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Transition metal dichalcogenides (TMDs) is an important member of two-dimensional material family, which has various crystal structures and physical properties, thus providing a broad platform for scientific research and device applications. The diversity of TMD's properties arises not only from their relatively large family but also from the variety of their crystal structure phases. The most common structure of TMD is the trigonal prismatic phase (H phase) and the octahedral phase (T phase). Studies have shown that, in addition to these two high-symmetry phases, TMD has other distorted phases. Distorted phase often exhibits different physical properties from symmetric phases and can perform better in certain systems. Because the structural differences between different distorted phases are sometimes very small, it is experimentally challenging to observe multiple distorted phases coexisting. Therefore, it is meaningful to theoretically investigate the structural stability and physical properties of different distorted phases. In this study, we investigate the structure and phase transition of monolayer RuSe2 through first-principles calculation. While confirming that its ground state is a the dimerized phase (
$T^\prime$ phase), we find the presence of another energetically competitive trimerized phase ($T^{\prime\prime\prime}$ phase). By comparing the energy values of four different structures and combining the results of phonon spectra and molecular dynamics simulations, we predict the stability of the$T^{\prime\prime\prime}$ phase at room temperature. Because the H phase and T phase of two-dimensional RuSe2 have already been observed experimentally, and considering the fact that$T^{\prime\prime\prime}$ phase has much lower energy than the H and T phases, it is highly likely that the$T^{\prime\prime\prime}$ phase exists in experiment. Combining the calculations of the phase transition barrier and the molecular dynamics simulations, we anticipate that applying a slight stress to the$T^\prime$ phase structure at room temperature can induce a lattice transition from$T^\prime$ phase to$T^{\prime\prime\prime}$ phase, resulting in significant changes in the band structure and carrier mobility, with the bandgap changing from an indirect bandgap of 1.11 eV to a direct bandgap of 0.71 eV, and the carrier mobility in the armchair direction increasing from$ 0.82 \times $ $ 10^3 \, {\rm cm}^{2}{\cdot}{\rm V}^{-1}{\cdot}{\rm s}^{-1}$ to$3.22 \times 10^3 \, {\rm cm}^{2}{\cdot}{\rm V}^{-1}{\cdot}{\rm s}^{-1}$ , an approximately threefold enhancement. In this work, two possible coexisting distorted phases in monolayer RuSe2 are compared with each other and studied, and their electronic structures and carrier mobilities are analyzed, thereby facilitating experimental research on two-dimensional RuSe2 materials and their applications in future electronic devices.
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Keywords:
- RuSe2 /
- phase transition /
- carrier mobility /
- first-principles calculation
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图 1 (a) 单层RuSe2 4种结构的相对能量, 以图中矩形超胞的长度作为横坐标进行排列, 绿球代表Ru原子, 红球代表Se原子; (b) RuSe2的$ T^\prime $相晶体结构; (c) RuSe2的$ T^{\prime\prime\prime} $相晶体结构
Figure 1. (a) The relative energies of four structures of monolayer RuSe2, arranged along the lengths of rectangular supercells, green spheres represent Ru atoms, while red spheres represent Se atoms; (b) crystal structure of RuSe2 in the $ T^\prime $ phase; (c) crystal structure of RuSe2 in the $ T^{\prime\prime\prime} $ phase.
图 2 (a) AIMD模拟300 K时$ T^{\prime\prime\prime} $相单层RuSe2总能量随时间的变化, 插图为始末状态的晶体结构图; (b) $ T^{\prime\prime\prime} $相单层RuSe2的声子谱
Figure 2. (a) Variation of the total energy of monolayer RuSe2 in the $ T^{\prime\prime\prime} $ phase during AIMD simulation at 300 K. The crystal structures of the initial and final states shown in the inset; (b) phonon spectrum of monolayer RuSe2 in the $ T^{\prime\prime\prime} $ phase.
图 3 (a) 单层RuSe2在$ T^\prime $相的能带结构; (b) 单层RuSe2 在$ T^{\prime\prime\prime} $相的能带结构; (c) $ T^\prime $相中的Ru-Se八面体结构; (d) $ T^{\prime\prime\prime} $相中的Ru-Se八面体结构; (e) Ru-Se 八面体的Ru-d轨道在不同晶相结构中的分裂情况示意图
Figure 3. (a) Band structure of monolayer RuSe2 in the $ T^\prime $ phase; (b) band structure of monolayer RuSe2 in the $ T^{\prime\prime\prime} $ phase; (c) octahedral structure of Ru-Se in the $ T^\prime $ phase; (d) octahedral structure of Ru-Se in the $ T^{\prime\prime\prime} $ phase; (e) schematic illustration of the splitting of Ru-d orbitals in the Ru-Se octahedron in different crystal phases.
图 4 (a) 单层RuSe2在$ T^\prime $与$ T^{\prime\prime\prime} $相下能量随zigzag方向晶格长度变化的关系曲线, 插图为部分位置处发生相变的NEB势垒图; (b) 300 K下, $ T^\prime $ 相在zigzag方向施加6.5%压缩应变时的分子动力学模拟, 其中的插图分别是0和15 ps的结构图
Figure 4. (a) The energy of monolayer RuSe2 in the $ T^\prime $ and $ T^{\prime\prime\prime} $ phases variation with the lattice along the zigzag direction. The insets are the NEB barriers showing phase transitions at certain positions; (b) AIMD of the $ T^\prime $ phase under 6.5% compressive strain along the zigzag direction at 300 K, with insets showing crystal structures at 0 and 15 ps.
表 1 计算得到的单层RuSe2在armchair和zigzag方向上的载流子有效质量$ m^*\left({m}_{0}\right) $, $ {{m}}_0 $为单个电子的质量; 弹性模量$C\;\left( {\rm N}{\cdot}{\rm m}^{-1}\right) $; 形变势$ E_1 \;(\text{eV}) $和迁移率$ \mathit{µ}\;\left({\rm cm}^{2}{\cdot}{\rm V}^{-1}{\cdot}{\rm s}^{-1}\right) $.
Table 1. Calculated effective mass of carriers $ m^*\left({m}_{0}\right) $, here the $ {m}_{0} $ represents the mass of a single electron; elastic modulus $ C\;\left({\rm N}{\cdot}{\rm m}^{-1}\right) $; deformation potential $ E_1 \; \left(\text{eV}\right)$; and mobility $\mathit{µ}\; \left({\rm cm}^{2}{\cdot}{\rm V}^{-1}{\cdot}{\rm s}^{-1}\right)$ of monolayer RuSe2 in the armchair and zigzag directions.
Phase/Carrier $ m^*_{{\mathrm{arm}}} $ $ m^*_{{\mathrm{zig}}} $ $ C_{11} $ $ C_{22} $ $ E_{1 {\mathrm{arm}}} $ $ E_{1 {\mathrm{zig}}} $ $ \mu_{\rm arm} $ $ \mu_{\rm zig} $ $ {m}_{0} $ $ /({\rm N}{\cdot}{\rm m}^{-1}) $ /eV $ /\left({\rm cm}^{2}{\cdot}{\rm V}^{-1}{\cdot}{\rm s}^{-1}\right) $ $ T^\prime \text{/e}$ 37.59 9.64 95.73 92.01 0.74 –2.87 2.44 3.53 $ T^\prime \text{/h}$ 3.21 1.22 1.46 –0.71 224.42 823.25 $ T^{\prime\prime\prime}\text{/e} $ 3.48 1.16 97.80 99.31 –1.46 –2.98 70.53 150.57 $ T^{\prime\prime\prime} \text{/h}$ 1.10 0.60 1.78 0.50 1182.65 3219.20 
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[1] Pinilla S, Coelho J, Li K, Liu J, Nicolosi V 2022 Nat. Rev. Mater. 7 717
Google Scholar
[2] Wan S J, Li X, Chen Y, Liu N N, Du Y, Dou S X, Jiang L, Cheng Q F 2021 Science 374 96
Google Scholar
[3] Jiang Y C, He A P, Zhao R, Chen Y, Liu G Z, Lu H, Zhang J L, Zhang Q, Wang Z, Zhao C, Long M S, Hu W D, Wang L, Qi Y P, Gao J, Wu Q Y, Ge X T, Ning J Q, Wee A T S, Qiu C W 2021 Phys. Rev. Lett. 127 217401
Google Scholar
[4] Zhu B R, Xiao K, Yang S Y, Watanabe K, Taniguchi T, Cui X D 2023 Phys. Rev. Lett. 131 036901
Google Scholar
[5] Liu X G, Pyatakov A P, Ren W 2020 Phys. Rev. Lett. 125 247601
Google Scholar
[6] Liu X E, Yang Y L, Hu T, Zhao G D, Chen C, Ren W 2019 Nanoscale 11 18575
Google Scholar
[7] Wang L, Shih E M, Ghiotto A, Xian L, Rhodes D A, Tan C, Claassen M, Kennes D M, Bai Y S, Kim B, Watanabe K, Taniguchi T, Zhu X Y, Hone J, Rubio A, Pasupathy A N, Dean C R 2020 Nat. Mater. 19 861
Google Scholar
[8] de la Barrera S C, Sinko M R, Gopalan D P, Sivadas N, Seyler K L, Watanabe K, Taniguchi T, Tsen A W, Xu X, Xiao D, Hunt B M 2018 Nat. Commun. 9 1427
Google Scholar
[9] Liu Y, Duan X D, Shin H J, Park S, Huang Y, Duan X F 2021 Nature 591 43
Google Scholar
[10] Wang S, ur Rehman Z, Liu Z F, Li T R, Li Y L, Wu Y B, Zhu H G, Cui S T, Liu Y, Zhang G B 2022 Chin. Phys. Lett. 39 077102
Google Scholar
[11] 郝国强, 张瑞, 张文静, 陈娜, 叶晓军, 李红波 2022 物理学报 71 240
Google Scholar
Hao G Q, Zhang R, Zhang W J, Chen N, Ye X J, Li H B 2022 Acta Phys. Sin. 71 240
Google Scholar
[12] 邓霖湄, 司君山, 吴绪才, 张卫兵 2022 物理学报 71 147101
Google Scholar
Deng L M, Si J S, Wu X C, Zhang W B 2022 Acta Phys. Sin. 71 147101
Google Scholar
[13] Zhao W, Pan J, Fang Y, Che X, Wang D, Bu K, Huang F 2018 Chem. Eur. J. 24 15942
Google Scholar
[14] Duerloo K A, Li Y, Reed E J 2014 Nat. Commun. 5 4214
Google Scholar
[15] Duvjir G, Choi B K, Ly T T, Lam N H, Chun S H, Jang K, Soon A, Chang Y J, Kim J 2019 Nanoscale 11 20096
Google Scholar
[16] Sun Y F, Wang Y X, Sun D, Carvalho B R, Read C G, Lee C H, Lin Z, Fujisawa K, Robinson J A, Crespi V H, Terrones M, Schaak R E 2016 Angew. Chem. Int. Ed. 55 2830
Google Scholar
[17] Liu Z Q, Li N, Su C, Zhao H Y, Xu L L, Yin Z Y, Li J, Du Y P 2018 Nano Energy 50 176
Google Scholar
[18] Kar I, Dolui K, Harnagea L, Kushnirenko Y, Shipunov G, Plumb N C, Shi M, Büchner B, Thirupathaiah S 2021 J. Phys. Chem. C 125 1150
Google Scholar
[19] Liu E F, Fu Y J, Wang Y J, Feng Y Q, Liu H M, Wan X G, Zhou W, Wang B G, Shao L B, Ho C H, Huang Y S, Cao Z Y, Wang L G, Li A D, Zeng J W, Song F Q, Wang X R, Shi Y, Yuan H T, Hwang H Y, Cui Y, Miao F, Xing D Y 2015 Nat. Commun. 6 6991
Google Scholar
[20] Niehues I, Deilmann T, Kutrowska-Girzycka J, Taghizadeh A, Bryja L, Wurstbauer U, Bratschitsch R, Jadczak J 2022 Phys. Rev. B 105 205432
Google Scholar
[21] Fang Y, Hu X, Zhao W, Pan J, Wang D, Bu K, Mao Y, Chu S, Liu P, Zhai T, Huang F 2019 J. Am. Chem. Soc. 141 790
Google Scholar
[22] Lipatov A, Chaudhary P, Guan Z, Lu H, Li G, Crégut O, Dorkenoo K D, Proksch R, Cherifi-Hertel S, Shao D F, Tsymbal E Y, Íñiguez J, Sinitskii A, Gruverman A 2022 npj 2D Mater. Appl. 6 18
Google Scholar
[23] Liu L, Chen S S, Lin Z Z, Zhang X 2020 J. Phys. Chem. Lett. 11 7893
Google Scholar
[24] Gao G, Jiao Y, Ma F, Jiao Y, Waclawik E, Du A 2015 J. Phys. Chem. C 119 13124
Google Scholar
[25] Fu Q, Han J, Wang X, Xu P, Yao T, Zhong J, Zhong W, Liu S, Gao T, Zhang Z, Xu L, Song B 2021 Adv. Mater. 33 e1907818
Google Scholar
[26] Keum D H, Cho S, Kim J H, Choe D H, Sung H J, Kan M, Kang H, Hwang J Y, Kim S W, Yang H, Chang K J, Lee Y H 2015 Nat. Phys. 11 482
Google Scholar
[27] Lai Z C, He Q Y, Ha Tran T, Repaka D V M, Zhou D D, Sun Y, Xi S B, Li Y X, Chaturvedi A, Tan C L, Chen B, Nam G H, Li B, Ling C Y, Zhai W, Shi Z Y, Hu D Y, Sharma V, Hu Z N, Chen Y, Zhang Z C, Yu Y F, Wang X R, Ramanujan R V, Ma Y M, Hippalgaonkar K, Zhang H 2021 Nat. Mater. 20 1113
Google Scholar
[28] Song M S, Shi Q, Kan D X, Wei S R, Xu F M, Huo W T, Chen K Y 2023 Appl. Surf. Sci. 612 155761
Google Scholar
[29] Tanimura H, Okamoto N L, Homma T, Sato Y, Ishii A, Takamura H, Ichitsubo T 2022 Phys. Rev. B 105 245402
Google Scholar
[30] Kiem D, Jeong M Y, Yoon H, Han M J 2022 Nanoscale 14 10009
Google Scholar
[31] Chen K, Deng J, Kan D, Yan Y, Shi Q, Huo W, Song M, Yang S, Liu J Z 2022 Phys. Rev. B 105 024414
Google Scholar
[32] Zhang M G, Chen L F, Feng L, Tuo H H, Zhang Y, Wei Q, Li P F 2023 Chin. Phys. B 32 086101
Google Scholar
[33] Zhao Y, Cong H, Li P, Wu D, Chen S, Luo W 2021 Angew. Chem. Int. Ed. 60 7013
Google Scholar
[34] Ersan F, Cahangirov S, Gökoglu G, Rubio A, Aktürk E 2016 Phys. Rev. B 94 155415
Google Scholar
[35] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[36] Kresse G, Hafner J 1994 Phys. Rev. B 49 14251
Google Scholar
[37] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
Google Scholar
[38] Grimme S 2006 J. Comput. Chem. 27 1787
Google Scholar
[39] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[40] Cococcioni M, de Gironcoli S 2005 Phys. Rev. B 71 035105
Google Scholar
[41] Togo A, Tanaka I 2015 Scr. Mater. 108 1
Google Scholar
[42] Bucher D, Pierce L C T, McCammon J A, Markwick P R L 2011 J. Chem. Theory Comput. 7 890
Google Scholar
[43] Lang H F, Zhang S Q, Liu Z R 2016 Phys. Rev. B 94 235306
Google Scholar
[44] Abdullahi Y Z, Ahmad S 2021 Phys. Chem. Chem. Phys. 23 16316
Google Scholar
[45] Zhang S H, Zhou J, Wang Q, Chen X S, Kawazoe Y, Jena P 2015 Proc. Natl. Acad. Sci. U.S.A. 112 2372
Google Scholar
[46] Zhang G T, Lu K J, Wang Y F, Wang H W, Chen Q 2022 Phys. Rev. B 105 235303
Google Scholar
[47] Wang Y T, Tang X H, Zhou Q H, Chen X Y, Chen Q, Xu Y H 2020 Phys. Rev. B 102 165428
Google Scholar
[48] Zhou Q H, Chen Q, Tong Y L, Wang J L 2016 Angew. Chem. Int. Ed. 55 11437
Google Scholar
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