energy difference from the conduction band valley to the valence band valley.

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图 5 K与K' 附近能带与Berry曲率　(a)磁矩+Z (θ = 0°)方向的能带, 插图为磁矩方向示意图; (b) 磁矩+Z (θ = 0°)方向的Berry曲率; (c)磁矩–Z (θ = 180°)方向的能带;(d)磁矩–Z (θ = 180°)方向的Berry曲率; 红色和蓝色代表自旋向上和向下的能带

Figure 5. Bands and Berry curvature near the K and K' points: (a) Band structures for the magnetic moment along the +Z (θ = 0°) direction, with an inset diagram illustrating the direction of the magnetic moment; (b) Berry curvature for the magnetic moment along the +Z (θ = 0°) direction; (c) bands structures for the magnetic moment along the –Z (θ = 180°) direction; (d) Berry curvature for the magnetic moment along the –Z (θ = 180°) direction; the red and blue circles correspond to spin-up and spin-down bands.

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图 6 (a)不同Cr磁矩方向的能谷及谷极化大小, 其中蓝色线条代表不同磁矩方向下的谷极化; (b)不同层间距下能谷及谷极化大小, 其中蓝色线条代表不同层间距下的谷极化${\text{|}}\Delta {E_\sigma }{\text{|}}$大小; 橙色和绿色柱状图分别表示了K与K' 处谷的能量

Figure 6. (a) Valley and valley polarization for different Cr magnetic moments, where blue lines represent the valley polarization under different magnetization angles; (b) valley and valley polarization under different interlayer distance, where blue lines represent the valley polarization magnitudes at different interlayer distance. The orange and green bar charts indicate the energy of the valleys at the K and K' , respectively.

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图 A1 WSeTe/CrI₃异质结六种不同堆叠方式下的俯视图与侧视图　(a) Se构型的T型、H型和R型堆叠方式; (b) Te构型的T型、H型和R型堆叠方式

Figure A1. Top and side views of six different stacking configurations of the WSeTe/CrI₃: (a) T-, H-, R-model with stacking configuration of Se; (b) T-, H-, R-model with stacking configuration of Te.

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图 A2 WSeTe/CrI₃异质结声子谱

Figure A2. Phonon spectra of the WSeTe/CrI₃ heterojunction.

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图 A3 WSeTe/CrI₃ T堆叠Te构型HSE06计算的能带结构(红色和蓝色代表自旋向上和向下的能带)

Figure A3. WSeTe/CrI₃’s band structures of the T-stacked Te model with hybrid functional HSE06. The red and blue circles correspond to spin-up and spin-down bands.

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表 A1 6种不同结构的晶格常数、层间距和结合能

Table A1. Lattice constant, interlayer distance, and binding energy for six different models.

堆叠方式	晶格常数a = b/Å	层间距d/Å	结合能E_b/eV
T-Te	6.84	3.79	–3.59
T-Se	6.84	3.61	–3.58
H-Te	6.83	3.85	–3.52
H-Se	6.83	3.67	–3.51
R-Te	6.84	3.78	–3.58
R-Se	6.84	3.52	–3.58

DownLoad: CSV

map

[1]	Gunawan O, Shkolnikov Y P, Vakili K, Gokmen T, De Poortere E P, Shayegan M 2006 Phys. Rev. Lett. 97 186404 Google Scholar
[2]	Rycerz A, Tworzydło J, Beenakker C W J 2007 Nat. Phys. 3 172 Google Scholar
[3]	Sun Z H, Guan H M, Fu L, Shen B, Tang N 2021 Acta Phys. Sin. 70 027302 [孙真昊, 管鸿明, 付雷, 沈波, 唐宁 2021 70 027302]Google Scholar Sun Z H, Guan H M, Fu L, Shen B, Tang N 2021 Acta Phys. Sin. 70 027302 Google Scholar
[4]	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
[5]	Xiao D, Liu G B, Feng W, Xu X, Yao W 2012 Phys. Rev. Lett. 108 196802 Google Scholar
[6]	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
[7]	MacNeill D, Heikes C, Mak K F, Anderson Z, Kormanyos A, Zolyomi V, Park J, Ralph D C 2015 Phys. Rev. Lett. 114 037401 Google Scholar
[8]	Srivastava A, Sidler M, Allain A V, Lembke D S, Kis A, Imamoğlu A 2015 Nat. Phys. 11 141 Google Scholar
[9]	Xu S, Si C, Li Y, Gu B L, Duan W 2021 Nano Lett. 21 1785 Google Scholar
[10]	Cheng Y C, Zhang Q Y, Schwingenschlögl U 2014 Phys. Rev. B 89 155429 Google Scholar
[11]	Ramasubramaniam A, Naveh D 2013 Phys. Rev. B 87 195201 Google Scholar
[12]	张德贺, 周文哲, 李奥林, 欧阳方平 2021 70 096301 Google Scholar Zhang D H, Zhou W Z, Li A L, Ouyang F P 2021 Acta Phys. Sin. 70 096301 Google Scholar
[13]	Qi J S, Li X, Niu Q, Feng J 2015 Phys. Rev. B 92 121403 Google Scholar
[14]	Zhang Q, Yang S A, Mi W, Cheng Y, Schwingenschlogl U 2016 Adv. Mater. 28 959 Google Scholar
[15]	Zheng G B, Zhang B, Duan H M, Zhou W Z, Ouyang F P 2023 Physica E 148 115616 Google Scholar
[16]	邓霖湄, 司君山, 吴绪才, 张卫兵 2022 71 147101 Google Scholar Deng L M, Si J S, Wu X C, Zhang W B 2022 Acta Phys. Sin. 71 147101 Google Scholar
[17]	Yao W, Xiao D, Niu Q 2008 Phys. Rev. B 77 235406 Google Scholar
[18]	Mak K F, He K, Shan J, Heinz T F 2012 Nat. Nanotechnol. 7 494 Google Scholar
[19]	Liu H, Zhang Z, Li Y, Wu Y, Wu Z, Li X, Zhang C, Xu F, Kang J 2023 Adv. Photon. Nexus 2 026007 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]	Abid A, Haneef M, Ali S, Dahshan A 2022 J. Solid State Chem. 311 123159 Google Scholar
[22]	Mehdipour H, Kratzer P 2024 Phys. Rev. B 109 085425 Google Scholar
[23]	Sattar S, Larsson J A, Canali C M, Roche S, Garcia J H 2022 Phys. Rev. B 105 L041402 Google Scholar
[24]	Norden T, Zhao C, Zhang P, Sabirianov R, Petrou A, Zeng H 2019 Nat. Commun. 10 4163 Google Scholar
[25]	Hu T, Zhao G D, Gao H, Wu Y B, Hong J S, Stroppa A, Ren W 2020 Phys. Rev. B 101 125401 Google Scholar
[26]	Zhang W L, Zhu H R, Zhang W Q, Wang J, Zhang T T, Yang S R, Shao B, Zuo X 2024 Appl. Surf. Sci. 647 158986 Google Scholar
[27]	Ye Y, Xiao J, Wang H L, Ye Z L, Zhu H R, Zhao M, Wang Y, Zhao J H, Yin X B, Zhang X 2016 Nat. Nanotechnol. 11 598 Google Scholar
[28]	Lu A Y, Zhu H R, Xiao J, Chuu C P, Han Y, Chiu M H, Cheng C C, Yang C W, Wei K H, Yang Y, Wang Y, Sokaras D, Nordlund D, Yang P, Muller D A, Chou M Y, Zhang X, Li L J 2017 Nat. Nanotechnol. 12 744 Google Scholar
[29]	Zhang J, Jia S, Kholmanov I, Dong L, Er D, Chen W, Guo H, Jin Z, Shenoy V B, Shi L, Lou J 2017 ACS Nano 11 8192 Google Scholar
[30]	Hajra D, Sailus R, Blei M, Yumigeta K, Shen Y, Tongay S 2020 ACS Nano 14 15626 Google Scholar
[31]	Trivedi D B, Turgut G, Qin Y, Sayyad M Y, Hajra D, Howell M, Liu L, Yang S, Patoary N H, Li H, Petric M M, Meyer M, Kremser M, Barbone M, Soavi G, Stier A V, Muller K, Yang S, Esqueda I S, Zhuang H, Finley J J, Tongay S 2020 Adv. Mater. 32 2006320 Google Scholar
[32]	Yang S Y, Shi D R, Wang T, Yue X Y, Zheng L, Zhang Q H, Gu L, Yang X Q, Shadike Z, Li H, Fu Z W 2020 J. Mater. Chem. A 8 25739 Google Scholar
[33]	Guo S D, Zhu J X, Yin M Y, Liu B G 2022 Phys. Rev. B 105 104416 Google Scholar
[34]	Zhang L, Zhao Y, Liu Y, Gao G 2023 Nanoscale 15 18910 Google Scholar
[35]	Chen Y K, Zhao X S, An Y K 2024 Phys. Rev. B 109 125421 Google Scholar
[36]	Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169 Google Scholar
[37]	Grimme S, Antony J, Ehrlich S, Krieg H 2010 J. Chem. Phys. 132 154104 Google Scholar
[38]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188 Google Scholar
[39]	Dudarev S L, Botton G A, Savrasov S Y, Humphreys C, Sutton A P 1998 Phys. Rev. B 57 1505 Google Scholar
[40]	Kim H J https://github.com/Infant83/VASPBERRY [2024-7-11]
[41]	Hu T, Jia F H, Zhao G D, Wu J Y, Stroppa A, Ren W 2018 Phys. Rev. B 97 235404 Google Scholar
[42]	Webster L, Yan J A 2018 Phys. Rev. B 98 144411 Google Scholar
[43]	Ma Z, Huang P, Li J, Zhang P, Zheng J X, Xiong W, Wang F, Zhang X W 2022 npj Comput. Mater. 8 11 Google Scholar
[44]	Zhang H J, Li Y F, Hou J H, Du A J, Chen Z F 2016 Nano Lett. 16 6124 Google Scholar
[45]	Shao Y, Shao M, Kawazoe Y, Shi X, Pan H 2018 J. Mater. Chem. A 6 10226 Google Scholar
[46]	Yang C, Li J, Liu X L, Bai C L 2023 Phys. Chem. Chem. Phys. 25 28796 Google Scholar

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Valley manipulation in WSeTe/CrI₃ van der Waals Heterostructures: A first-principles study

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Valley manipulation in WSeTe/CrI3 van der Waals Heterostructures: A first-principles study

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Valley manipulation in WSeTe/CrI₃ van der Waals Heterostructures: A first-principles study