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Investigation of ab initio nonadiabatic molecular dynamics of excited carriers in condensed matter systems

## Investigation of ab initio nonadiabatic molecular dynamics of excited carriers in condensed matter systems

Zheng Zhen-Fa, Jiang Xiang, Chu Wei-Bin, Zhang Li-Li, Guo Hong-Li, Zhao Chuan-Yu, Wang Ya-Nan, Wang Ao-Lei, Zheng Qi-Jing, Zhao Jin
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• #### Abstract

The excited state dynamics is always an important and challenging problem in condensed matter physics. The dynamics of excited carriers can have different relaxation channels, in which the complicated interactions between different quasi-particles come into play collectively. To understand such ultrafast processes, the ab initio investigations are essential. Combining the real-time time-dependent density functional theory with fewest switches surface hopping scheme, we develop time-dependent ab initio nonadiabatic molecular dynamics (NAMD) code Hefei-NAMD to simulate the excited carrier dynamics in condensed matter systems. Using this method, we investigate the interfacial charge transfer dynamics, the electron–hole recombination dynamics, and the excited spin-polarized hole dynamics in different condensed matter systems. Moreover, we combine ab initio nonadiabatic molecular dynamics with GW plus real-time Bethe-Salpeter equation for the spin-resolved exciton dynamics. We use it to study the spin-valley exciton dynamics in MoS2. It provides a powerful tool for exciton dynamics in solid systems. The state-of-the-art NAMD studies provide a unique insight into a understanding of the ultrafast dynamics of the excited carriers in different condensed matter systems on an atomic scale.

#### Cited By

• 图 1  激发态载流子动力学中的AD和NA过程示意图(图片经文献[20]允许转载, 版权归2019 Wiley Periodicals, Inc.所有)

Figure 1.  Schematics of the AD and NA charge transfer process (Reprinted with permission from Ref. [20]. Copyright 2019 Wiley Periodicals, Inc.)

图 2  (a) 单层CH3OH在TiO2表面的三种不同吸附结构; (b) 空穴捕获过程; (c) 空穴释放过程; (d) 空穴能量弛豫过程(图片经文献[47]允许转载, 版权归2016 American Chemical Society所有)

Figure 2.  (a) Three types of adsorption stuctures; (b) averaged forward hole transfer; (c) averaged reverse hole transfer; (d) time dependence of energy relaxation of photogenerated holes (Reprinted with permission from Ref. [47]. Copyright 2016 American Chemical Society)

图 3  TiO2表面CO2光还原示意图[56]　(a) 吸附在氧空位的CO2被光激发形成“瞬态”${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$; (b) “瞬态”${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$激发弯曲模式和非对称拉伸模式声子, LUMO能量下降至CBM以下, 并捕获热电子, 形成稳定的 ${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$; (c) 捕获热电子之后的${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$解离形成CO; (d) CO2分子吸附在TiO2(110)表面氧缺陷和Ti5C位置的结构示意图(图片经文献[56]允许转载, 版权归2016 American Chemical Society所有)

Figure 3.  Photo-reduction diagram of CO2 on TiO2 surface: (a) Photo excitation generates a transient ${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$; (b) transient ${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$ excites the bending and antisymmetric stretching vibrations, which induce LUMO reduce to CBM, hot electron trapped by CO2 and form a new ${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$; (c) ${{\rm{C}}{\rm{O}}}_{2}^{\cdot -}$ dissociates in Ov; (d) geometry structure of CO2 trapped on TiO2 (110) surface (Reprinted with permission from Ref. [56]. Copyright 2016 American Chemical Society)

图 4  (a) H2O分子吸附在p型LAO/STO异质结表面的结构图; (b) 湿电子态的轨道空间分布图; (c) LAO, STO和H2O的分层电子态密度, 分别用绿色, 蓝色, 和红色表示; (d) H2O/LAO/STO的能带结构, 其中湿电子态的能带用红色三角形标记; (e) 最低湿电子态能量和CBM能量随LAO层厚的变化情况. 在图 (c)—(e) 中, 能量零点为费米能(图片经文献[65]允许转载, 版权归2018 American Chemical Society所有)

Figure 4.  (a) Geometric structure of H2O adsorbed on p-type LAO/STO heterostructure. (b) Spatial orbital distribution of the solvated state in H2O layer. (c) Layer-resolved DOS for every LAO, STO, and H2O layer, represented by green, blue, and red. (d) Band structure of one ML H2O adsorbed on p-type LAO/STO. The solvated electron band is marked by red triangles. (e) Dependence of solvated electron band minimum and CBM energies on LAO thickness. The energy of VBM is set as the reference in panels (c)–(e) (Reprinted with permission from Reference 65. Copyright 2018 American Chemical Society)

图 5  MoS2/C60界面电荷分离示意图(图片经文献[69]允许转载, 版权归2018 American Chemical Society所有)

Figure 5.  Charge separation diagram of MoS2/C60 interface (Reprinted with permission from Ref. [69]. Copyright 2018 American Chemical Society)

图 6  (a) MoS2/WS2形成第二类能带匹配示意图; (b) MoS2/WS2异质结界面能带图(图片经文献[81]允许转载, 版权归2017 American Chemical Society所有)

Figure 6.  (a) Schematic of the photoexcitation and hole transfer in a MoS2/WS2 heterostructure; (b) band structures of the MoS2/WS2 heterostructure (Reprinted with permission from Ref. [81]. Copyright 2017 American Chemical Society)

图 7  C7堆积或T堆积结构布里渊区Γ点((a), (b), (e), (f))和K点((c), (d), (g), (h))空穴的空间分布随时间变化曲线, 温度分别为300和100 K. 插图给出了空穴在动量空间的演化过程(图片经文献[81]允许转载, 版权归2017 American Chemical Society所有)

Figure 7.  Time-dependent spatial hole localization at the K and Γ points for the C7 and T stackings at 300 K (K point ((a), (b)), Γ point ((c), (d))] and 100 K (K point ((e), (f)), Γ point ((g), (h))]. The major hole relaxation routes in momentum space are schematically shown in the insets (Reprinted with permission from Ref. [81]. Copyright 2017 American Chemical Society)

图 8  MoSe2/WSe2和MoS2/WS2异质结光激发电子非绝热分子动力学模拟结果[82]　(a)—(c) MoSe2/WSe2异质结光激发电子的转移过程, 能量变化和动量弛豫路径; (d)—(f) MoS2/WS2异质结光激发电子的转移过程, 能量变化和动量弛豫路径(图片经文献[82]允许转载, 版权归2018 American Physical Society所有)

Figure 8.  Nonadiabatic molecular dynamics results: (a)–(c) Time-dependent electron spatial localization, energy evolution and relaxation in the momentum space of the MoSe2/WSe2 heterostructure; (d)–(f) time-dependent electron spatial localization, energy evolution and relaxation in the momentum space of the MoS2/WS2 heterostructure (Reprinted with permission from Ref. [82]. Copyright 2018 American Physical Society)

图 9  外加不同应力的情况下MoS2/WS2异质结中的电荷转移　(a)—(c) 电子空穴转移动力学; (d)—(f) 和动量空间转移路径(图片经文献[83]允许转载, 版权归2020 American Chemical Society所有)

Figure 9.  Charge transfer dynamics in the MoS2/WS2 heterostructure under different tensile strain: (a)–(c) Time-dependent electron and hole spatial localization; (d)–(f) charge transfer in the momentum space (Reprinted with permission from Ref. [83]. Copyright 2020 American Chemical Society)

图 10  Zigzag和Armchair横向异质结在100和300 K下(a)—(d)激发态电子空间分布随时间的演化以及(e)—(h)对应的平均能量随时间的演化, 能量零点取平均的VBM值(图片经文献[84]允许转载, 版权归2019 IOP Publishing Ltd所有)

Figure 10.  Nonadiabatic dynamics of excited elctron in the Zigzag and Armchair MoS2/WS2 at 100 K and 300 K, respectively: (a)–(d) Time-dependent spatial localization; (e)–(h) average energy evolution. The energy of the averaged VBM is set as the reference (Reprinted with permission from Ref. [84]. Copyright 2019 IOP Publishing Ltd)

图 11  无缺陷A/R异质结中的时间分辨电荷转移动力学过程　(a)电子态的能量随时间演化图, 红色和蓝色线分别代表Anatase和Rutile贡献的电子态; (b), (c) 激发态电子和空穴的能量随着时间的演化图, 颜色条表明电子和空穴在不同态上的分布情况; (d)—(i) 电子和空穴分别投影到Anatase、界面和Rutile区域上的空间分布随时间的演化曲线. 能量零点为VBM的平均能量(图片经文献[93]允许转载, 版权归2018 American Chemical Society所有)

Figure 11.  Time-dependent charge-transfer dynamics in stoichiometric A/R mixed-phase structure: (a) Time-dependent energy states evolution. The red and blue lines represent the states’ contribution by anatase and rutile, respectively. (b), (c) Time-dependent energy change of excited electron and hole. The color strips indicate the electron/hole distribution on different energy states and the dashed line represents the averaged electron/hole energy. (d)–(i) Time-dependent electron and hole localization projected onto the anatase, interface, and rutile regions, represented by red, olive, and blue, respectively. The energy of the averaged VBM is set as the reference in panels (a)–(c) (Reprinted with permission from Ref. [93]. Copyright 2018 American Chemical Society)

图 12  有氧空位A/R异质结的电荷转移动力学过程　(a) 电子态的能量随时间演化图, 红色和蓝色线分别代表Anatase和Rutile贡献的电子态; (b), (c) 激发态电子和空穴的能量随时间的演化图, 颜色条表明电子和空穴在不同态上的分布情况; (d)—(i) 电子和空穴分别投影到Anatase、界面和Rutile区域上的空间分布随时间的演化曲线. 体系VBM的平均能量作为能量零点(图片经文献[93]允许转载, 版权归2018 American Chemical Society所有)

Figure 12.  Time-dependent charge-transfer dynamics in defective A/R mixed-phase structure: (a) Time-dependent energy states evolution. The red and blue lines represent the states’ contribution by anatase and rutile, respectively. (b), (c) Time-dependent energy change of excited electron and hole. The color strips indicate the electron/hole distribution on different energy states and the dashed line represents the averaged electron/hole energy. (d)–(i) Time-dependent electron and hole localization projected onto the anatase, interface, and rutile regions, represented by red, olive, and blue, respectively. The energy of the averaged VBM is set as the reference in panels (a)–(c) (Reprinted with permission from Ref. [93]. Copyright 2018 American Chemical Society)

图 13  不同掺杂方案的TiO2体系的电子结构和含时演化的电子/空穴复合动力学过程以及非绝热耦合值, 包括: 干净的TiO2、Cr-N掺杂和V-N掺杂的TiO2体系　(a)—(c) 体系的总态密度及杂质原子的分态密度分布. (d)—(f) 体系在300 和100 K温度下e-h复合的含时演化. 颜色条表示电子/空穴弛豫到不同能态上的分布, 虚线表示电子/空穴的平均能量值. 图中的能级都是以平均的VBM能量为零点. (g)—(i) 相关能级之间的NAC (图片经文献[95]允许转载, 版权归2018 American Chemical Society所有)

Figure 13.  Electronic structures and the time-dependent electron/hole (e/h) dynamics in undoped, Cr–N- and V–N-doped TiO2: (a)–(c) The total and partial DOS. (d)–(f) The averaged time-dependent e/h energy relaxation at 300 K. The color strip indicates the e/h distribution on different energy states, and the dashed line represents the averaged e/h energy. The energy reference is the average VBM energy. (g)–(i) The averaged NAC elements in undoped and Cr–N- and V–N-doped TiO2 at 300 K. The inset in panel b shows the spatial distribution of the excess charge induced by Cr–N codoping, in which the Ti, O, Cr, and N atoms are marked by large light blue, small red, large deep blue, and small purple balls, respectively (Reprinted with permission from Ref. [95]. Copyright 2018 American Chemical Society)

图 14  通过激发单一声子模式来研究e-h复合动力学　(a), (b) 激发Cr-N掺杂TiO2中的杂质声子模式; (c), (d) 激发Cr-N掺杂TiO2中的体相声子模式; (e), (f) 激发V-N掺杂TiO2体系中的杂质声子模式. 图中的能量零点为平均的VBM. (a), (c), (e) 中的颜色条表示的是能级轨道分布的投影(黑色代表投影到TiO2上的权重, 黄色代表投影到杂质原子上的权重). (b), (d), (f) 中的颜色条代表含时演化过程中电子/空穴弛豫到不同能级上的分布(图片经文献[95]允许转载, 版权归2018 American Chemical Society所有)

Figure 14.  Frozen phonon NAMD results for time evolutions of the energy states near VBM and CBM and the averaged time-dependent e/h energy relaxation for Cr–N- and V–N-co-doped TiO2: (a), (b) IPM for Cr–N-doped TiO2; (c), (d) A single bulk mode for Cr–N-doped TiO2; (e), (f) IPM for V–N-doped TiO2. The energy reference is the average VBM energy. The color map in (a) indicates the orbital localization (black on TiO2 and yellow on dopant). The color map in (b) indicates the e/h distribution on different energy states (Reprinted with permission from Ref. [95]. Copyright 2018 American Chemical Society)

图 15  不同掺杂元素的TiO2体系的e-h复合时间与杂质声子局域度的关系[95]. 虚线表示拟合得到的指数曲线(图片经文献[95]允许转载, 版权归2018 American Chemical Society所有)

Figure 15.  e-h recombination time in different doped TiO2. The fitting exponential correlation is shown with dashed lines (Reprinted with permission from Ref. [95]. Copyright 2018 American Chemical Society)

图 16  (a) 纯净的BP单层, (b) Pv, (c) Pint和(d) Pad缺陷体系中e-h复合动力学过程. 初始态对应的是VBM上占据一个空穴. VBM, CBM以及缺陷态的空穴占据数分别用黑色、蓝色和红色线条表示. (c) 图中的小插图表示的是在Pini体系中空穴在VBM和缺陷态之间迅速达到一个平衡, 这是由于两个能态之间几乎简并的原因(图片经文献[97]允许转载, 版权归2019 American Chemical Society所有)

Figure 16.  e–h recombination dynamics in (a) pristine BP monolayer, (b) Pv, (c) Pint, and (d) Pad systems. The initial state corresponds to the electron excitation from the VBM to the CBM. Populations of the excited, ground, and defect states are shown by the black, blue, and red lines, respectively. The inset in panel (c) demonstrates fast hole equilibration between the VBM and the defect state attributed to the near-degeneracy between them (Reprinted with permission from Ref. [97]. Copyright 2019 American Chemical Society)

图 17  (a) 纯净的BP单层, (b) Pv, (c) Pint和(d) Pad缺陷体系中VBM, CBM及缺陷态之间能级差含时振荡的FT变换(图片经文献[97]允许转载, 版权归2019 American Chemical Society所有)

Figure 17.  FT phonon-induced fluctuations of the energy gaps between the VBM, the CBM, and the defect states for (a) pristine BP monolayer, (b) Pv, (c) Pint, and (d) Pad systems (Reprinted with permission from Ref. [97]. Copyright 2019 American Chemical Society)

图 18  五种缺陷构型和无缺陷构型的能态态密度以及对应的晶胞结构. 能量零点为费米能, 圆圈表示缺陷的位置(图片经文献[102]允许转载, 版权归2020 American Association for the Advancement of Science所有)

Figure 18.  Atom-projected DOS for different defective and pristine MAPbI3. ((a)–(f)) Defective and Pristine systems of MAPbI3. The energy reference is located at the Fermi level. Inset shows corresponding atomic structure, with blue circle indicating the defect location (Reprinted with permission from Ref. [102]. Copyright 2020 American Association for the Advancement of Science)

图 19  不同构型的MAPbI3中e-h复合过程　(a) e-h直接复合和通过缺陷能级的间接复合过程示意图; (b) 2 ns后不同构型的e-h复合率, 蓝色和绿色彩条分别表示直接和间接复合; (c) 直接复合过程中复合率随时间的变化; (d) 间接复合过程中复合率随时间的变化(图片经文献[102]允许转载, 版权归2020 American Association for the Advancement of Science所有)

Figure 19.  The e-h recombination process in MAPbI3 systems: (a) Schematic map of the direct and by-defect e-h recombination processes. (b) e-h recombined percentage for different systems after 2 ns. The direct and by-defect e-h recombined percentages are shown by blue and green color bars. (c), (D) Time-dependent e-h recombined percentage for different systems (Reprinted with permission from Ref. [102]. Copyright 2020 American Association for the Advancement of Science)

图 20  不同构型的MAPbI3中VBM, CBM和缺陷态的含时能量振荡的FT谱(图片经文献[102]允许转载, 版权归2020 American Association for the Advancement of Science所有)

Figure 20.  The Fourier transform spectra of the autocorrelation function of the VBM, the CBM, and the defect state energies (Reprinted with permission from Ref. [102]. Copyright 2020 American Association for the Advancement of Science)

图 21  单层MoSe2在不同氧化物衬底上的超快光子动力学　(a) 界面电声耦合示意图; (b) 在不同衬底上单层MoSe2的光生载流子动力学(图片经文献[106]允许转载)

Figure 21.  Ultrafast photocarrier dynamics of monolayer MoSe2 on different oxide substrates: (a) Illustration of interfacial electron–phonon (e–ph) coupling; (b) photocarrier dynamics of monolayer MoSe2 on different substrates (Reprinted with permission from Ref. [106])

图 22  在HfO2, Al2O3和SiO2衬底上单层MoSe2中e-h复合动力学　(a)—(c) 光激发电子在MoSe2上的空间分布随时间的变化; (d)—(i) CBM, VBM附近能级能量随时间的演化及其对应的FT谱, 其中红色箭头标记了主要的声子模式和对应的波数, 黑色区域和粉红色区域分别代表体系声子的总态密度以及在MoSe2上的投影(图片经文献[106]允许转载)

Figure 22.  The nonadiabatic molecular dynamics of e–h recombination in monolayers MoSe2 on HfO2, Al2O3 and SiO2 substrates: (a)–(c) Time-dependent electron localization on CBM of MoSe2; (d)–(i) Time evolutions of the energy states and their corresponding FT spectra, where red arrows have marked main phonon modes and its corresponding wavenumbers. The whole phonon DOS of the MoSe2-oxide substrate systems (black area) and the projection from MoSe2 (pink area) are also plotted in panels (g)–(i) (Reprinted with permission from Ref. [106])

图 23  (a) Cu掺杂单层MoS2体系自旋极化的能带结构和投影态密度; (b) Cu掺杂单层MoS2的杂质态轨道空间分布. 图(a)中的箭头显示了自旋极化的空穴在杂质态之间进行弛豫的过程(图片经文献[107]允许转载, 版权归2017 American Physical Society所有)

Figure 23.  (a) Spin-polarized band structure and the projected density of states; (b) orbital spatial distribution of the Cu doped MoS2. The process of spin hole relaxation within the impurity states is indicated by the arrow in panel (a) (Reprinted with permission from Ref. [107]. Copyright 2017 American Physical Society)

图 24  在100和50 K的不同温度下, 杂质态本征能量的含时演化　((a), (c))及其自关联函数的FT谱((b), (d)), 以及每一个声子本征振动模式的空间局域度分别在Cu杂质原子和MoS2上的投影 ((e), (f))(图片经文献[107]允许转载, 版权归2017 American Physical Society所有)

Figure 24.  (a), (c) Time-dependent evolution of the energy of the impurity states; (b), (d) FT spectra to the autocorrelation function of the energy evolutionat 100 and 50 K, respectively; (e), (f) spatial localization of each normal phonon mode projected on the Cu impurity and MoS2 host, respectively (Reprinted with permission from Ref. [107]. Copyright 2017 American Physical Society)

图 25  50和100 K环境温度下的光激发自旋极化空穴的动力学. 图 (a), (c) 和 (b), (d) 分别是空穴的初始激发在杂质态1和杂质态2上的情况. 每个图的上半部分所示为空穴的平均能量以及空穴在每一个杂质态上的布居数; 下半部分所示为能量弛豫过程中的AD和NA过程分别做的贡献(图片经文献[107]允许转载, 版权归2017 American Physical Society所有)

Figure 25.  Dynamics of a photogenerated hole at 50 and 100 K, respectively. The averaged energy of the hole and the population on each impurity state are shown in the upper panel, and the AD and NA contributions to the energy relaxation are shown in the lower panel with the initial state specified at the impurity state 1 ((a), (c)) and 2 ((b), (d)) (Reprinted with permission from Ref. [107]. Copyright 2017 American Physical Society)

图 26  GW+rtBSE程序流程图

Figure 26.  Work chart of GW+rtBSE package.

图 27  MoS2自旋谷激子动力学示意图　(a) MoS2的六个自旋谷; (b)不同的激子弛豫通道; (c)8种能量最低的亮、暗激子(图片经文献[117]允许转载, 版权归2021 American Association for the Advancement of Science所有)

Figure 27.  Schematic showing spin-valley dynamics in TMD systems: (a) Band structure at the band edges near K and K'; (b) intervalley bright exciton transition and bright-to-dark exciton transition processes are shown; (c) e-h pairs involved during the exciton dynamics (Reprinted with permission from Ref. [117]. Copyright 2021 American Association for the Advancement of Science)

图 28  MoS2材料中的含时激子动力学　(a) K谷亮激子X1激发之后, 不同激子态占据数随时间的变化; (b) 没有交换相互作用的情况下, K谷亮激子X1激发之后, 不同激子态占据数随时间的变化; 非绝热耦合矩阵中电子空穴(c)库仑相互作用(W), (d)交换相互作用(v), (e)自旋轨道耦合(SOI)以及(f)电声耦合(e-ph)的贡献(图片经文献[117]允许转载, 版权归2021 American Association for the Advancement of Science所有)

Figure 28.  Dynamics results and nonadiabatic couplings: (a), (b) Time evolution of the population on X1 to X8 (a) with and (b) without the e-h interaction W and v in the NAMD simulation. The time-dependent valley polarization is inserted in panel (a). (c)–(f) Averaged NACs contributed by W, v, SOI, and e-ph, respectively (Reprinted with permission from Ref. [117]. Copyright 2021 American Association for the Advancement of Science)

图 29  材料中激子弛豫的不同通道与物理机制示意图(图片经文献[117]允许转载, 版权归2021 American Association for the Advancement of Science所有)

Figure 29.  Schematic map of the exciton dynamics channels and the correlated mechanisms (Reprinted with permission from Ref. [117]. Copyright 2021 American Association for the Advancement of Science)

•  Citation:
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• Abstract views:  1530
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##### Publishing process
• Received Date:  02 April 2021
• Accepted Date:  07 May 2021
• Available Online:  07 June 2021
• Published Online:  05 September 2021

## Investigation of ab initio nonadiabatic molecular dynamics of excited carriers in condensed matter systems

###### Corresponding author: Zhao Jin, zhaojin@ustc.edu.cn
• 1. Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, ICQD/Hefei National Laboratory for Physical Sciences at Microscale, Department of Physics, University of Science and Technology of China, Hefei 230026, China
• 2. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh 15260, America

Abstract: The excited state dynamics is always an important and challenging problem in condensed matter physics. The dynamics of excited carriers can have different relaxation channels, in which the complicated interactions between different quasi-particles come into play collectively. To understand such ultrafast processes, the ab initio investigations are essential. Combining the real-time time-dependent density functional theory with fewest switches surface hopping scheme, we develop time-dependent ab initio nonadiabatic molecular dynamics (NAMD) code Hefei-NAMD to simulate the excited carrier dynamics in condensed matter systems. Using this method, we investigate the interfacial charge transfer dynamics, the electron–hole recombination dynamics, and the excited spin-polarized hole dynamics in different condensed matter systems. Moreover, we combine ab initio nonadiabatic molecular dynamics with GW plus real-time Bethe-Salpeter equation for the spin-resolved exciton dynamics. We use it to study the spin-valley exciton dynamics in MoS2. It provides a powerful tool for exciton dynamics in solid systems. The state-of-the-art NAMD studies provide a unique insight into a understanding of the ultrafast dynamics of the excited carriers in different condensed matter systems on an atomic scale.

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