凝聚态体系中激发态载流子动力学研究

郑镇法; 蒋翔; 褚维斌; 张丽丽; 郭宏礼; 赵传寓; 王亚南; 王傲雷; 郑奇靖; 赵瑾

doi:10.7498/aps.70.20210626

摘要

激发态动力学是凝聚态物理中至关重要且富有挑战的科学问题, 不仅需要从时间、空间、能量和动量等多个维度来描述, 同时还需要考虑各种准粒子的相互作用以及多体效应. 本文聚焦凝聚态体系激发态动力学的理论和应用研究, 结合含时密度泛函、GW-BSE与面跳跃方法, 发展了激发态动力学第一性原理计算软件Hefei-NAMD, 构建了可以同时从时间、空间、动量、能量、自旋等多个维度研究凝聚态体系激发态动力学的理论和程序框架, 并实现了自旋分辨的GW+ real-time BSE(GW+rtBSE)激子动力学. 利用这套方法, 研究了凝聚态体系激发态动力学的许多问题, 包括界面电荷转移动力学、电子空穴复合动力学以及二维TMD材料的谷激子动力学等. 这些研究从第一性原理计算的角度, 模拟激发态载流子在实空间、能量空间和动量空间的含时演化, 为凝聚态体系的激发态动力学及准粒子耦合过程提供了深刻细致的理解.

关键词:

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.

Keywords:

作者及机构信息

1.
中国科学技术大学物理系, 合肥微尺度物质科学国家研究中心国际功能材料量子设计中心,中科院强耦合量子材料物理重点实验室, 合肥　230026

2.
匹兹堡大学物理与天文系, 匹兹堡　15260

通信作者: 郑奇靖, zqj@ustc.edu.cn ; 赵瑾, zhaojin@ustc.edu.cn

作者简介:

郑奇靖, 2009年毕业于中国科学技术大学物理系, 2016 年于中国科学技术大学物理系获得博士学位. 2016 年6 月至2018年9月在中国科学技术大学微尺度物质科学国家研究中心从事博士后研究. 2018年10月至今在中国科学技术大学物理系任特任副研究员, 主要致力于第一性原理计算研究凝聚态体系中激发态动力学的方法发展及应用, 参与开发了第一性原理激发态动力学计算软件Hefei-NAMD. 博士毕业以来共发表SCI文章29篇, 以第一或通讯作者发表14篇SCI文章, 包括8篇 J. Phys. Chem. Lett., 3 篇 Phys. Rev. B, 2 篇 Nano Lett., 1 篇 J. Am. Chem. Soc., 1 篇JPCM, 1 篇综述文章 WIREs Comput. Mol. Sci

赵瑾, 1998 年毕业于中国科学技术大学物理系, 2003 年于中国科学技术大学理化科学中心获得博士学位(指导教师: 侯建国院士, 杨金龙院士). 2004 年3 月起在美国匹兹堡大学Hrvoje Petek教授组内工作. 2008 年8 月起成为匹兹堡大学物理系研究助理教授, 2010 年初成为中国科学技术大学物理系及合肥微尺度国家实验室教授. 赵瑾教授的研究小组关注于利用第一性原理计算激发态动力学, 发展了具有独立知识产权、自主可控的激发态动力学第一性原理计算软件Hefei-NAMD, 初步构建了可以同时从时间、空间、动量、能量、自旋等多个维度研究凝聚态体系激发态动力学的理论和程序框架, 率先实现了自旋分辨的real-time GW+BSE (GW+rtBSE)激子动力学. 共发表SCI文章121篇, 作为第一/理论第一/通讯作者共发表Science 3篇, Chem. Rev. 2篇, Nat. Photo. 1篇, Sci. Adv. 2篇, Nat. Commun. 1篇, Phys. Rev. Lett. 5篇, JACS 3篇等, 全部论文他引次数4000余次, H因子35

基金项目: 国家自然科学基金(批准号: 11974322, 11620101003)和国家重点研发计划(批准号: 2017YFA0204904)资助的课题

Authors and contacts

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

Corresponding author: Zheng Qi-Jing, zqj@ustc.edu.cn ; Zhao Jin, zhaojin@ustc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974322, 11620101003) and the National Key R&D Program of China (Grant No. 2017YFA0204904)

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施引文献

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)

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

下载: 全尺寸图片幻灯片

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)

Fig. 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)

下载: 全尺寸图片幻灯片

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Ti_5C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)

Fig. 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)

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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)

Fig. 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)

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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)

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

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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图 16 (a) 纯净的BP单层, (b) P_v, (c) P_int和(d) P_ad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P_ini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)

Fig. 16. e–h recombination dynamics in (a) pristine BP monolayer, (b) P_v, (c) P_int, and (d) P_ad 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)

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图 17 (a) 纯净的BP单层, (b) P_v, (c) P_int和(d) P_ad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)

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

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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])

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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)

Fig. 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])

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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图 26 GW+rtBSE程序流程图

Fig. 26. Work chart of GW+rtBSE package.

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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)

Fig. 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)

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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)

Fig. 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)

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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)

Fig. 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)

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