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The nanoscale periodic energy potential is introduced by moiré pattern in two stacked transition metal dichalcogenide monolayers with lattice mismatch or crystal orientation misalignment. It is demonstrated that the moiré potential can act as a diffusion barrier that affects interlayer exciton transport, providing an opportunity for studying the electronic and optical properties of moiré excitons. However, the current research on the modulation of exciton moiré potential in twisted homobilayers is limited. In this paper the effect of externally applied perpendicular electric field on the exciton moiré potential in twisted WSe2 homobilayers with different rotation angles is studied by using first principle calculations. It is found that the amplitude and shape of the interlayer exciton moiré potential are dependent on the relative rotation angle between the layers and electric field intensity. The amplitude and shape of the moiré potential in the twisted WSe2 homobilayers with different rotation angles vary with the electric field intensity (
$\leqslant $ 1 V/nm). These results provide theoretical basis and data prediction for modulating the local and the non-local transition of interlayer excitons, and are of great significance in promoting the development of semiconductor devices such as artificial excitonic crystals and nanoarray lasers.-
Keywords:
- transition metal dichalcogenide /
- corner homobilayers /
- exciton moiré potential /
- first principle calculation
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图 1 (a) 转角θ接近0°晶胞AA-WSe2的图示; (b) 单层WSe2第一布里渊区(绿色六边形)及其倒格矢
${\boldsymbol{G}}_{j}$ ; (c) WSe2晶格的${\hat{C}}_{3}$ 对称操作, 黑色箭头表示由${\hat{C}}_{3}$ 导致的相位变化; (d) 双层WSe2转角同质结莫尔单胞的布里渊区及相应的倒格矢${\boldsymbol{b}}_{j}$ Figure 1. (a) Illustration of AA-WSe2 homobilayer with a small twist angle θ; (b) first-shell reciprocal lattice vectors Gj of a monolayer WSe2 triangular lattice and the corresponding Brillouin zone (green hexagon); (c)
${\hat{C}}_{3}$ transformation of the WSe2 lattice (Black arrows denote the phase change by${\hat{C}}_{3}$ ); (d) moiré reciprocal lattice vectors bj and corresponding Brillouin zone.
图 2 (a) 转角接近0°的莫尔条纹及莫尔超晶格; (b), (c) 分别为AA-WSe2和3R-WSe2晶格结构的俯视图(上)和侧视图(下); (d) 转角接近60°的莫尔条纹及莫尔超晶格; (e)—(g) 分别为2H-WSe2, AB'-WSe2和A'B-WSe2晶格结构的俯视图和侧视图
Figure 2. (a) Schematic of the long-period moiré superlattice formed in real space at 0°; (b), (c) top (top) and side (bottom) views of two high-symmetry stacking patterns of AA-WSe2 and 3R-WSe2; (d) schematic of the long-period moiré superlattice formed in real space at 60°; (e)–(g) top and side views of two high-symmetry stacking patterns at 60° of 2H-WSe2, AB'-WSe2 and A'B-WSe2.
图 3 (a) 电场强度为0, 1 V/nm时2H-WSe2的能带结构图; (b) 2H-WSe2在K点处对应价带的放大图; (c) 2H-WSe2在Q点处CBM及K点处VBM的W原子的二维电荷密度图; (d) 不同电场强度下5种堆叠次序的双层WSe2 在K点对应的能隙; (e) K-K激子莫尔势随实空间位置变化的三维及二维投影示意图, 可以将激子(红色和黑色小球)束缚在莫尔势最低位置处; (f) 转角接近0°/60°的双层WSe2中K-K激子莫尔势大小随电场强度的变化
Figure 3. (a) Band structure diagram of 2H-WSe2 when the electric field is 0, 1 V/nm; (b) enlarged view of the valence band maximum at K-point of 2H-WSe2; (c) 2D plots of partial charge density CBM and VBM states of 2H-WSe2 at Q-point and K-point of W atom, respectively; (d) band gap corresponding to K-point in momentum space of double-layer WSe2 with five stacking orders under different electric filed intensity; (e) illustrations of the K-K moiré potentials in both 3D and 2D projections that can trap interlayer excitons (red and black spheres) in the local minima; (f) electric field intensity-dependent of K-K moiré potentials in twisted WSe2 homobilayers with rotation angle close to 0°/60°.
图 4 电场强度不同时, 转角接近(a)—(c) 0°和(d)—(f) 60°的双层WSe2 中K-K激子莫尔势随实空间位置变化的二维投影图 (a), (d) 0 V/nm; (b), (e) 0.5 V/nm; (c), (f) 1.0 V/nm
Figure 4. Illustrations of 2D projections of K-K moiré potentials in WSe2 homobilayers with rotation angle close to (a)–(c) 0° and (d)–(f) 60° with different electric field intensity: (a), (d) 0 V/nm, (b), (e) 0.5 V/nm; (c), (f) 1.0 V/nm.
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[1] Geim A K, Grigorieva I V 2013 Nature 499 419
Google Scholar
[2] 卢晓波, 张广宇 2015 物理学报 64 077305
Google Scholar
Lu X B, Zhang G Y 2015 Acta Phys. Sin. 64 077305
Google Scholar
[3] 吕新宇, 李志强 2019 物理学报 68 220303
Google Scholar
Lv X Y, Li Z Q 2019 Acta Phys. Sin. 68 220303
Google Scholar
[4] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M 2013 Nature 497 598
Google Scholar
[5] Hunt B, Sanchez-Yamagishi J D, Young A F, Yankowitz M, LeRoy B J, Watanabe K, Taniguchi T, Moon P, Koshino M, Jarillo-Herrero P 2013 Science 340 1427
Google Scholar
[6] Ponomarenko L, Gorbachev R, Yu G, Elias D, Jalil R, Patel A, Mishchenko A, Mayorov A, Woods C, Wallbank J 2013 Nature 497 594
Google Scholar
[7] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E 2018 Nature 556 80
Google Scholar
[8] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43
Google Scholar
[9] Cao T, Wang G, Han W, Ye H, Zhu C, Shi J, Niu Q, Tan P, Wang E, Liu B 2012 Nat. Commun. 3 1
Google Scholar
[10] Rivera P, Yu H, Seyler K L, Wilson N P, Yao W, Xu X 2018 Nat. Nanotechnol. 13 1004
Google Scholar
[11] Shabani S, Halbertal D, Wu W, Chen M, Liu S, Hone J, Yao W, Basov D N, Zhu X, Pasupathy A N 2021 Nat. Phys. 17 720
Google Scholar
[12] Jin C, Regan E C, Yan A, Utama M I B, Wang D, Zhao S, Qin Y, Yang S, Zheng Z, Shi S 2019 Nature 567 76
Google Scholar
[13] Alexeev E M, Ruiz-Tijerina D A, Danovich M, Hamer M J, Terry D J, Nayak P K, Ahn S, Pak S, Lee J, Sohn J I 2019 Nature 567 81
Google Scholar
[14] Tran K, Moody G, Wu F, Lu X, Choi J, Kim K, Rai A, Sanchez D A, Quan J, Singh A 2019 Nature 567 71
Google Scholar
[15] Seyler K L, Rivera P, Yu H, Wilson N P, Ray E L, Mandrus D G, Yan J, Yao W, Xu X 2019 Nature 567 66
Google Scholar
[16] Yu H, Liu G B, Tang J, Xu X, Yao W 2017 Sci. Adv. 3 e1701696
Google Scholar
[17] Zhang C, Chuu C P, Ren X, Li M Y, Li L J, Jin C, Chou M Y, Shih C K 2017 Sci. Adv. 3 e1601459
Google Scholar
[18] Carr S, Fang S, Kaxiras E 2020 Nat. Rev. Mater. 5 748
Google Scholar
[19] Jung J, Raoux A, Qiao Z, MacDonald A H 2014 Phys. Rev. B 89 205414
Google Scholar
[20] Wu F, Lovorn T, MacDonald A 2018 Phys. Rev. B 97 035306
Google Scholar
[21] Wu F, Lovorn T, MacDonald A H 2017 Phys. Rev. Lett. 118 147401
Google Scholar
[22] Wu F, Lovorn T, Tutuc E, MacDonald A H 2018 Phys. Rev. Lett. 121 026402
Google Scholar
[23] Wu F, Lovorn T, Tutuc E, Martin I, MacDonald A 2019 Phys. Rev. Lett. 122 086402
Google Scholar
[24] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[25] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
Google Scholar
[26] Grimme S 2004 J. Comput. Chem. 25 1463
Google Scholar
[27] Yuan L, Zheng B, Kunstmann J, Brumme T, Kuc A B, Ma C, Deng S, Blach D, Pan A, Huang L 2020 Nat. Mater. 19 617
Google Scholar
[28] Zipfel J, Kulig M, Perea-Causin R, Brem S, Ziegler J D, Rosati R, Taniguchi T, Watanabe K, Glazov M M, Malic E, Chernikov A 2020 Phys. Rev. B 101 115430
Google Scholar
[29] Choi J, Hsu W T, Lu L S, Sun L, Cheng H Y, Lee M H, Quan J, Tran K, Wang C Y, Staab M 2020 Sci. Adv. 6 eaba8866
Google Scholar
[30] Bai Y, Zhou L, Wang J, Wu W, McGilly L J, Halbertal D, Lo C F B, Liu F, Ardelean J, Rivera P 2020 Nat. Mater. 19 1068
Google Scholar
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