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具有本征磁性的二维半导体材料在实现低功耗、小尺寸和高效率的自旋电子学器件方面具有重要应用前景. 一些拥有特殊晶格结构的二维材料, 如笼目晶格结构, 凭借其在磁性和电学方面的新颖性质而受到研究者的青睐. 最近, 一种新的具有笼目晶格结构的二维磁性半导体材料Nb3Cl8单层被成功制备出来, 为探索具有笼目结构的二维磁性半导体器件提供了新机会. 本文通过第一性原理方法研究了Nb3Cl8单层的电子结构、磁各向异性, 构造了其p-n结二极管结构, 并研究了其自旋输运性质. 结果表明, Nb3Cl8单层易磁化轴在平面内, 沿x轴方向, Nb原子对磁各向异性起主要贡献, 且相关磁性可通过应力应变进行调控. 此外, 基于Nb3Cl8单层的p-n结二极管纳米器件表现出整流效应、自旋过滤效应以及负微分电阻现象. 这些结果表明了Nb3Cl8单层在下一代高性能自旋电子器件方面具有较大的应用潜力.Two-dimensional semiconductor materials with intrinsic magnetism have great application prospects in realizing spintronic devices with low power consumption, small size and high efficiency. Some two-dimensional materials with special lattice structures, such as kagome lattice crystals, are favored by researchers because of their novel properties in magnetism and electronic properties. Recently, a new two-dimensional magnetic semiconductor material Nb3Cl8 monolayer with kagome lattice structure was successfully prepared, which provides a new platform for exploring two-dimensional magnetic semiconductor devices with kagome structure. In this work, we study the electronic structure and magnetic anisotropy of Nb3Cl8 monolayer. We also further construct its p-n junction diode and study its spin transport properties by using density functional theory combined with non-equilibrium Green’s function method. The results show that the phonon spectrum of the Nb3Cl8 monolayer has no negative frequency, confirming its dynamic stability. The band gap of the spin-down state (1.157 eV) is significantly larger than that of the spin-up state (0.639 eV). The magnetic moment of the Nb3Cl8 monolayer is 0.997 μB, and its easy magnetization axis is in the plane and along the x-axis direction based on its energy of magnetic anisotropy. The Nb atoms make the main contribution to the magnetic anisotropy. When the strain is applied, the band gap of the spin-down states will decrease, while the band gap of the spin-up state monotonically decreases from the negative (compress) to positive (tensile) strain. As the strain variable goes from –6% to 6%, the contribution of Nb atoms to the total magnetic moment gradually increases. Moreover, strain causes the easy magnetization axis of the Nb3Cl8 monolayer to flip vertically from in-plane to out-plane. The designed p-n junction diode nanodevice based on Nb3Cl8 monolayer exhibits an obvious rectification effect. In addition, the current in the spin-up state is larger than that in the spin-down state, exhibiting a spin-polarized transport behavior. Moreover, a negative differential resistance (NDR) phenomenon is also observed, which could be used in the NDR devices. These results demonstrate that the Nb3Cl8 monolayer material has great potential applications in the next-generation high-performance spintronic devices, and further experimental verification and exploration of this material and related two-dimensional materials are needed.
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Keywords:
- Nb3Cl8 monolayer /
- magnetic material /
- magnetic anisotropy /
- spin electron transport
[1] 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 265Google Scholar
[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar
[3] An M, Dong S 2020 APL Mater. 8 110704Google Scholar
[4] Ataca C, Sahin H, Ciraci S 2012 J. Phys. Chem. C 116 8983Google Scholar
[5] Du Y C, Yang L M, Liu H, Ye P D 2014 APL Mater. 2 092510Google Scholar
[6] Li G P, Yao K L, Gao G Y 2018 Nanotechnology 29 015204Google Scholar
[7] Li X X, Fan Z Q, Liu P Z, Chen M L, Liu X, Jia C K, Sun D M, Jiang X W, Han Z, Bouchiat V, Guo J J, Chen J H, Zhang Z D 2017 Nat. Commun. 8 970Google Scholar
[8] Yuan J, Chen Y, Xie Y, Zhang X, Rao D, Guo Y, Yan X, Feng Y P, Cai Y 2020 Proc. Natl. Acad. Sci. U.S.A. 117 6362Google Scholar
[9] An Y P, Gong S J, Hou Y S, Li J, Wu R Q, Jiao Z Y, Wang T X, Jiao J T 2020 J. Phys. Condens. Matter 32 055503Google Scholar
[10] An Y P, Hou Y S, Wang H, Li J, Wu R Q, Wang T X, Da H X, Jiao J T 2019 Phys. Rev. A 11 064031Google Scholar
[11] An Y P, Jiao J T, Hou Y S, Wang H, Wu D P, Wang T X, Fu Z M, Xu G L, Wu R Q 2018 Phys. Chem. Chem. Phys. 20 21552Google Scholar
[12] An Y P, Jiao J T, Hou Y S, Wang H, Wu R Q, Liu C, Chen X N, Wang T X, Wang K 2019 J. Phys. Condens. Matter 31 065301Google Scholar
[13] Feng B, Zhang J, Zhong Q, Li W, Li S, Li H, Cheng P, Meng S, Chen L, Wu K 2016 Nat. Chem. 8 563Google Scholar
[14] Mannix A J, Zhou X F, Kiraly B, Wood J D, Alducin D, Myers B D, Liu X, Fisher B L, Santiago U, Guest J R, Yacaman M J, Ponce A, Oganov A R, Hersam M C, Guisinger N P 2015 Science 350 1513Google Scholar
[15] Arcudia J, Kempt R, Cifuentes-Quintal M E, Heine T, Merino G 2020 Phys. Rev. Lett. 125 196401Google Scholar
[16] Jin Z H, Mullen J T, Kim K W 2016 Appl. Phys. Lett. 109 053108Google Scholar
[17] Lu J, Fan Z Q, Gong J, Chen J Z, ManduLa H, Zhang Y Y, Yang S Y, Jiang X W 2018 Phys. Chem. Chem. Phys. 20 5699Google Scholar
[18] Sibari A, Kerrami Z, Kara A, Benaissa M 2020 J. Appl. Phys. 127 225703Google Scholar
[19] An Y P, Wang K, Gong S J, Hou Y S, Ma C L, Zhu M F, Zhao C X, Wang T X, Ma S H, Wang H Y, Wu R Q, Liu W M 2021 npj Comput. Mater. 7 45Google Scholar
[20] Feng Y L, Wang Z L, Zuo X, Gao G Y 2022 Appl. Phys. Lett. 120 092405Google Scholar
[21] Gao Y F, Liao J B, Wang H Y, Wu Y, Li Y L, Wang K, Ma C L, Gong S J, Wang T X, Dong X, Jiao Z Y, An Y P 2022 Phys. Rev. A 18 034033Google Scholar
[22] Yan H J, Guan Q Y, Chen H F, Cui X Y, Shu Z, Liang D, Wang B W, Cai Y Q 2022 J. Mater. Chem. A 10 23744Google Scholar
[23] Liu Q, Li J J, Wu D, Deng X Q, Zhang Z H, Fan Z Q, Chen K Q 2021 Phys. Rev. B 104 045412Google Scholar
[24] Fan Z Q, Jiang X W, Chen J Z, Luo J W 2018 ACS Appl. Mater. Interfaces 10 19271Google Scholar
[25] Fan Z Q, Jiang X W, Luo J W, Jiao L Y, Huang R, Li S S, Wang L W 2017 Phys. Rev. B 96 165402Google Scholar
[26] Fan Z Q, Zhang Z H, Yang S Y 2020 Nanoscale 12 21750Google Scholar
[27] 王贺岩, 高怡帆, 廖家宝, 陈俊彩, 李怡莲, 吴怡, 徐国亮, 安义鹏 2022 物理学报 71 097502Google Scholar
Wang H Y, Gao Y F, Liao J B, Chen J C, Li Y L, Wu Y, Xu G L, An Y P 2022 Acta Phys. Sin. 71 097502Google Scholar
[28] Chen J C, Guo Y L, Ma C L, Gong S J, Zhao C X, Wang T X, Dong X, Jiao Z Y, Ma S H, Xu G L, An Y P 2023 Phys. Rev. A 19 054013Google Scholar
[29] Chen S B, Huang C X, Sun H S, Ding J F, Jena P, Kan E 2019 J. Phys. Chem. C 123 17987Google Scholar
[30] Dayen J F, Ray S J, Karis O, Vera-Marun I J, Kamalakar M V 2020 Appl. Phys. Rev. 7 011303Google Scholar
[31] Žutić I, Fabian J, Das Sarma S 2004 Rev. Mod. Phys. 76 323Google Scholar
[32] Lin H L, Yan F G, Hu C, Zheng Y H, Sheng Y, Zhu W K, Wang Z, Zheng H Z, Wang K Y 2022 Nanoscale 14 2352Google Scholar
[33] Zhu W K, Xie S H, Lin H L, Zhang G J, Wu H, Hu T G, Wang Z, Zhang X M, Xu J H, Wang Y J, Zheng Y H, Yan F G, Zhang J, Zhao L X, Patané A, Zhang J, Chang H X, Wang K Y 2022 Chin. Phys. Lett. 39 128501Google Scholar
[34] Zhu W K, Lin H L, Yan F G, Hu C, Wang Z, Zhao L X, Deng Y C, Kudrynskyi Z R, Zhou T, Kovalyuk Z D, Zheng Y H, Patanè A, Žutić I, Li S S, Zheng H Z, Wang K Y 2021 Adv. Mater. 33 2104658Google Scholar
[35] Zhu W K, Zhu Y M, Zhou T, Zhang X P, Lin H L, Cui Q R, Yan F G, Wang Z, Deng Y C, Yang H X, Zhao L X, Žutić I, Belashchenko K D, Wang K Y 2023 Nat. Commun. 14 5371Google Scholar
[36] Wang Z A, Xue W S, Yan F G, Zhu W K, Liu Y, Zhang X H, Wei Z M, Chang K, Yuan Z, Wang K Y 2023 Nano Lett. 23 710Google Scholar
[37] Ugeda M M, Brihuega I, Guinea F, Gómez-Rodríguez J M 2010 Phys. Rev. Lett. 104 096804Google Scholar
[38] Mishra R, Zhou W, Pennycook S J, Pantelides S T, Idrobo J C 2013 Phys. Rev. B 88 144409Google Scholar
[39] 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 270Google Scholar
[40] Zhang Z W, Shang J Z, Jiang C Y, Rasmita A, Gao W B, Yu T 2019 Nano Lett. 19 3138Google Scholar
[41] Cai X H, Song T C, Wilson N P, Clark G, He M H, Zhang X O, Taniguchi T, Watanabe K, Yao W, Xiao D, McGuire M A, Cobden D H, Xu X D 2019 Nano Lett. 19 3993Google Scholar
[42] Rosenberg E, DeStefano J M, Guo Y, Oh J S, Hashimoto M, Lu D, Birgeneau R J, Lee Y, Ke L, Yi M, Chu J-H 2022 Phys. Rev. B 106 115139Google Scholar
[43] Zelenskiy A, Monchesky T L, Plumer M L, Southern B W 2022 Phys. Rev. B 106 144433Google Scholar
[44] Yi X W, Ma X Y, Zhang Z, Liao Z W, You J Y, Su G 2022 Phys. Rev. B 106 L220505Google Scholar
[45] Ghimire N J, Dally R L, Poudel L, Jones D C, Michel D, Magar N T, Bleuel M, McGuire M A, Jiang J S, Mitchell J F, Lynn J W, Mazin I I 2020 Sci. Adv. 6 eabe2680Google Scholar
[46] Kang M G, Ye L D, Fang S A, You J S, Levitan A, Han M Y, Facio J I, Jozwiak C, Bostwick A, Rotenberg E, Chan M K, McDonald R D, Graf D, Kaznatcheev K, Vescovo E, Bell D C, Kaxiras E, van den Brink J, Richter M, Prasad Ghimire M, Checkelsky J G, Comin R 2020 Nat. Mater. 19 163Google Scholar
[47] Li M, Wang Q, Wang G, Yuan Z, Song W, Lou R, Liu Z, Huang Y, Liu Z, Lei H, Yin Z, Wang S 2021 Nat. Commun. 12 3129Google Scholar
[48] Ye L D, Kang M G, Liu J W, von Cube F, Wicker C R, Suzuki T, Jozwiak C, Bostwick A, Rotenberg E, Bell D C, Fu L, Comin R, Checkelsky J G 2018 Nature 555 638Google Scholar
[49] Yin J X, Zhang S S, Li H, Jiang K, Chang G Q, Zhang B J, Lian B, Xiang C, Belopolski I, Zheng H, Cochran T A, Xu S Y, Bian G, Liu K, Chang T R, Lin H, Lu Z Y, Wang Z Q, Jia S, Wang W H, Hasan M Z 2018 Nature 562 91Google Scholar
[50] Xu X T, Yin J X, Ma W, Tien H J, Qiang X B, Reddy P V S, Zhou H, Shen J, Lu H Z, Chang T R, Qu Z, Jia S 2022 Nat. Commun. 13 1197Google Scholar
[51] Sun Z Y, Zhou H, Wang C X, Kumar S, Geng D Y, Yue S S, Han X, Haraguchi Y, Shimada K, Cheng P, Chen L, Shi Y G, Wu K H, Meng S, Feng B J 2022 Nano Lett. 22 4596Google Scholar
[52] Jiang J, Liang Q, Meng R, Yang Q, Tan C, Sun X, Chen X 2017 Nanoscale 9 2992Google Scholar
[53] Smidstrup S, Stradi D, Wellendorff J, Khomyakov P A, Vej-Hansen U G, Lee M E, Ghosh T, Jónsson E, Jónsson H, Stokbro K 2017 Phys. Rev. B 96 195309Google Scholar
[54] Brandbyge M, Mozos J L, Ordejón P, Taylor J, Stokbro K 2002 Phys. Rev. B 65 165401Google Scholar
[55] Marmolejo-Tejada J M, Dolui K, Lazic P, Chang P H, Smidstrup S, Stradi D, Stokbro K, Nikolić B K 2017 Nano Lett. 179 5626Google Scholar
[56] Smidstrup S, Markussen T, Vancraeyveld P, Wellendorff J, Schneider J, Gunst T, Verstichel B, Stradi D, Khomyakov P A, Vej-Hansen U G, Lee M E, Chill S T, Rasmussen F, Penazzi G, Corsetti F, Ojanperä A, Jensen K, Palsgaard M L N, Martinez U, Blom A, Brandbyge M, Stokbro K 2020 J. Phys. Condens. Matter 32 015901Google Scholar
[57] van Setten M J, Giantomassi M, Bousquet E, Verstraete M J, Hamann D R, Gonze X, Rignanese G M 2017 Comput. Phys. Commun. 226 39Google Scholar
[58] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar
[59] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar
[60] Mortazavi B, Zhuang X, Rabczuk T 2022 Appl. Phys. A 128 934Google Scholar
[61] Meng R S, Pereira L D, Locquet J P, Afanas'ev V, Pourtois G, Houssa M 2022 npj Comput. Mater. 8 230Google Scholar
[62] Lado J L, Fernández-Rossier J 2017 2D Mater. 4 035002Google Scholar
[63] Daalderop G H O, Kelly P J, Schuurmans M F H 1990 Phys. Rev. B 41 11919Google Scholar
[64] 姜楠, 李奥林, 蘧水仙, 勾思, 欧阳方平 2022 物理学报 71 206303Google Scholar
Jiang N, Li A L, Qu S X, Gou S, Ouyang F P 2022 Acta Phys. Sin. 71 206303Google Scholar
[65] Lv H Y, Lu W J, Shao D F, Liu Y, Sun Y P 2015 Phys. Rev. B 92 214419Google Scholar
[66] Webster L, Yan J A 2018 Phys. Rev. B 98 144411Google Scholar
[67] Stradi D, Martinez U, Blom A, Brandbyge M, Stokbro K 2016 Phys. Rev. B 93 155302Google Scholar
[68] Gunst T, Markussen T, Stokbro K, Brandbyge M 2016 Phys. Rev. B 93 035414Google Scholar
[69] Lee I H, Martin R M 1997 Phys. Rev. B 56 7197Google Scholar
[70] Büttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207Google Scholar
-
图 1 (a) Nb3Cl8单层晶体结构的俯视图(上)和侧视图(下), x轴代表锯齿型方向; (b) 声子谱以及投影声子态密度; 自旋向上(c)和向下(d)状态的元素投影电子能带以及投影态密度; Γ点附近自旋向上(e)和向下(f)状态的导带与价带的三维视图以及在第一布里渊区的二维投影; 色卡显示了图(e)、图(f)中从低(红色)到高(紫色)的能量本征值; 费米能级(EF)设置在能量零点位置
Fig. 1. (a) Top view (top) and side view (bottom) of Nb3Cl8 monolayer crystal structure, x axis refers to the zigzag irection; (b) phonon spectrum and phonon projected density of states; element-projected electronic band and density of states for the spin-up (c) and spin-down (d) states; 3D views for the spin-up (e) and spin-down (f) states of the conduction and valence bands around the Γ point, and 2D views in the first Brillouin zone projection. Color map shows the values for (e), (f) from low (red) to high (purple). the Fermi level (EF) is set at the energy zero position.
图 2 (a) x-y平面内EMA随极角θ和ϕ的变化; (b) y-z平面内EMA随极角θ和ϕ的变化, 插图显示极坐标; (c) θ = 90°, ϕ = 90°(y轴方向)的EMA轨道投影; (d) θ = 90°, ϕ = 0°(x轴方向)的EMA轨道投影; y轴(θ = 90°, ϕ = 90°)和z轴(θ = 0°, ϕ = 90°)方向的能量设置为x-y和y-z平面的零参考
Fig. 2. (a) EMA variation with polar angles θ and ϕ in the x-y plane; (b) EMA variation with polar angles θ and ϕ in the y-z plane, inset shows polar coordinates; orbital projections of EMA corresponding to polar angles of (c) θ = 90°, ϕ = 90° (y axis direction) and (d) θ = 90°, ϕ = 0° (x axis direction). Energy of y axis (θ = 90°, ϕ = 90°) and z axis (θ = 0°, ϕ = 90°) directions are set as zero reference of the x-y and y-z plane.
图 3 (a) Nb3Cl8单层自旋向上态与自旋向下态带隙随应力应变的变化; (b) Nb3Cl8单层能量变化量($ \Delta E $)和Nb原子对总磁矩的贡献($ {{{M_{{\mathrm{Nb}}}}} / {{M_{{\mathrm{Total}}}}}} $)随应力应变的变化
Fig. 3. (a) Variation of the band gap with strain in the spin-up and spin-down states of Nb3Cl8 monolayer; (b) variation of the energy change ($ \Delta E $) and the contribution of Nb atoms to the total magnetic moment ($ {{{M_{{\mathrm{Nb}}}}} / {{M_{{\mathrm{Total}}}}}} $) with strain in the Nb3Cl8 monolayer.
图 4 (a) Z型Nb3Cl8单层p-n结二极管示意图; (b) Z型Nb3Cl8单层p-n结二极管I-V曲线; (c) Z型Nb3Cl8单层p-n结二极管的微分电导(dI/dV)曲线; (d) Z型Nb3Cl8单层p-n结二极管整流比(RR)和极化比(PR)
Fig. 4. (a) Schematic diagram of Z-type Nb3Cl8 monolayer p-n junction diode; (b) I-V curve of Z-type Nb3Cl8 monolayer p-n junction diode; (c) differential conductance (dI/dV) curve of Z-type Nb3Cl8 monolayer p-n junction diode; (d) rectification ratio (RR) and polarization ratio (PR) of Z-type Nb3Cl8 monolayer p-n junction diode.
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[1] 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 265Google Scholar
[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666Google Scholar
[3] An M, Dong S 2020 APL Mater. 8 110704Google Scholar
[4] Ataca C, Sahin H, Ciraci S 2012 J. Phys. Chem. C 116 8983Google Scholar
[5] Du Y C, Yang L M, Liu H, Ye P D 2014 APL Mater. 2 092510Google Scholar
[6] Li G P, Yao K L, Gao G Y 2018 Nanotechnology 29 015204Google Scholar
[7] Li X X, Fan Z Q, Liu P Z, Chen M L, Liu X, Jia C K, Sun D M, Jiang X W, Han Z, Bouchiat V, Guo J J, Chen J H, Zhang Z D 2017 Nat. Commun. 8 970Google Scholar
[8] Yuan J, Chen Y, Xie Y, Zhang X, Rao D, Guo Y, Yan X, Feng Y P, Cai Y 2020 Proc. Natl. Acad. Sci. U.S.A. 117 6362Google Scholar
[9] An Y P, Gong S J, Hou Y S, Li J, Wu R Q, Jiao Z Y, Wang T X, Jiao J T 2020 J. Phys. Condens. Matter 32 055503Google Scholar
[10] An Y P, Hou Y S, Wang H, Li J, Wu R Q, Wang T X, Da H X, Jiao J T 2019 Phys. Rev. A 11 064031Google Scholar
[11] An Y P, Jiao J T, Hou Y S, Wang H, Wu D P, Wang T X, Fu Z M, Xu G L, Wu R Q 2018 Phys. Chem. Chem. Phys. 20 21552Google Scholar
[12] An Y P, Jiao J T, Hou Y S, Wang H, Wu R Q, Liu C, Chen X N, Wang T X, Wang K 2019 J. Phys. Condens. Matter 31 065301Google Scholar
[13] Feng B, Zhang J, Zhong Q, Li W, Li S, Li H, Cheng P, Meng S, Chen L, Wu K 2016 Nat. Chem. 8 563Google Scholar
[14] Mannix A J, Zhou X F, Kiraly B, Wood J D, Alducin D, Myers B D, Liu X, Fisher B L, Santiago U, Guest J R, Yacaman M J, Ponce A, Oganov A R, Hersam M C, Guisinger N P 2015 Science 350 1513Google Scholar
[15] Arcudia J, Kempt R, Cifuentes-Quintal M E, Heine T, Merino G 2020 Phys. Rev. Lett. 125 196401Google Scholar
[16] Jin Z H, Mullen J T, Kim K W 2016 Appl. Phys. Lett. 109 053108Google Scholar
[17] Lu J, Fan Z Q, Gong J, Chen J Z, ManduLa H, Zhang Y Y, Yang S Y, Jiang X W 2018 Phys. Chem. Chem. Phys. 20 5699Google Scholar
[18] Sibari A, Kerrami Z, Kara A, Benaissa M 2020 J. Appl. Phys. 127 225703Google Scholar
[19] An Y P, Wang K, Gong S J, Hou Y S, Ma C L, Zhu M F, Zhao C X, Wang T X, Ma S H, Wang H Y, Wu R Q, Liu W M 2021 npj Comput. Mater. 7 45Google Scholar
[20] Feng Y L, Wang Z L, Zuo X, Gao G Y 2022 Appl. Phys. Lett. 120 092405Google Scholar
[21] Gao Y F, Liao J B, Wang H Y, Wu Y, Li Y L, Wang K, Ma C L, Gong S J, Wang T X, Dong X, Jiao Z Y, An Y P 2022 Phys. Rev. A 18 034033Google Scholar
[22] Yan H J, Guan Q Y, Chen H F, Cui X Y, Shu Z, Liang D, Wang B W, Cai Y Q 2022 J. Mater. Chem. A 10 23744Google Scholar
[23] Liu Q, Li J J, Wu D, Deng X Q, Zhang Z H, Fan Z Q, Chen K Q 2021 Phys. Rev. B 104 045412Google Scholar
[24] Fan Z Q, Jiang X W, Chen J Z, Luo J W 2018 ACS Appl. Mater. Interfaces 10 19271Google Scholar
[25] Fan Z Q, Jiang X W, Luo J W, Jiao L Y, Huang R, Li S S, Wang L W 2017 Phys. Rev. B 96 165402Google Scholar
[26] Fan Z Q, Zhang Z H, Yang S Y 2020 Nanoscale 12 21750Google Scholar
[27] 王贺岩, 高怡帆, 廖家宝, 陈俊彩, 李怡莲, 吴怡, 徐国亮, 安义鹏 2022 物理学报 71 097502Google Scholar
Wang H Y, Gao Y F, Liao J B, Chen J C, Li Y L, Wu Y, Xu G L, An Y P 2022 Acta Phys. Sin. 71 097502Google Scholar
[28] Chen J C, Guo Y L, Ma C L, Gong S J, Zhao C X, Wang T X, Dong X, Jiao Z Y, Ma S H, Xu G L, An Y P 2023 Phys. Rev. A 19 054013Google Scholar
[29] Chen S B, Huang C X, Sun H S, Ding J F, Jena P, Kan E 2019 J. Phys. Chem. C 123 17987Google Scholar
[30] Dayen J F, Ray S J, Karis O, Vera-Marun I J, Kamalakar M V 2020 Appl. Phys. Rev. 7 011303Google Scholar
[31] Žutić I, Fabian J, Das Sarma S 2004 Rev. Mod. Phys. 76 323Google Scholar
[32] Lin H L, Yan F G, Hu C, Zheng Y H, Sheng Y, Zhu W K, Wang Z, Zheng H Z, Wang K Y 2022 Nanoscale 14 2352Google Scholar
[33] Zhu W K, Xie S H, Lin H L, Zhang G J, Wu H, Hu T G, Wang Z, Zhang X M, Xu J H, Wang Y J, Zheng Y H, Yan F G, Zhang J, Zhao L X, Patané A, Zhang J, Chang H X, Wang K Y 2022 Chin. Phys. Lett. 39 128501Google Scholar
[34] Zhu W K, Lin H L, Yan F G, Hu C, Wang Z, Zhao L X, Deng Y C, Kudrynskyi Z R, Zhou T, Kovalyuk Z D, Zheng Y H, Patanè A, Žutić I, Li S S, Zheng H Z, Wang K Y 2021 Adv. Mater. 33 2104658Google Scholar
[35] Zhu W K, Zhu Y M, Zhou T, Zhang X P, Lin H L, Cui Q R, Yan F G, Wang Z, Deng Y C, Yang H X, Zhao L X, Žutić I, Belashchenko K D, Wang K Y 2023 Nat. Commun. 14 5371Google Scholar
[36] Wang Z A, Xue W S, Yan F G, Zhu W K, Liu Y, Zhang X H, Wei Z M, Chang K, Yuan Z, Wang K Y 2023 Nano Lett. 23 710Google Scholar
[37] Ugeda M M, Brihuega I, Guinea F, Gómez-Rodríguez J M 2010 Phys. Rev. Lett. 104 096804Google Scholar
[38] Mishra R, Zhou W, Pennycook S J, Pantelides S T, Idrobo J C 2013 Phys. Rev. B 88 144409Google Scholar
[39] 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 270Google Scholar
[40] Zhang Z W, Shang J Z, Jiang C Y, Rasmita A, Gao W B, Yu T 2019 Nano Lett. 19 3138Google Scholar
[41] Cai X H, Song T C, Wilson N P, Clark G, He M H, Zhang X O, Taniguchi T, Watanabe K, Yao W, Xiao D, McGuire M A, Cobden D H, Xu X D 2019 Nano Lett. 19 3993Google Scholar
[42] Rosenberg E, DeStefano J M, Guo Y, Oh J S, Hashimoto M, Lu D, Birgeneau R J, Lee Y, Ke L, Yi M, Chu J-H 2022 Phys. Rev. B 106 115139Google Scholar
[43] Zelenskiy A, Monchesky T L, Plumer M L, Southern B W 2022 Phys. Rev. B 106 144433Google Scholar
[44] Yi X W, Ma X Y, Zhang Z, Liao Z W, You J Y, Su G 2022 Phys. Rev. B 106 L220505Google Scholar
[45] Ghimire N J, Dally R L, Poudel L, Jones D C, Michel D, Magar N T, Bleuel M, McGuire M A, Jiang J S, Mitchell J F, Lynn J W, Mazin I I 2020 Sci. Adv. 6 eabe2680Google Scholar
[46] Kang M G, Ye L D, Fang S A, You J S, Levitan A, Han M Y, Facio J I, Jozwiak C, Bostwick A, Rotenberg E, Chan M K, McDonald R D, Graf D, Kaznatcheev K, Vescovo E, Bell D C, Kaxiras E, van den Brink J, Richter M, Prasad Ghimire M, Checkelsky J G, Comin R 2020 Nat. Mater. 19 163Google Scholar
[47] Li M, Wang Q, Wang G, Yuan Z, Song W, Lou R, Liu Z, Huang Y, Liu Z, Lei H, Yin Z, Wang S 2021 Nat. Commun. 12 3129Google Scholar
[48] Ye L D, Kang M G, Liu J W, von Cube F, Wicker C R, Suzuki T, Jozwiak C, Bostwick A, Rotenberg E, Bell D C, Fu L, Comin R, Checkelsky J G 2018 Nature 555 638Google Scholar
[49] Yin J X, Zhang S S, Li H, Jiang K, Chang G Q, Zhang B J, Lian B, Xiang C, Belopolski I, Zheng H, Cochran T A, Xu S Y, Bian G, Liu K, Chang T R, Lin H, Lu Z Y, Wang Z Q, Jia S, Wang W H, Hasan M Z 2018 Nature 562 91Google Scholar
[50] Xu X T, Yin J X, Ma W, Tien H J, Qiang X B, Reddy P V S, Zhou H, Shen J, Lu H Z, Chang T R, Qu Z, Jia S 2022 Nat. Commun. 13 1197Google Scholar
[51] Sun Z Y, Zhou H, Wang C X, Kumar S, Geng D Y, Yue S S, Han X, Haraguchi Y, Shimada K, Cheng P, Chen L, Shi Y G, Wu K H, Meng S, Feng B J 2022 Nano Lett. 22 4596Google Scholar
[52] Jiang J, Liang Q, Meng R, Yang Q, Tan C, Sun X, Chen X 2017 Nanoscale 9 2992Google Scholar
[53] Smidstrup S, Stradi D, Wellendorff J, Khomyakov P A, Vej-Hansen U G, Lee M E, Ghosh T, Jónsson E, Jónsson H, Stokbro K 2017 Phys. Rev. B 96 195309Google Scholar
[54] Brandbyge M, Mozos J L, Ordejón P, Taylor J, Stokbro K 2002 Phys. Rev. B 65 165401Google Scholar
[55] Marmolejo-Tejada J M, Dolui K, Lazic P, Chang P H, Smidstrup S, Stradi D, Stokbro K, Nikolić B K 2017 Nano Lett. 179 5626Google Scholar
[56] Smidstrup S, Markussen T, Vancraeyveld P, Wellendorff J, Schneider J, Gunst T, Verstichel B, Stradi D, Khomyakov P A, Vej-Hansen U G, Lee M E, Chill S T, Rasmussen F, Penazzi G, Corsetti F, Ojanperä A, Jensen K, Palsgaard M L N, Martinez U, Blom A, Brandbyge M, Stokbro K 2020 J. Phys. Condens. Matter 32 015901Google Scholar
[57] van Setten M J, Giantomassi M, Bousquet E, Verstraete M J, Hamann D R, Gonze X, Rignanese G M 2017 Comput. Phys. Commun. 226 39Google Scholar
[58] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar
[59] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar
[60] Mortazavi B, Zhuang X, Rabczuk T 2022 Appl. Phys. A 128 934Google Scholar
[61] Meng R S, Pereira L D, Locquet J P, Afanas'ev V, Pourtois G, Houssa M 2022 npj Comput. Mater. 8 230Google Scholar
[62] Lado J L, Fernández-Rossier J 2017 2D Mater. 4 035002Google Scholar
[63] Daalderop G H O, Kelly P J, Schuurmans M F H 1990 Phys. Rev. B 41 11919Google Scholar
[64] 姜楠, 李奥林, 蘧水仙, 勾思, 欧阳方平 2022 物理学报 71 206303Google Scholar
Jiang N, Li A L, Qu S X, Gou S, Ouyang F P 2022 Acta Phys. Sin. 71 206303Google Scholar
[65] Lv H Y, Lu W J, Shao D F, Liu Y, Sun Y P 2015 Phys. Rev. B 92 214419Google Scholar
[66] Webster L, Yan J A 2018 Phys. Rev. B 98 144411Google Scholar
[67] Stradi D, Martinez U, Blom A, Brandbyge M, Stokbro K 2016 Phys. Rev. B 93 155302Google Scholar
[68] Gunst T, Markussen T, Stokbro K, Brandbyge M 2016 Phys. Rev. B 93 035414Google Scholar
[69] Lee I H, Martin R M 1997 Phys. Rev. B 56 7197Google Scholar
[70] Büttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207Google Scholar
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