Letter Cite This: J. Phys. Chem. Lett. 2017, 8, 5771-5778
pubs.acs.org/JPCL
Disparity in Photoexcitation Dynamics between Vertical and Lateral MoS2/WSe2 Heterojunctions: Time-Domain Simulation Emphasizes the Importance of Donor−Acceptor Interaction and Band Alignment Yating Yang, Wei-Hai Fang,* and Run Long* College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing 100875, People’s Republic of China S Supporting Information *
ABSTRACT: Two-dimensional transition metal dichalcogenides (TMDs) heterojunctions are appealing candidates for optoelectronics and photovoltaics. Using time-domain density functional theory combined with nonadiabatic (NA) molecular dynamics, we show that photoexcitation dynamics exhibit a significant difference in the vertical and lateral MoS2/WSe2 heterojunctions arising from the disparity in the donor−acceptor interaction and fundamental band alignment. The obtained electron transfer time scale in the vertical heterojunction shows excellent agreement with experiment. Hole transfer proceeds 1.5 times slower. The electron− hole recombination is 3 orders of magnitude longer than the charge separation, which favors solar cell applications. On the contrary, the lateral heterojunction shows no band offsets steering charge separation. The excited electron is localized at the interface that attracts holes to form an exciton-like state due to Coulomb interaction, suggesting potential applications in light-emitting devices. The coupled electron and hole wave functions increase NA coupling and the coherence time, accelerating electron−hole recombination by a factor of 3 compared with the vertical case. The atomistic studies advance our understanding of the photoinduced charge−phonon dynamics in TMDs heterojunctions.
T
demonstrated that the WS2/WSe2 heterojunction can form lateral p−n diodes with excellent current rectification behavior and photocurrent generation characteristics.40 Then, lateral TMDs heterojunctions have attracted increasing attention, and many other structures have been innovated.40−42 Due to efficient charge separation and slow recombination observed in the vertical heterojunctions43−45 and mechanical stability together with unique electronic properties of the lateral heterostructures,46−49 researchers put great efforts into controlled growth of high-quality films dedicated to fabrication of novel optoelectronic, photovoltaic, photocatalytic, and electronic devices.40,42,46,50 Photoinduced charge and energy flow play key roles in determining the performance of such devices and draw considerable attention of experiments.51,52 Recently, Loh and co-workers reported that electron transfer from WSe2 into MoS2 occurs in 470 fs in a type-II MoS2/WSe2 vertical heterojunction,53 using time-resolved photoluminescence spectra. Other experiments reported ultrafast electron and hole transfer and extremely slow recombination at a MoS2/ MoSe2 vertical heterojunction,54 ensuing that this structure is an excellent candidate for photovoltaic solar cells. We rationalize that quantum coherence facilities charge delocalization and transfer in the MoS2/MoSe2 vdW heterojunctions by atomistic nonadiabatic molecular dynamics (NAMD) simu-
wo-dimensional (2D) transition metal dichalcogenides (TMDs)1−5 have attracted considerable interest due to their excellent transport, electronic, and optical properties, making them hold great potential for electronic devices,6−16 nonlinear optics,17 photovoltaics,4,18,19 catalysis,20,21 energy storage, and conversion.20,22,23 Layered TMDs have strong covalent bonds within each layer and possess weak van der Waals (vdW) interactions between layers. Such mechanic properties allow one to easily fabricate monolayer and few-layer TMDs by mechanical exfoliation.24 Monolayer TMDs are typically direct bandgap semiconductors and have strong light− matter interactions. Increasing the number of layers, the bandgap occurs a direct-to-indirect transition and inevitably degrades the light harvesting ability. Interestingly, dozens of experiments25,26 and theoretical calculations27 demonstrate that most vertical TMDs heterojunctions not only maintain monolayer pristine properties28−30 due to the weak interlayer vdW interaction but also bring up many novel properties.31−33 For instance, vertical vdW WSe2/MoS2 and TMDs/graphene heterojunctions show interesting gate-controllable optoelectronic responses and electroluminescence as well as high photocatalytic activity under visible-light irradiation.34−37 However, vertical heterojunctions are chemically unstable under high temperature and other extreme conductions due to the weak interlayer interaction.38 Inspired by synthesis of BNC-based 2D lateral heterostructures,39 Duan and co-workers prepared the first 2D lateral MoS2/MoSe2 and WS2/WSe2 heterojunctions using a lateral heteroepitaxial approach and © XXXX American Chemical Society
Received: October 19, 2017 Accepted: November 11, 2017 Published: November 12, 2017 5771
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
Letter
The Journal of Physical Chemistry Letters lations.55 Although many lateral TMDs heterojunctions including MoS2/WSe2 have been successfully synthesized,41,46 no experiment reports the photoexcitation charge dynamics in these systems yet. One may wonder what difference there is in the photoinduced charge and energy dynamics in both the vertical and lateral heterojunctions due to the presence of weak vdW interaction and strong covalent bonding, respectively. Therefore, an atomistic time-domain is called to study the photogenerated charge separation and recombination in real time in both vertical and lateral MoS2/WSe2 heterojunctions and to provide mechanistic understanding of ultrafast charge carrier dynamics for rational design of high-performance 2D electronic, optoelectronic, and photovoltaic devices. In this Letter, we model photoinduced electron and hole transfer in the vertical MoS2/WSe2 heterojunction as well as charge recombination in both the vertical and lateral interfaces, directly mimicking the time-resolved ultrafast pump−probe spectroscopy experiment,53 using quantum−classical NAMD combined with time-domain density functional theory.55−58 Our calculations demonstrate that the vertical MoS2/WSe2 heterojunction shows a type-II band alignment, while no energy offsets are observed in the lateral case between the conduction band minimum (CBM) and valence band maximum (VBM) of MoS2 and WSe2. The calculated 304 fs electron transfer time scale in the vertical MoS2/WSe2 heterojunction agrees well with the experiment.53 The electron transfer proceeds faster than hole transfer due to stronger NA coupling and interacting with more and higher vibrational modes. The electron−hole recombination proceeds 3 orders of magnitude slower than charge separation because electron and hole states are localized on two different materials and because of fast quantum decoherence. The calculated time scale is comparable with other vdW TMDs heterojunctions.54,59,60 The long-lived charge-separated state at the interface suggests that vertical heterojunctions are excellent candidates for photovoltaic solar cells. In contrast, the electron is localized at the interface rather than the overall whole monolayer in the lateral MoS2/WSe2 heterojunction. The localized electron-attracting hole via Coulomb interaction forms an interfacial exciton-like state that favors light emission. The coupled electron and hole states enhance NA electron−phonon coupling and increase quantum coherence time, accelerating electron−hole recombination by a factor of 2.5 with respect to the vertical heterojunction. Both the vertical and lateral MoS2/WSe2 heterojunctions are represented by a same size simulation cell that contains 12atom MoS2 and 12-atom WSe2. The vertical heterojunction is constructed as described in ref 61 while the lateral heterojunction is built based on the strategy adopted in ref 62 that gives rise to a negligible lattice mismatch between the two materials. A vacuum layer of 15 Å is applied perpendicular to the nonperiod direction to screen off the spurious interactions between periodic layers in both the vertical and lateral MoS2/WSe2 heterojunctions. The NAMD simulations are performed with the fewest switching surface hopping (FSSH) technique63−65 implemented within the time-dependent Kohn−Sham density functional theory,56,57 with the classical path approximation (CPA) for the purpose of reducing the computational costs at the ab initio level. The heavier and slower nuclei are described classically, while the lighter and faster electrons are treated quantum mechanically. The quantum decoherence correction66 is necessary for the study of electron−hole recombination because of the much shorter
decoherence time compared with the quantum transition time, which occurs on a sub-500 ps time scale.67−69 The approach has been applied to study of photoexcitation dynamics in a broad range of systems, including black phosphorus (BP),70 BP/MoS2,71 a MoS2/MoSe2 heterojunction,60 TiO2 sensitized with semiconducting nanoparticles,72 and a superconductor.73 A detailed description of the method is described in refs 60 and 70−73. The geometry optimization, electronic structure, and adiabatic MD simulations are carried out using the Vienna ab initio simulation package (VASP).74,75 The generalized gradient approximation (GGA) of the Perdew−Burke−Ernzerhof (PBE) electronic exchange−correlation functional,76 projector-augmented wave (PAW) pseudopotentials,77 and a 400 eV energy cutoff were used. The vdW interaction was introduced to stabilize the system during geometry optimization, and adiabatic MD was described by Grimme’s DFT-D3 method.78,79 The geometry optimization was performed with the Monhorst−Pack80 12 × 12 × 1 k-point mesh and a more dense 31 × 31 × 1 k-point mesh for electronic structure calculations. The optimization stopped until the calculated Hellmann− Feynman force was less than 0.05 eV/Å. The system was then heated to 300 K according to the experiment by repeated velocity rescaling. Then, 6 ps adiabatic MD trajectories in the microcanonical ensemble were generated with a 1 fs time step. To simulate charge transfer and electron−hole recombination, 1000 geometries were randomly selected from these adiabatic trajectories and were used for the initial states for NAMD with a 1 attosecond electronic time-step. Figure 1a shows the energy levels involved in the photoinduced charge separation and recombination at the
Figure 1. (a) Electronic energy levels involved in the photoinduced charge separation due to ① either electron transfer or hole transfer at the MoS2/WSe2 interface. Following charge separation, electron and hole recombination occurs ②. Side views of the (b) vertical and (c) lateral MoS2/WSe2 heterojunctions.
MoS2/WSe2 heterojunction. Absorption of a photon by WSe2 leads to electron transfer from WSe2 to MoS2, while excitation of MoS2 causes hole transfer from MoS2 to WSe2, ①. This is the key to solar cells because only excitons dissociating into free electrons and holes can take part in the photoelectric effect. After charge separation, the electron and hole can recombine at the interface, ②. Generally, electron and hole states localized on two different materials favor achieving a long-lived excited-state lifetime and are beneficial for photovoltaic solar cells. On the contrary, an exciton-like state facilitates light emission. Figure 1b,c illustrates the side view of the vertical and lateral MoS2/ WSe2 simulation cells, respectively. Figure 2a,c demonstrates the projected density of states (PDOS) of both the vertical and lateral MoS 2 /WSe 2 heterojunctions calculated using a specific snapshot selecting from a 6 ps trajectory at 300 K, separated into the contributions 5772
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
Letter
The Journal of Physical Chemistry Letters
Figure 2. PDOS of the vertical (a) and the lateral (c) MoS2/WSe2 heterojunctions calculated using a representative geometry taken from a MD trajectory at 300 K. Charge densities of the donor and acceptor states for the electron and hole transfer are shown in (b) vertical and (d) lateral heterojunctions, respectively. In the vertical heterojunction, the electron donor state is significantly delocalized between WSe2 and MoS2, facilitating electron transfer due to forming coherent superpositions between the two materials. The electron acceptor is localized on MoS2. On the contrary, both the hole donor and acceptor states are localized on MoS2 and WSe2 due to large donor−acceptor energy offsets in this case. Interestingly, there are no energy offsets between the CBM and VBM of the two materials in the lateral heterojunction. The electron state is localized at the interface and is able to attract the hole to form an exciton-like state due to Coulomb interaction. The exciton facilitates light emission. To confirm this observation, a more rigorous GW method is applied to repeat the electronic structure calculation and reproduce the same band alignment to the PBE level, evidenced by the PDOS shown in Figure S1 of the SI.
becomes negligible and the charge separation is steered by NA electron−phonon coupling. The above discussion focuses on the key electronic states participating in electron and hole transfer. For electron−hole recombination, the CBM and VBM of the vertical MoS2/WSe2 heterojunction constitute the initial and finial states that are localized on the MoS2 and WS2, respectively, Figure 2b. The decoupled electron and hole wave functions weaken their interactions and are inclined to suppress electron−hole recombination. Interestingly, the electron state is primarily localized on the interfacial region in the lateral MoS2/ WSe2 heterojunction due to formation of strong in-plane W−S covalent bonding, right-hand side of Figure 2d, while the hole state is mostly localized on the WS2 closer to the interface, lefthand side of Figure 2d. Generally, a localized electron can attract a hole to the interface via Coulomb interaction that leads to formation of an exciton-like state and favors light emission. Therefore, we only investigate electron and hole transfer in the vertical heterojunction while studying electron−hole recombination in both cases. Vibrational motions induce charge transfer and lead to energy losses to heat. Figure 3 presents the spectral densities computed from Fourier transform (FT) of the fluctuations of the energy gap between initial and final states of the vertical MoS2/WSe2 heterojunction. Figure 3a shows the FT of energy gap fluctuations between the MoS2 and WSe2 CBMs, while Figure 3b displays the FT of energy gap fluctuations between MoS2 and WSe2 VBMs. They characterize the phonon modes participating in electron and hole transfer, respectively. The phonons involved in the electron transfer couple to more and higher frequencies, compared to hole transfer. NA coupling is proportional to wave function overlap ⟨φ̃ m|∇R|φ̃ k⟩ and to velocities of nuclei dR/dt. Therefore, faster and more modes create larger NA coupling and accelerate electron transfer. The dominant peak at 180 cm−1 for electron transfer can be assigned to the in-plane W−Se mode at 180 cm−1.81 The 400 cm−1 peak is associated with the out-of-plane S−Mo A1g mode.82 The side peaks at around 100, 240, and 500 cm−1 can be attributed to complex modes of WSe2 and MoS2.83 The very high frequency mode at 680 cm−1 originates from the overtone of these lower frequencies. MoS2 modes contributing to electron transfer is reasonable because the electron initial state is significantly delocalized between donor WSe2 and acceptor MoS2, Figure 2b. Hole transfer couples exclusively to
from WSe2 (black line) and MoS2 (red line) monolayers. The charge densities of the key electron and hole orbitals are shown in Figure 2b,d. The vertical arrows pointing from the bottom panel to the top panel correspond to the energies of these states. Figure 2a shows the formation of a type-II heterojunction in the vertical MoS2/WSe2. The canonically averaged CBM and VBM offsets are 0.2 and 0.3 eV, indicating that energy is lost to vibrations of 0.2 and 0.3 eV during electron and hole transfer processes, respectively. Interestingly, Figure 2c shows that no energy offsets are observed between CBMs and VBMs of the lateral heterojunction using the PBE functional. To test the validity of the PBE calculation, a more rigorous GW method is used to repeat the PDOS calculation for the vertical MoS2/WSe2 heterojunction and reproduces the same result, evidenced by the PDOS shown in Figure S1 of the Supporting Information (SI). In order to test whether the reported band alignment of the lateral heterojunction is robust with respect to the size of the simulation cell, we performed additional electronic structure calculations for 96-atom lateral heterojunction using PBE functional.76 The simulation cell and PDOSs are shown in Figure S2 of SI. The band alignment was very similar to the results obtained with a small simulation cell at both the PBE and GW levels, Figures 2c and S1, indicating that the 24-atom simulation cell is sufficient to characterize the pristine physical properties of lateral heterojunctions fabricated experimentally.41 Generally, the wave functions mixing between the initial and final states reflects the NA electron−phonon coupling and affects charge dynamics. For the vertical heterojunction, the electron donor state is shared by MoS2 and WSe2, and the electron acceptor state is localized on the MoS2, Figure 2b. The situation favors electron and hole wave function overlap and enhances NA coupling. On the contrary, hole donor and acceptor wave functions are localized on each material respectively, decoupling each other and reducing NA coupling. One should note that strong donor−acceptor coupling facilitates charge separation but does not guarantee this process to be ultrafast. Quantum coherence is another important factor affecting charge separation.60 Long coherence time favors fast dynamics, while short coherence time retards dynamics. Typically, charge separation happens within the manifold of electronic states in a small energy range that has strong electron coupling. As a result, the influence of quantum coherence 5773
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
Letter
The Journal of Physical Chemistry Letters
relaxation cannot be fitted properly by a function combining one or two exponents or Gaussians due to the low charge density within a significant energy range involved in hole transfer. The calculated 304 fs electron transfer time is in excellent agreement with the experimentally measured 470 fs time scale in the vertical vdW MoS2/WSe2 heterojunction,53 while hole transfer proceeds a bit slower than electron transfer due to several reasons. The electron acceptor MoS2 density is higher than the hole acceptor WSe2 density, Figure 2a. The donor−acceptor interaction for the electron transfer is stronger than that for the hole transfer, as verified by the significantly delocalized electron state between WSe2 and MoS2 vs the localized hole state on MoS2, the very right-hand side and lefthand side of Figure 2b. Additionally, the calculated averaged absolute NA coupling for the electron transfer is larger than that for the hole transfer, 7.37 vs 4.30 meV. The same reasons rationalize that the electron energy relaxation is faster than the hole energy relaxation, Figure 4c,d. The slow hole energy relaxation maintains the “hot” hole for a relatively long- time and benefits hole transport. In addition to charge separation, electron−hole recombination is another key to the performance of modern electronic and photovoltaic devices. Figure 5a,b characterizes the vibrational modes, computed from FT of the fluctuations of the CBM−VBM energy gap in the vertical and lateral MoS2/ WSe2 heterojunctions, that drive the electron−hole recombination. For the vertical heterojunction, Figure 5a shows that the electronic degrees of freedom couple primarily to frequencies of 250 and 410 cm−1, which correspond to the Raman-active inplane E2g1 mode of W−Se at 250.1 cm−184 and the out-of-plane A1g mode of Mo−S at 402.3 cm−1.84 For the lateral heterostructure, Figure 5b illustrates that the major peak at 250 cm−1 is also presented that creates the largest NA coupling because in-plane atomic motions alter wave function localization.84 The second main peak at 210 cm−1 may be associated with the A1g(M) mode of W−S at 231 cm−185 due to formation of new W−S chemical bonds at the interface. This mode is significantly important because it modulates interfacial geometry and localizes the wave functions, right panel of Figure 2d, enhancing the NA electron−phonon coupling further. Figure 5c demonstrates the nonradiative electron− hole recombination, which constitutes the major pathway for charge and energy losses. The calculated bandgap of 0.86 eV of the vertical MoS2/WSe2 heterojunction using the PBE functional was scaled to an experimental value of 1.14 eV.86 The same constant is added on the calculated bandgap of 1.49 eV of the lateral heterojunction to scale the gap to 1.78 eV, assuming that DFT has an identical error for both systems. The times shown in Figure 5c are obtained using exponential fitting
Figure 3. Spectral density computed from FT of the fluctuations of the energy gaps between the donor and acceptor states for (a) electron and (b) hole transfer in the vertical MoS2/WSe2 heterojunction. Electrons couple to a broad range of phonon modes ranging from lowto high-frequency, while holes couple exclusively to the 260 cm−1 mode. More and higher-frequency phonons create larger NA coupling, leading to faster electron transfer than hole transfer.
the 260 cm−1 vibrations. This frequency can be assigned to the out-of-plane S−Mo A1g mode at 260.1 cm−1.53 Figure 4 shows the dynamics of the photoinduced charge transfer and the corresponding intraband energy relaxation in
Figure 4. Charge separation dynamics in the vertical MoS2/WSe2 heterojunction. (a,b) Time evolution population of the electron and hole donor states. (c,d) Time evolution decay of the electron and hole energies. The data shown in (a−c) are fitted exponentially,
( t)
( t)
f (t ) = a ∗ exp − τ + b. The hole energy decay (d) exhibits complex
f (t ) = exp − τ . The inset of Figure 5c gives the pure-
behavior due to a relatively low density of states near the band edge, Figure 2a. It cannot be fitted by a simple function. The charge transfer proceeds faster than the energy decay. The electron transfer is faster than hole transfer due to a higher density of acceptor states and larger NA coupling.
dephasing functions for the lateral and vertical heterojunctions calculated from optical response theory.87,88 The times shown ⎡ t 2⎤ in the inset are fitted by Gaussian, f (t ) = −0.5⎢exp − τ ⎥. ⎣ ⎦ The decoherence correction is extremely important for electron−hole recombination because loss of coherence takes places within sub-10 fs and is much faster than quantum transition.89−91 The recombination time in the vertical MoS2/ WSe2 heterojunction is 2.5 times faster than that in the lateral heterojunction due to the following factors. The calculated absolute average NA coupling is 1.71 and 2.05 meV for the vertical and lateral MoS2/WSe2 heterojunctions. The larger NA
( )
the vertical MoS2/WSe2 heterojunction. Panels (a) and (b) give the charge transfer, and panels (c) and (d) show the energy decay. Electron transfer is a little bit faster than hole transfer, and the energy decay is always slower than charge transfer. The time constants reported in Figure 4a−c are obtained by
( t)
exponential fitting, f (t ) = a ∗exp − τ + b. The hole energy 5774
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
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The Journal of Physical Chemistry Letters
Figure 5. Spectral density computed from FT of the fluctuations of the CBM−VBM energy gaps in the (a) vertical and (b) lateral MoS2/WSe2 heterojunctions for electron−hole recombination. (c) Electron−hole recombination for the vertical and lateral MoS2/WSe2 heterojunction. The inset of (c) shows the pure-dephasing functions.
like state to favor light emission, accelerating the electron−hole recombination by a factor of 2.5 compared with the vertical case. Efficient charge separation and slow electron−hole recombination suggest that the vertical MoS2/WSe2 heterojunctions hold great potential for photovoltaic and photocatalytic applications, while the lateral MoS2/WSe2 heterojunctions are excellent candidates for light-emitting devices due to the exciton-like state being a benefit for light emission. The reported simulations advance our understanding of the photoinduced charge and energy dynamics in the TMDs heterojunctions and provide valuable guidance for design of the TMD-related modern photovoltaics and optoelectronics via rationally controlled growth of either vdW or chemical bonding heterojunctions.
coupling in the lateral heterojunction is because the wave functions of initial and final states are localized on the interfacial region, Figure 2d. On the contrary, electron and hole wave functions are localized on the MoS2 and WSe2 monolayers, respectively, in the vertical MoS2/WSe2 heterojunction, the two middle panels of Figure 2c. Higher frequencies in the vertical case lead to faster loss of coherence than the lateral case, 6.8 vs 9.1 fs. NA coupling and decoherence are two major factors to determine the electron−hole recombination rate. The small NA coupling and fast decoherence beat the small bandgap, which delays electron−hole recombination in the vertical MoS 2/WSe2 heterojunction. A long-lived excited electron lifetime exhibited in the vertical MoS2/WSe2 heterojunction minimizes energy losses and helps to maintain a high open-circuit voltage in a photovoltaic solar cell, while the exciton-like state in the lateral MoS2/WSe2 heterojunction favors light emission for design of light-emitting devices. In summary, we have investigated the photoexcitation charge transfer and energy relaxation dynamics in the vertical and lateral MoS2/WSe2 heterojunctions using time-domain density functional theory combined with NAMD. The simulations show that charge occurs rapid separation and slow recombination at the vertical interface due to formation of a type-II heterojunction, while only electron−hole recombination takes place in the vertical case due to the absence of band edge offsets. The calculated subpicosecond electron transfer time scale in the vertical MoS2/WSe2 heterojunction, in excellent agreement with the experiment, proceeds 1.5 times faster than hole transfer due to the larger NA coupling, the higher density of electron acceptor states, and more phonon modes involved. The same factors are responsible for the faster electron energy decay with respect to the hole transfer. Electron−hole recombination is much slower than charge transfer due to fast loss of quantum coherence, a wide energy gap, and small NA coupling stemming from electron and hole states localized on two different materials. On the contrary, the electron state is localized at the interface in the lateral MoS2/WSe2 heterojunction that attracts the hole due to Coulomb interaction. The coupled electron and hole enhances NA electron−phonon coupling due to formation of new W−S chemical bonds at the interface, increases quantum coherence, and forms an exciton-
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b02779. PDOS of the small vertical MoS2/WSe2 heterojunction obtained using the GW method and the large vertical MoS2/WSe2 simulation cell together with PDOS calculated using the PBE functional (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (W.-H.F.). *E-mail:
[email protected] (R.L.). ORCID
Wei-Hai Fang: 0000-0002-1668-465X Run Long: 0000-0003-3912-8899 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to the National Science Foundation of China, Grant No. 21573022, 21688102, 21590801, and 21421003. R.L. acknowledges the Recruitment Program of Global Youth Experts of China, the Beijing Normal University Startup Package, and the Fundamental Research Funds for the Central Universities. 5775
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
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The Journal of Physical Chemistry Letters
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(21) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L.-J.; Loh, K. P.; Zhang, H. The Chemistry of Two-Dimensional Layered Transition Metal Dichalcogenide Nanosheets. Nat. Chem. 2013, 5, 263−275. (22) Sun, Y.; Gao, S.; Xie, Y. Atomically-Thick Two-Dimensional Crystals: Electronic Structure Regulation and Energy Device Construction. Chem. Soc. Rev. 2014, 43, 530−546. (23) Yang, S.; Gong, Y.; Zhang, J.; Zhan, L.; Ma, L.; Fang, Z.; Vajtai, R.; Wang, X.; Ajayan, P. M. Exfoliated Graphitic Carbon Nitride Nanosheets as Efficient Catalysts for Hydrogen Evolution under Visible Light. Adv. Mater. 2013, 25, 2452−2456. (24) Coleman, J. N.; Lotya, M.; O’Neill, A.; Bergin, S. D.; King, P. J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R. J.; et al. TwoDimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials. Science 2011, 331, 568−571. (25) Fang, H.; Battaglia, C.; Carraro, C.; Nemsak, S.; Ozdol, B.; Kang, J. S.; Bechtel, H. A.; Desai, S. B.; Kronast, F.; Unal, A. A.; et al. Strong Interlayer Coupling in Van Der Waals Heterostructures Built from Single-Layer Chalcogenides. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 6198−6202. (26) Lui, C. H.; Ye, Z.; Ji, C.; Chiu, K.-C.; Chou, C.-T.; Andersen, T. I.; Means-Shively, C.; Anderson, H.; Wu, J.-M.; Kidd, T.; et al. Observation of Interlayer Phonon Modes in Van Der Waals Heterostructures. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 165403. (27) Kumar, H.; Er, D.; Dong, L.; Li, J.; Shenoy, V. B. Elastic Deformations in 2D Van Der Waals Heterostructures and Their Impact on Optoelectronic Properties: Predictions from a Multiscale Computational Approach. Sci. Rep. 2015, 5, 10872. (28) Shi, J.; Ma, D.; Han, G.-F.; Zhang, Y.; Ji, Q.; Gao, T.; Sun, J.; Song, X.; Li, C.; Zhang, Y.; et al. Controllable Growth and Transfer of Mono Layer MoS2 on Au Foils and Its Potential Application in Hydrogen Evolution Reaction. ACS Nano 2014, 8, 10196−10204. (29) Xiao, D.; Liu, G.-B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides. Phys. Rev. Lett. 2012, 108, 196802. (30) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (31) Lopez-Sanchez, O.; Alarcon Llado, E.; Koman, V.; Fontcuberta i Morral, A.; Radenovic, A.; Kis, A. Light Generation and Harvesting in a Van Der Waals Heterostructure. ACS Nano 2014, 8, 3042−3048. (32) Lin, Y.-C.; Ghosh, R. K.; Addou, R.; Lu, N.; Eichfeld, S. M.; Zhu, H.; Li, M.-Y.; Peng, X.; Kim, M. J.; Li, L.-J.; et al. Atomically Thin Resonant Tunnel Diodes Built from Synthetic Van Der Waals Heterostructures. Nat. Commun. 2015, 6, 7311. (33) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (34) Duan, X.; Wang, C.; Pan, A.; Yu, R.; Duan, X. Two-Dimensional Transition Metal Dichalcogenides as Atomically Thin Semiconductors: Opportunities and Challenges. Chem. Soc. Rev. 2015, 44, 8859−8876. (35) Cheng, R.; Li, D.; Zhou, H.; Wang, C.; Yin, A.; Jiang, S.; Liu, Y.; Chen, Y.; Huang, Y.; Duan, X. Electroluminescence and Photocurrent Generation from Atomically Sharp WSe2/ MoS2 Heterojunction P-N Diodes. Nano Lett. 2014, 14, 5590−5597. (36) Kou, L.; Frauenheim, T.; Chen, C. Nanoscale Multilayer Transition-Metal Dichalcogenide Heterostructures: Band Gap Modulation by Interfacial Strain and Spontaneous Polarization. J. Phys. Chem. Lett. 2013, 4, 1730−1736. (37) Du, A. Silico Engineering of Graphene-Based Van Der Waals Heterostructured Nanohybrids for Electronics and Energy Applications. Wiley Interdiscip. Rev.-Comput. Mol. Sci. 2016, 6, 551−570. (38) Kumar, H.; Dong, L.; Shenoy, V. B. Limits of Coherency and Strain Transfer in Flexible 2D Van Der Waals Heterostructures: Formation of Strain Solitons and Interlayer Debonding. Sci. Rep. 2016, 6, 21516. (39) Ci, L.; Song, L.; Jin, C.; Jariwala, D.; Wu, D.; Li, Y.; Srivastava, A.; Wang, Z. F.; Storr, K.; Balicas, L.; et al. Atomic Layers of
REFERENCES
(1) Lee, C.-H.; Lee, G.-H.; van der Zande, A. M.; Chen, W.; Li, Y.; Han, M.; Cui, X.; Arefe, G.; Nuckolls, C.; Heinz, T. F.; et al. Atomically Thin P-N Junctions with Van Der Waals Heterointerfaces. Nat. Nanotechnol. 2014, 9, 676−681. (2) Britnell, L.; Gorbachev, R. V.; Jalil, R.; Belle, B. D.; Schedin, F.; Mishchenko, A.; Georgiou, T.; Katsnelson, M. I.; Eaves, L.; Morozov, S. V.; et al. Field-Effect Tunneling Transistor Based on Vertical Graphene Heterostructures. Science 2012, 335, 947−950. (3) Dean, C. R.; Wang, L.; Maher, P.; Forsythe, C.; Ghahari, F.; Gao, Y.; Katoch, J.; Ishigami, M.; Moon, P.; Koshino, M.; et al. Hofstadter’s Butterfly and the Fractal Quantum Hall Effect in Moire Superlattices. Nature 2013, 497, 598−602. (4) Britnell, L.; Ribeiro, R. M.; Eckmann, A.; Jalil, R.; Belle, B. D.; Mishchenko, A.; Kim, Y. J.; Gorbachev, R. V.; Georgiou, T.; Morozov, S. V.; et al. Strong Light-Matter Interactions in Heterostructures of Atomically Thin Films. Science 2013, 340, 1311−1314. (5) Wendumu, T. B.; Seifert, G.; Lorenz, T.; Joswig, J.-O.; Enyashin, A. Optical Properties of Triangular Molybdenum Disulfide Nanoflakes. J. Phys. Chem. Lett. 2014, 5, 3636−3640. (6) Tu, Z.; Wu, M.; Zeng, X. C. Two-Dimensional Metal-Free Organic Multiferroic Material for Design of Multifunctional Integrated Circuits. J. Phys. Chem. Lett. 2017, 8, 1973−1978. (7) Wu, C.-C.; Jariwala, D.; Sangwan, V. K.; Marks, T. J.; Hersam, M. C.; Lauhon, L. J. Elucidating the Photoresponse of Ultrathin MoS2 Field-Effect Transistors by Scanning Photocurrent Microscopy. J. Phys. Chem. Lett. 2013, 4, 2508−2513. (8) Xi, J.; Zhao, T.; Wang, D.; Shuai, Z. Tunable Electronic Properties of Two-Dimensional Transition Metal Dichalcogenide Alloys: A First-Principles Prediction. J. Phys. Chem. Lett. 2014, 5, 285− 291. (9) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Black Phosphorus Field-Effect Transistors. Nat. Nanotechnol. 2014, 9, 372−377. (10) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699− 712. (11) Fiori, G.; Bonaccorso, F.; Iannaccone, G.; Palacios, T.; Neumaier, D.; Seabaugh, A.; Banerjee, S. K.; Colombo, L. Electronics Based on Two-Dimensional Materials. Nat. Nanotechnol. 2014, 9, 768−779. (12) Novoselov, K. S.; Fal’ko, V. I.; Colombo, L.; Gellert, P. R.; Schwab, M. G.; Kim, K. A Roadmap for Graphene. Nature 2012, 490, 192−200. (13) Yin, Z.; Li, H.; Li, H.; Jiang, L.; Shi, Y.; Sun, Y.; Lu, G.; Zhang, Q.; Chen, X.; Zhang, H. Single-Layer Mos2 Phototransistors. ACS Nano 2012, 6, 74−80. (14) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150. (15) Chhowalla, M.; Jena, D.; Zhang, H. Two-Dimensional Semiconductors for Transistors. Nat. Rev. Mater. 2016, 1, 16052. (16) Komsa, H.-P.; Krasheninnikov, A. V. Two-Dimensional Transition Metal Dichalcogenide Alloys: Stability and Electronic Properties. J. Phys. Chem. Lett. 2012, 3, 3652−3656. (17) Sun, Z.; Martinez, A.; Wang, F. Optical Modulators with 2D Layered Materials. Nat. Nat. Photonics 2016, 10, 227−238. (18) Xue, Y.; Zhang, Y.; Liu, Y.; Liu, H.; Song, J.; Sophia, J.; Liu, J.; Xu, Z.; Xu, Q.; Wang, Z.; et al. Scalable Production of a Few-Layer MoS2/WS2 Vertical Heterojunction Array and Its Application for Photodetectors. ACS Nano 2016, 10, 573−580. (19) Peng, B.; Ang, P. K.; Loh, K. P. Two-Dimensional Dichalcogenides for Light-Harvesting Applications. Nano Today 2015, 10, 128−137. (20) Ouyang, Y.; Ling, C.; Chen, Q.; Wang, Z.; Shi, L.; Wang, J. Activating Inert Basal Planes of MoS2 for Hydrogen Evolution Reaction through the Formation of Different Intrinsic Defects. Chem. Mater. 2016, 28, 4390−4396. 5776
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
Letter
The Journal of Physical Chemistry Letters Hybridized Boron Nitride and Graphene Domains. Nat. Mater. 2010, 9, 430−435. (40) Duan, X.; Wang, C.; Shaw, J. C.; Cheng, R.; Chen, Y.; Li, H.; Wu, X.; Tang, Y.; Zhang, Q.; Pan, A.; et al. Lateral Epitaxial Growth of Two-Dimensional Layered Semiconductor Heterojunctions. Nat. Nanotechnol. 2014, 9, 1024−1030. (41) Son, Y.; Li, M.-Y.; Cheng, C.-C.; Wei, K.-H.; Liu, P.; Wang, Q. H.; Li, L.-J.; Strano, M. S. Observation of Switchable Photoresponse of a Monolayer WSe2-MoS2 Lateral Heterostructure Via Photocurrent Spectral Atomic Force Microscopic Imaging. Nano Lett. 2016, 16, 3571−3577. (42) Zhang, X.-Q.; Lin, C.-H.; Tseng, Y.-W.; Huang, K.-H.; Lee, Y.H. Synthesis of Lateral Heterostructures of Semiconducting Atomic Layers. Nano Lett. 2015, 15, 410−415. (43) Hong, X.; Kim, J.; Shi, S.-F.; Zhang, Y.; Jin, C.; Sun, Y.; Tongay, S.; Wu, J.; Zhang, Y.; Wang, F. Ultrafast Charge Transfer in Atomically Thin MoS2/WS2 Heterostructures. Nat. Nanotechnol. 2014, 9, 682− 686. (44) Wang, H.; Bang, J.; Sun, Y.; Liang, L.; West, D.; Meunier, V.; Zhang, S. The Role of Collective Motion in the Ultrafast Charge Transfer in Van Der Waals Heterostructures. Nat. Commun. 2016, 7, 11504. (45) Xu, W.; Liu, W.; Schmidt, J. F.; Zhao, W.; Lu, X.; Raab, T.; Diederichs, C.; Gao, W.; Seletskiy, D. V.; Xiong, Q. Correlated Fluorescence Blinking in Two-Dimensional Semiconductor Heterostructures. Nature 2016, 541, 62−67. (46) Li, M.-Y.; Shi, Y.; Cheng, C.-C.; Lu, L.-S.; Lin, Y.-C.; Tang, H.L.; Tsai, M.-L.; Chu, C.-W.; Wei, K.-H.; He, J.-H.; et al. Epitaxial Growth of a Monolayer WSe2-MoS2 Lateral P-N Junction with an Atomically Sharp Interface. Science 2015, 349, 524−528. (47) Chen, X.; Qiu, Y.; Yang, H.; Liu, G.; Zheng, W.; Feng, W.; Cao, W.; Hu, W.; Hu, P. In-Plane Mosaic Potential Growth of Large-Area 2D Layered Semiconductors MoS2-MoSe2 Lateral Heterostructures and Photodetector Application. ACS Appl. Mater. Interfaces 2017, 9, 1684−1691. (48) Ullah, F.; Sim, Y.; Le, C. T.; Seong, M.-J.; Jang, J. I.; Rhim, S. H.; Tran Khac, B. C.; Chung, K.-H.; Park, K.; Lee, Y.; et al. Growth and Simultaneous Valleys Manipulation of Two-Dimensional MoSe2-WSe2 Lateral Heterostructure. ACS Nano 2017, 11, 8822−8829. (49) Cao, Z.; Harb, M.; Lardhi, S.; Cavallo, L. Impact of Interfacial Defects on the Properties of Monolayer Transition Metal Dichalcogenide Lateral Heterojunctions. J. Phys. Chem. Lett. 2017, 8, 1664−1669. (50) Gong, Y.; Lin, J.; Wang, X.; Shi, G.; Lei, S.; Lin, Z.; Zou, X.; Ye, G.; Vajtai, R.; Yakobson, B. I.; et al. Vertical and in-Plane Heterostructures from WS2/MoS2 Monolayers. Nat. Mater. 2014, 13, 1135−1142. (51) Lin, Z.; McCreary, A.; Briggs, N.; Subramanian, S.; Zhang, K.; Sun, Y.; Li, X.; Borys, N. J.; Yuan, H.; Fullerton-Shirey, S. K.; et al. 2D Materials Advances: From Large Scale Synthesis and Controlled Heterostructures to Improved Characterization Techniques, Defects and Applications. 2D Mater. 2016, 3, 042001. (52) Zhao, M.; Chang, M.-J.; Wang, Q.; Zhu, Z.-T.; Zhai, X.-P.; Zirak, M.; Moshfegh, A. Z.; Song, Y.-L.; Zhang, H.-L. Unexpected Optical Limiting Properties from Mos2 Nanosheets Modified by a Semiconductive Polymer. Chem. Commun. 2015, 51, 12262−12265. (53) Peng, B.; Yu, G.; Liu, X.; Liu, B.; Liang, X.; Bi, L.; Deng, L.; Sum, T. C.; Loh, K. P. Ultrafast Charge Transfer in MoS2/WSe2 P-N Heterojunction. 2D Mater. 2016, 3, 025020. (54) Ceballos, F.; Bellus, M. Z.; Chiu, H.-Y.; Zhao, H. Ultrafast Charge Separation and Indirect Exciton Formation in a MoS2-MoSe2 Van Der Waals Heterostructure. ACS Nano 2014, 8, 12717−12724. (55) Stier, W.; Prezhdo, O. V. Nonadiabatic Molecular Dynamics Simulation of Light-Induced, Electron Transfer from an Anchored Molecular Electron Donor to a Semiconductor Acceptor. J. Phys. Chem. B 2002, 106, 8047−8054. (56) Craig, C. F.; Duncan, W. R.; Prezhdo, O. V. Trajectory Surface Hopping in the Time-Dependent Kohn-Sham Approach for ElectronNuclear Dynamics. Phys. Rev. Lett. 2005, 95, 163001.
(57) Fischer, S. A.; Habenicht, B. F.; Madrid, A. B.; Duncan, W. R.; Prezhdo, O. V. Regarding the Validity of the Time-Dependent KohnSham Approach for Electron-Nuclear Dynamics Via Trajectory Surface Hopping. J. Chem. Phys. 2011, 134, 024102. (58) Habenicht, B. F.; Prezhdo, O. V. Nonradiative Quenching of Fluorescence in a Semiconducting Carbon Nanotube: A Time-Domain Ab Initio Study. Phys. Rev. Lett. 2008, 100, 197402. (59) Rivera, P.; Schaibley, J. R.; Jones, A. M.; Ross, J. S.; Wu, S.; Aivazian, G.; Klement, P.; Seyler, K.; Clark, G.; Ghimire, N. J.; et al. Observation of Long-Lived Interlayer Excitons in Monolayer MoSe2WSe2 Heterostructures. Nat. Commun. 2015, 6, 6242. (60) Long, R.; Prezhdo, O. V. Quantum Coherence Facilitates Efficient Charge Separation at a MoS2/MoSe2 Van Der Waals Junction. Nano Lett. 2016, 16, 1996−2003. (61) Su, X.; Ju, W.; Zhang, R.; Guo, C.; Zheng, J.; Yong, Y.; Li, X. Bandgap Engineering of MoS2/MX2 (MX2 = WS2, MoSe2 and WSe2) Heterobilayers Subjected to Biaxial Strain and Normal Compressive Strain. RSC Adv. 2016, 6, 18319−18325. (62) Wei, W.; Dai, Y.; Huang, B. Straintronics in Two-Dimensional in-Plane Heterostructures of Transition-Metal Dichalcogenides. Phys. Chem. Chem. Phys. 2017, 19, 663−672. (63) Parandekar, P. V.; Tully, J. C. Mixed Quantum-Classical Equilibrium. J. Chem. Phys. 2005, 122, 094102. (64) Tully, J. C. Molecular-Dynamics with Electronic-Transitions. J. Chem. Phys. 1990, 93, 1061−1071. (65) Akimov, A. V.; Prezhdo, O. V. The Pyxaid Program for NonAdiabatic Molecular Dynamics in Condensed Matter Systems. J. Chem. Theory Comput. 2013, 9, 4959−4972. (66) Jaeger, H. M.; Fischer, S.; Prezhdo, O. V. Decoherence-Induced Surface Hopping. J. Chem. Phys. 2012, 137, 22A545. (67) Bittner, E. R.; Rossky, P. J. Quantum Decoherence in Mixed Quantum-Classical Systems - Nonadiabatic Processes. J. Chem. Phys. 1995, 103, 8130−8143. (68) Schwartz, B. J.; Bittner, E. R.; Prezhdo, O. V.; Rossky, P. J. Quantum Decoherence and the Isotope Effect in Condensed Phase Nonadiabatic Molecular Dynamics Simulations. J. Chem. Phys. 1996, 104, 5942−5955. (69) Tao, G. Multi-State Trajectory Approach to Non-Adiabatic Dynamics: General Formalism and the Active State Trajectory Approximation. J. Chem. Phys. 2017, 147, 044107. (70) Long, R.; Fang, W.; Akimov, A. V. Nonradiative Electron-Hole Recombination Rate Is Greatly Reduced by Defects in Monolayer Black Phosphorus: Ab Initio Time Domain Study. J. Phys. Chem. Lett. 2016, 7, 653−659. (71) Long, R.; Guo, M.; Liu, L.; Fang, W. Nonradiative Relaxation of Photoexcited Black Phosphorus Is Reduced by Stacking with MoS2: A Time Domain Ab Initio Study. J. Phys. Chem. Lett. 2016, 7, 1830− 1835. (72) Long, R.; Prezhdo, O. V. Instantaneous Generation of ChargeSeparated State on TiO2 Surface Sensitized with Plasmonic Nanoparticles. J. Am. Chem. Soc. 2014, 136, 4343−4354. (73) Long, R.; Prezhdo, O. V. Time-Domain Ab Initio Modeling of Electron-Phonon Relaxation in High-Temperature Cuprate Superconductors. J. Phys. Chem. Lett. 2017, 8, 193−198. (74) Kresse, G.; Hafner, J. Abinitio Molecular-Dynamics for LiquidMetals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (75) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (76) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (77) Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (78) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (Dft-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. 5777
DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
Letter
The Journal of Physical Chemistry Letters (79) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456−1465. (80) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (81) Tongay, S.; Zhou, J.; Ataca, C.; Liu, J.; Kang, J. S.; Matthews, T. S.; You, L.; Li, J.; Grossman, J. C.; Wu, J. Broad-Range Modulation of Light Emission in Two-Dimensional Semiconductors by Molecular Physisorption Gating. Nano Lett. 2013, 13, 2831−2836. (82) Chen, S.-Y.; Zheng, C.; Fuhrer, M. S.; Yan, J. Helicity-Resolved Raman Scattering of MoS2, MoSe2, WS2, and WSe2 Atomic Layers. Nano Lett. 2015, 15, 2526−2532. (83) Zhang, X.; Qiao, X.-F.; Shi, W.; Wu, J.-B.; Jiang, D.-S.; Tan, P.H. Phonon and Raman Scattering of Two-Dimensional Transition Metal Dichalcogenides from Monolayer, Multilayer to Bulk Material. Chem. Soc. Rev. 2015, 44, 2757−2785. (84) Chiu, M.-H.; Li, M.-Y.; Zhang, W.; Hsu, W.-T.; Chang, W.-H.; Terrones, M.; Terrones, H.; Li, L.-J. Spectroscopic Signatures for Interlayer Coupling in MoS2-WSe2 Van Der Waals Stacking. ACS Nano 2014, 8, 9649−9656. (85) Zhang, X.; Tan, Q.-H.; Wu, J.-B.; Shi, W.; Tan, P.-H. Review on the Raman Spectroscopy of Different Types of Layered Materials. Nanoscale 2016, 8, 6435−6450. (86) Zhang, C.; Chuu, C.-P.; Ren, X.; Li, M.-Y.; Li, L.-J.; Jin, C.; Chou, M.-Y.; Shih, C.-K. Interlayer Couplings, Moire Patterns, and 2D Electronic Superlattices in MoS2/WSe2 Hetero-Bilayers. Sci. Adv. 2017, 3, e1601459. (87) Liu, J.; Kilina, S. V.; Tretiak, S.; Prezhdo, O. V. Ligands Slow Down Pure-Dephasing in Semiconductor Quantum Dots. ACS Nano 2015, 9, 9106−9116. (88) Akimov, A. V.; Prezhdo, O. V. Advanced Capabilities of the Pyxaid Program: Integration Schemes, Decoherenc:E Effects, Multiexcitonic States, and Field-Matter Interaction. J. Chem. Theory Comput. 2014, 10, 789−804. (89) Jasper, A. W.; Nangia, S.; Zhu, C. Y.; Truhlar, D. G. Non-BornOppenheimer Molecular Dynamics. Acc. Chem. Res. 2006, 39, 101− 108. (90) Bittner, E. R.; Rossky, P. J. Decoherent Histories and Nonadiabatic Quantum Molecular Dynamics Simulations. J. Chem. Phys. 1997, 107, 8611−8618. (91) Xiong, H.-N.; Lo, P.-Y.; Zhang, W.-M.; Feng, D. H.; Nori, F. Non-Markovian Complexity in the Quantum-to-Classical Transition. Sci. Rep. 2015, 5, 13353.
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DOI: 10.1021/acs.jpclett.7b02779 J. Phys. Chem. Lett. 2017, 8, 5771−5778
