Quantum Coherence Facilitates Efficient Charge Separation at a

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Quantum Coherence Facilitates Efficient Charge Separation at a MoS2/MoSe2 van der Waals Junction Run Long*,†,‡ and Oleg V. Prezhdo*,§ †

College of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, 100875, People’s Republic of China ‡ School of Physics and Complex and Adaptive Systems Lab, University College Dublin, Dublin 4, Ireland § Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *

ABSTRACT: Two-dimensional transition metal dichalcogenides (MX2, M = Mo, W; X = S, Se) hold great potential in optoelectronics and photovoltaics. To achieve efficient lightto-electricity conversion, electron−hole pairs must dissociate into free charges. Coulomb interaction in MX2 often exceeds the charge transfer driving force, leading one to expect inefficient charge separation at a MX2 heterojunction. Experiments defy the expectation. Using time-domain density functional theory and nonadiabatic (NA) molecular dynamics, we show that quantum coherence and donor−acceptor delocalization facilitate rapid charge transfer at a MoS2/ MoSe2 interface. The delocalization is larger for electron than hole, resulting in longer coherence and faster transfer. Stronger NA coupling and higher acceptor state density accelerate electron transfer further. Both electron and hole transfers are subpicosecond, which is in agreement with experiments. The transfers are promoted primarily by the out-of-plane Mo−X modes of the acceptors. Lighter S atoms, compared to Se, create larger NA coupling for electrons than holes. The relatively slow relaxation of the “hot” hole suggests long-distance bandlike transport, observed in organic photovoltaics. The electron−hole recombination is notably longer across the MoS2/MoSe2 interface than in isolated MoS2 and MoSe2, favoring long-lived charge separation. The atomistic, time-domain studies provide valuable insights into excitation dynamics in two-dimensional transition metal dichalcogenides. KEYWORDS: MoS2/MoSe2 van der Waals heterojunction, nonadiabatic molecular dynamics, time-domain density functional theory, quantum coherence, charge separation and recombination, nonradiative relaxation

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and reduce interfacial electron−hole recombination. Because of low dielectric constants, the Coulomb interaction is poorly screened in the 2D MX2 materials. Theoretical studies have predicted exciton binding energies ranging from 0.5 to 1.1 eV in MX2 monolayers.14−16 For most MX2 heterojunctions, such values are consistently larger than the charge separation driving force, determined by the offset between the donor and acceptor CBM for electron transfer, and the offset between the VBM for hole transfer. In particular, the CBM and VBM offsets in the MoS2/MoSe2 heterojunction are 0.37 and 0.63 eV, respectively.13,17 The corresponding offsets are 0.31 and 0.36 eV for the MoS2/WS2 heterojunction.17 The CBM and VBM offsets in the MoS2/WSe2 heterojunction are 0.76 and 0.83 eV, as determined using the X-ray photoelectron spectroscopy and scanning tunneling spectroscopy.18 Comparison between the exciton binding energies and the charge transfer driving forces

an der Waals heterojunctions constructed with twodimensional (2D) transition metal dichalcogenides (MX2, M = Mo, W; X = S, Se) have received broad interest in optoelectronic and photovolatic applications.1,2 Many MX2 monolayers are direct band gap semiconductors3,4 capable of strong light-matter interactions.5−7 It is particularly important that MX2 monolayers maintain their direct band structure in a heterojunction.8,9 This is possible because the layers couple by weak van der Waals interaction. Single-layer MX2 is often advantageous over few-layer MX2, which undergoes direct-toindirect band gap transition with increasing number of layers. The optical absorption of a MX2 heterojunction is expected to be a sum of the absorptions of the individual components.10 Further, MX2 materials constitute promising candidate for Li−S batteries and efficient hydrogen production.11 First-principles calculations predict that most MX2 heterojunctions have type-II band alignment, where the conduction band minimum (CBM) and the valence band maximum (VBM) reside in different monolayers.8,12,13 Such alignment can facilitate efficient separation of photoexcited electrons and holes,9,13 result in long photogenerated charge carrier lifetimes, © XXXX American Chemical Society

Received: December 24, 2015 Revised: February 13, 2016

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Kohn−Sham theory.30,31 Quantum decoherence effects are described using the optical response theory32 and a semiclassical correction to the NA dynamics.33 The method was proven reliable in application to photoinduced processes in a variety of materials,33−39 including TiO2 sensitized by a semiconducting39 and metallic37 nanoparticles, carbon nanotubes,33 graphane,38 and a fullerene-quantum dot composite.34 A detailed description of the method is presented in our previous publications30,33,40−44 and in the Supporting Information. While it is desirable to incorporate explicit electron−hole interaction, such as that described by the Bethe-Salpeter theory, calculations of this type are very expensive. Time-dependent Bethe-Salpeter theory has been applied only to systems with fixed nuclei.45−47 The chosen approach incorporates electron correlation effects implicitly in the density functional. Currently, it is the most rigorous ab initio method available for modeling the processes under investigation. The present work is motivated by both recent experiments19,20,24 and theoretical works9,13−17 showing that charges undergo efficient separation at the MoS2/MoSe2 interface and other 2D MX2 heterojunctions, even though the driving force is consistently weaker than electron−hole binding. The simulations relate most directly to the experimental work by Zhao and co-workers,19 focusing on the electron transfer from MoSe2 to MoS2, the hole transfer from MoS2 to MoSe2, and the electron−hole recombination at the MoS2/MoSe2 interface and in isolated MoS2 and MoSe2 monolayers. Figure 1a demonstrates the energy levels involved in the photoinduced charge separation and recombination dynamics

suggests that photoexcited electron−hole pairs should not dissociate effectively into free charge carriers in two separate layers at a MX2 heterojunction. This is not the case, however, because many experiments demonstrate efficient charge separation at MX2 heterojunctions via photoinduced electron and/or hole transfer.19,20 Recent experiments reported quenching of photoluminescence (PL) in the MoS2/WSe2 heterojunction,21 originating from the photoinduced interlayer charge transfer. Application of the MoS2/WSe2 heterojunction in photovoltaic devices22 and field effect transistors23 were demonstrated. Other experiments showed that the ultrafast hole transfer from MoS2 to WS2 occurred within 50 fs after photoexcitation20 and revealed an extremely long time scale of electron−hole recombination in the MoSe2/WSe2 heterojunction.24 More recently, Zhao et al. investigated systematically in time-domain the dynamics of electron and hole transfer, as well as electron− hole recombination in the MoS2/MoSe2 heterojunction using transient absorption measurements.19 The reported electron and hole transfer time-scales were subpicosecond. Once transferred, the electrons and holes formed spatially indirect excitons, which had longer lifetimes (up to 240 ps)19 than the excitons in individual MoS2 (∼100 ps)25,26 and MoSe2 (∼125 ps).27 Little is known theoretically about the ultrafast charge transfer dynamics in these 2D heterojunctions. For instance, it is not clear why excitons separate efficiently, and electrons and holes are transferred on ultrafast time scales. The mechanisms of the photoinduced charge transfer and electron−hole recombination across the interface and inside each material are not established. The phonon modes promoting these nonradiative processes are not identified. An atomistic understanding of the charge separation and energy relaxation dynamics is necessary for design of high-performance devices based on 2D transition metal dichalcogenides. The paper presents the first time-domain ab initio simulation of the photoinduced charge separation and recombination dynamics at a MoS2/MoSe2 heterojunction. It reveals that quantum coherence at the interface, facilitated by significant delocalization of photoexcited states between the donor and acceptor materials, helps to overcome the electron−hole pair attraction and leads to efficient charge separation. The obtained subpicosecond time scales for electron and hole transfers are in excellent agreement with the available experimental observations.19 The electron transfer is faster than the hole transfer due to longer coherence, stronger nonadiabatic (NA) coupling, higher density of acceptor states, and interaction with higher frequency vibrational modes. The same factors rationalize the differences in the electron and hole energy relaxations. The relatively long lifetime of the “hot” hole facilitates long-distance bandlike transport observed in organic systems. Driven by outof-plane S−Mo and Se−Mo motions, electrons recombine with holes in isolated MoS2 and MoSe2 within one hundred picoseconds, which is in good agreement with experiments.26−28 The electron−hole recombination across the interface is several times longer, also in excellent agreement with the measurement.19 The rapid subpicosecond electron and hole transfer emphasizes the role of quantum coherence, and guarantees that both MoS2 and MoSe2 can be used as sun-light absorbers in solar energy harvesting. The long exciton lifetime at the interface indicates that van der Waals heterojunctions can be used to design efficient photovoltaic devices. NA molecular dynamics are simulated using fewest-switches surface hopping29 implemented within the time-dependent

Figure 1. (a) Electronic energy levels involved in the photoinduced charge separation and recombination dynamics at the MoSe2/MoS2 interface. Absorption of a photon hv by either MoSe2 or the MoS2 leads to charge separation ① due to electron or hole transfer, respectively. Competing with the separation, the weakly bound electron and hole can undergo recombination ② inside either material. Following the separation, the charges can recombine at the interface ③. (b) Pairs of electronic state forming coherent superpositions during the ultrafast electron and hole transfer at the interface between MoSe2 and MoS2, processes 1 and 2, and during intraband charge relaxation inside MoSe2 or MoS2, process 3. The decoherence times are shown in Table 1. The relatively long coherence ensures rapid interfacial charge transfer. Longer coherence results in faster transfer and faster relaxat ion of electrons compared to holes, Figure 4.

at the type-II MoS2/MoSe2 photovoltaic heterojunction. Excitation of MoSe2 leads to electron transfer, while MoS2 excitation results in hole transfer, ①. Competing with the separation, the electron and hole can recombine inside either material, ②. Following the separation, the charges can recombine at the interface, ③. Electronic degrees of freedom couple to vibrations, leading to loss of quantum coherence. B

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The charge densities of the key electron and hole orbitals are shown in Figure 2b. The vertical arrows pointing from panel b to panel a indicate the energies of these states. Figure 2b shows that both photoexcited states are delocalized between the two materials, indicating significant donor−acceptor coupling; consider the MoSe2 CBM shown in the right-most picture and the MoS2 VBM shown in the left-most picture. The situation is different for the acceptor states. The electron final state, that is, the MoS2 CBM, is slightly delocalized onto MoSe2, while the hole final state, that is, MoSe2 VBM, is strongly localized on MoSe2. The difference arises due to the difference in the band offsets: the MoSe2 VBM is isolated energetically from the MoS2 states, while the MoS2 CBM is energetically close to the MoSe2 states. The mixing of the donor and acceptor states alone does not guarantee ultrafast charge separation. Quantum dynamics requires formation of coherent superpositions of the states. Long lifetimes of quantum superpositions facilitate fast dynamics, while short coherence time slows dynamics down, resulting in the quantum Zeno effect in the limit of infinitely fast decoherence.48−51 The mixing between the donor and acceptor states has a significant effect on quantum coherence, because decoherence time is directly related to fluctuations of the energy gaps between the initial and final states, and the fluctuations are determined by the corresponding wave functions. Electronic Coherence. In order to characterize the phonon-induced loss of electronic coherence, we computed the pure-dephasing functions for the dephasing processes labeled by 1, 2, and 3 in Figure 1b. The time scales, obtained by Gaussian fitting, f(t) = exp[−0.5(−t/τ)2], are summarized in Tables 1 and 2 for electron−hole separation and recombina-

Processes 1 and 2 shown in Figure 1b represent loss of coherence between pairs of states involved in electron and hole transfer between MoS2 and MoSe2. Process 3 in Figure 1b refers to decoherence between different electronic states within the same material. This process is relevant to electron and hole energy relaxation. We also consider decoherence for the CBM− VBM state pairs of either the same or different materials involved in electron−hole recombination. Electronic Structure of the MoS2/MoSe2 Heterojunction. Figure 2a shows the projected density of states (PDOS)

Figure 2. (a) PDOS of the MoS2 and MoSe2 monolayers in the MoS2/ MoSe2 heterojunction. The driving force for the charge separation is determined by the donor−acceptor band edge energy offsets. (b) Charge densities of the donor and acceptor states for the electron and hole transfer. Both electron and hole donor states are significantly delocalized between MoSe2 and MoS2, forming coherent superpositions between the two materials. The electron acceptor state is slightly delocalized onto the donor, due to a small donor−acceptor energy offset in this case, panel a. On the contrary, the hole acceptor state is fully localized on the MoSe2 monolayer because the donor− acceptor energy offset is large. The vertical arrows between panels (a) and (b) relate the donor and acceptor orbital densities to the energies.

Table 1. Phonon-Induced Decoherence Times (fs) for Superpositions of States Involved in Electron and Hole Transfer (1 and 2) and Relaxation (3)a electrons

holes

25 30 37

10.4 10.5 20

1 2 3

of the MoS2/MoSe2 heterojunction, separated into the contributions from the MoS2 and MoSe2 monolayers (black and red lines). The PDOS indicates formation of a type-II heterojunction. The canonically averaged CBM and VBM offsets are 0.06 and 0.50 eV. The lowest energy excited state formed at the heterojunction is a charge transfer state with the electron localized at the MoS2 CBM and the hole localized at the MoSe2 VBM. Photoexcitation of MoSe2 results in electron transfer to MoS2, while photoexcitation of MoS2 induces hole transfer to MoSe2. The energies lost to vibrational motions during the electron and hole transfers are 0.06 and 0.50 eV, respectively. A total of 8.5 times more energy is lost after MoS2 excitation than after MoSe2 excitation. In order to rationalize the experimentally observed efficient photoinduced charge separation despite significant electron− hole interaction,19,20,24 one needs to consider details of the interfacial interaction and dynamics. The average distance between the MoS2 and MoSe2 monolayers decreases from 3.10 Å at 0 K to 2.79 Å at room temperature, indicating that the donor−acceptor interaction is enhanced due to thermal fluctuations. Atomic motions at a finite temperature distort the perfect geometries of the 2D materials, providing additional interaction opportunities.

a The processes are defined in Figure 1b. Longer coherence leads to faster transfer and relaxation of electrons compared to holes, Figure 4.

tion, respectively. Loss of coherence between states involving two complementary materials occurs faster than between states of the same material. This is true for both charge separation, compare processes 1 and 2 versus process 3 (Figure 1b and Table 1), and recombination, Table 2. States localized within Table 2. Non-Adiabatic Coupling, and Elastic (Decoherence) and Inelastic (Recombination) Times Characterizing Electron-Phonon Interactions during Electron-Hole Recombination Insider Pure MoSe2, Pure MoS2, and MoSe2/MoS2 Interfacea

MoSe2 MoS2 MoS2/MoSe2

NA coupling (meV)

decoherence (fs)

recombination (ps)

0.440 0.257 0.135

7.0 8.6 6.2

63 41 680

a

Recombination across the interface is longest as a result of smaller coupling and shorter coherence.

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Figure 3. FT of the energy gaps between the donor and acceptor states for the electron (a) and hole (b) transfer. The inserts show the unnormalized ACF of the energy gaps, eq 8 of Supporting Information. The ACF value at time zero, Cun(0), gives the mean square fluctuation of the energy gap. Holes couple to lower frequency modes and exhibit a higher FT amplitude than electrons. Low-frequency vibrations strongly influence the energies of the delocalized donor and acceptor states, resulting in a large gap fluctuation, Cun(0), which fluctuation favors faster decoherence, Table 1. Highfrequency phonons have higher velocities and create larger nonadiabatic coupling, eq 5 of Supporting Information. Longer coherence and larger coupling lead to faster electron transfer, compared to hole transfer, Figure 4a,b, respectively.

because both initial and final states are delocalized between the two materials, which is not the case for the hole, Figure 2b. The phonons involved in the electron transfer have higher frequencies, compared to hole transfer, Figure 3. The electron dynamics involves acceptor states localized inside MoS2, containing light S atoms, to be compared to the hole acceptor states localized in MoSe2, with heavier Se atoms, Figure 2. The electron transfer couples primarily to the 400 cm−1 mode, while the hole transfer involves the 300 cm−1 mode. In addition, the electron couples to several higher frequency phonons, while the hole couples to a lower frequency mode. Faster modes create larger NA coupling, because at a given temperature they have larger nuclear velocities, dR/dt, that enter the NA coupling dR matrix element, −iℏ⟨ϕk̃ |∇R |ϕm̃ ⟩ dt . The dominant 400 cm−1 peak for electron transfer can be assigned to the out-of-plane S−Mo A1g mode.56−59 The peak at 460 cm−1 can be attributed to either the double overtone of the A1g mode of MoSe2 or the MoS2 out-of-plane A21g mode at 463.84 cm−1.57 The very high-frequency mode at 850 cm−1 is the overtone of these lower frequencies. For hole transfer, the major peak at 300 cm−1 corresponds to the Raman-active E1g mode of MoSe2 at 285.90 cm−1. It can also be assigned to the in-plane E2g mode of MoS2 at 283.78 cm−1.57 The small peak at 460 cm−1 corresponds to the 463.84 cm−1 out-of-plane A21g mode of MoS2.57 The 700 cm−1 frequency is an overtone of the lower frequencies. It is not surprising that both MoS2 and MoSe2 modes participate in electron and hole transfer, because the initially photoexcited states for both processes are delocalized significantly between MoS2 and MoSe2, Figure 2b. The outof-plane displacements of Mo, S, and Se have a strong effect on the electron, hole, and energy relaxation dynamics, because these motions modulate the energies of the MoS2 and MoSe2 electronic states and change the donor−acceptor coupling.

the same material oscillate more coherently, subject to the same phonon modes. Decoherence is slower for electron transfer than for hole transfer, Table 1. This fact can be also rationalized by state localization. Both initial and final states for electron transfer are delocalized between the two materials, while only the initial state for hole transfer is delocalized, Figure 2b. The relatively long coherence ensures rapid interfacial transfer52 rationalizing efficient charge separation at the MoS2/MoSe2 interface19 and other MX2 heterojunctions.20 Longer coherence results in faster dynamics of electrons than holes, as discussed below. A similar effect of quantum coherence enhancement of charge separation was reported in organic photovoltaic blends on the basis of both experimental and theoretical work.53,54 Coherences between the pairs of states involved in the electron−hole recombination, Table 2, are shorter than coherences formed during the charge separation, Table 1. Combined with the large energy gaps involved in the recombination processes, small coherence times rationalize long electron−hole lifetimes. Phonon Modes Participating in Charge Separation. Vibrational motions promote charge transfer. At the same time, they are responsible for energy losses to heat. Figure 3 presents the spectral densities, computed by Fourier transforms (FT) of the energy offsets between the initial and final states for the electron and hole transfer. Figure 3a shows FT of the gap between the MoS2 and MoSe2 CBMs, while Figure 3b depicts FT of the gap between the MoS2 and MoSe2 VBMs. The insets in Figure 3a show the unnormalized autocorrelation functions (ACF) of the energy gaps. The ACF initial values give the energy gap fluctuation squared. The magnitude of the gap fluctuation has a strong effect on coherence time.55 The fluctuation is notably smaller for the electron transfer than for the hole transfer, corresponding to slower dephasing, Table 1. The fluctuation magnitude is smaller for the electron transfer, D

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Figure 4. Charge separation dynamics. Top panels (a,b) show decay of the population of the electron and hole donor states, due to charge transfer to the corresponding acceptor. Bottom panels (c,d) show evolution of the electron and hole energies. The data shown in (a−c) are fitted by the exponential, eq 2. The hole energy decay (d) exhibits a complex behavior due to a relatively low density of states near the band edge, Figure 2. It cannot be fitted by a simple function. The charge transfer is faster than the energy relaxation. Both electron and hole transfer occur on ultrafast times scales due to high density of acceptor states compared to density of donor states, significant nonadiabatic coupling, and relatively long coherence times.

Figure 5. (a) Electron−hole recombination dynamics across (a) isolated MoS2 and MoSe2, and (b) MoS2/MoSe2 heterojunction, respectively. The insets of (a,b) are the pure-dephasing functions. The time scales are summarized in Table 2. The interfacial electron−hole recombination is slower than recombinations inside each material, enhancing carrier lifetimes. Panels (c,d) show FT of the corresponding donor−acceptor energy gaps. The charge recombination processes are facilitated by well-defined vibrational modes.

Charge Separation Dynamics at the MoS2/MoSe2 Interface. The dynamics of the photoinduced charge separation and the subsequent intraband energy relaxation are

characterized in Figure 4. Parts a and b represent charge transfer, while parts c and d give energy relaxation. The time constants reported in Figure 4a−c are obtained by exponential E

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Nano Letters fitting, f(t) = exp(−t/τ). The hole energy relaxation cannot be fitted reliably by a function combining one or two exponents or Gaussians. This is because the hole relaxation involves electronic states with a relatively low density, extending over a significant energy range, Figure 2a. The initial Gaussian or cosine type dynamics, characteristic of a Rabi oscillation, slowly develop into Fermi golden rule type exponential decay, once multiple state become accessible. The subpicosecond electron and hole transfer time scale agrees well with the experimental data.19 The electron transfer occurs faster than the hole transfer for several reasons. Quantum coherence persists for a longer time for electrons than holes, Table 1. The density of MoS2 states accepting the electron is higher than the density of MoSe2 states accepting the hole, Figure 2a. The donor−acceptor interaction is stronger for the electron transfer than the hole transfer, as indicated by the notable delocalization of the final state of the electrontransfer process, the third panel of Figure 2b. Finally, the computed average absolute value of the NA coupling is larger for the electron transfer than the hole transfer, 8.8 and 3.2 meV, respectively. Electrons lose energy to vibrations much faster than holes, Figure 4c,d. The relatively long relaxation time of the “hot” hole can facilitate rapid, bandlike transport to long distances, known in organic photovoltaic blends.53,54 Electron−Hole Recombination. In addition to charge separation and relaxation, solar cell performance is affected by charge recombination. Figure 5 shows the electron−hole recombination dynamics in isolated MoS2 and MoSe2 and at the MoS2/MoSe2 heterojunction. The times are obtained using the short-time linear approximation to the exponential decay, f(t) = exp(−t/τ) ≈ 1 − t/τ. The decoherence effects are particularly important here because loss of coherence occurs much faster than the corresponding quantum transition.40 The time scales of coherence loss, Table 2, also known as puredephasing in the optical response theory,32 determine the homogeneous line widths of the corresponding optical transitions, which can be measured for isolated MoS2 and MoSe2 monolayers. The optical line width for light emission from the interfacial charge transfer state is harder to detect, because the state has low optical activity due to weak overlap of the initial and final state wave functions. The computed 40 and 60 ps electron−hole recombination times for the MoS2 and MoSe2 monolayers, Table 2, are in good agreement with the available experimental data for MoS2 (100 ps)25,26 and MoSe2 (125 ps).27 The discrepancy may be attributed to the small size of the simulation cell, possibly overestimating electron−phonon interactions. The 680 ps nonradiative electron−hole recombination time for the interfacial process also agrees well with the experimental 240 ps time. 19 The smaller experimental number may be rationalized by interfacial defects expected in experimental samples. Defects create states inside the bandgap, accelerating the recombination.33,60 Panels c and d of Figure 5 depict spectral densities of the CBM-VBM energy gap for the MoS2, MoSe2, and MoS2/MoSe2 systems, characterizing the phonon modes promoting the recombinations. The electronic subsystem of the MoSe2 monolayer couples primarily to the 240 cm−1 out-of-plane Se−Mo vibrational mode.61,62 Both MoS2 and MoS2/MoSe2 show a strong contribution at the higher frequency of 400 cm−1, which can be assigned to the out-of-plane S−Mo A1g phonon mode.56,58,59 The weak 340 cm−1 peak seen with the

MoS2/MoSe2 heterojunction can be attributed to the out-ofplane A1g motion of MoSe2.57 In order to test reliability of the present DFT calculations with the more rigorous many-body GW method,63−65 we computed the PDOS of the small periodical 6-atom MoS2/ MoSe2 unit cell using the DFT and GW methods with a dense 20 × 20 × 1 Monkhorst−Pack k-point mesh,66 Figure S1. As expected, GW gives a larger bandgap than the DFT calculations. At the same time, the PDOS obtained from GW shows similar behavior to the DFT results of both small and large cells, Figure S1a and Figure 2a, indicating our current DFT calculation is suitable to describe the electronic bands and their relative alignment in the MoS2/MoSe2 van der Waals heterojunction. More rigorous Bethe-Salpeter calculations significantly decrease the optical excitation energy in these materials, bringing it closer to the experiment and the DFT bandgaps.67,68 It should be emphasized that both GW and particularly the Bethe-Salpeter theory are very computationally expensive and cannot be used for the present purpose of investigation of phonon-driven electron dynamics in the timedomain. In order to test the sensitivity of the electron−hole recombination times to the bandgap values, we scaled the gaps to experiment and repeated the NAMD calculations for MoSe2 and MoS2 monolayers and the MoS2/MoSe2 interface. The MoSe2 and MoS2 gaps were scaled to the experimental values of 1.5569 and 1.85 eV,70 respectively. The bandgap of the heterojunction was scaled to match the experimental gap of MoSe2. The resulting electron−hole recombination time scales in MoSe2, MoS2, and MoS2/MoSe2 are 79, 58, and 830 ps. These results show similar trend to the original data shown in Table 2. The similarity of the shapes and offsets of the GW and DFT valence and conductions bands of the two materials in the heterojunction supports our findings on the photoinduced charge separation. The moderate dependence of the electron− hole recombination dynamics on the bandgap, validates our conclusions on the nonradiative charge losses. Concluding Remarks. Many applications of van der Waals heterojunctions were proposed under the assumption of weak coupling at the interface. Large interfacial spacing between the materials, compared to typical chemical bond distances, allows one to assume that these materials maintain their individual properties. As a result, one often invokes the traditional incoherent mechanism of charge transfer. The ultrafast time scales measured for this process question the incoherent mechanism. Indeed, we find that the interfacial charge transfer occurs by a coherent mechanism. The incoherent and coherent charge transfer mechanisms exhibit notably different properties, for instance, in excitation energy dependence,71 and in sensitivity to defects72 and densities of donor and acceptor states.73 Related discoveries have been made recently regarding photoinduced charge transfer from metallic systems, such as graphene and plasmonic nanoparticles, into semiconductors. Here, one wonders how photoinduced charge transfer can happen despite rapid electron and holes recombination, typical of metals. Experiments have shown that plasmon-driven charge transfer from metallic particles into TiO2 cannot be explained by the traditional incoherent mechanism.71 The corresponding theoretical prediction was published a year earlier.37 A coherent mechanism was established for the photoinduced charge injection from graphene into TiO2.72 The latter case differs qualitatively from the current van der Waals heterojunction, F

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ACKNOWLEDGMENTS R.L. is grateful to the National Science Foundation of China (Grant 21573022) and the Science Foundation Ireland SIRG Program (Grant 11/SIRG/E2172). O.V.P. acknowledges support from the U.S. Department of Energy (Grant DESC0014429).

because graphene shows strong chemical-like interaction with TiO2. The importance of quantum coherence in charge and energy transport has been demonstrated in a number of other biological74,75 and nanoscale76,77 systems. In summary, we have investigated the photoinduced electron and hole transfer dynamics in a MoS2/MoSe2 van der Waals heterojunction using time-domain density functional theory combined with NA molecular dynamics. The simulations show that longer quantum coherence favors more rapid charge separation. The importance of coherence in quantum dynamics has been established in several biological57,78−81 and materials82−84 systems. We demonstrate that coherence is important for efficient and rapid charge separation in the van der Waals heterojunction. Longer coherence leads to faster transfer of electron compared to hole. Electron−hole recombination is much slower than charge injection and is associated with faster decoherence. The coherence time is directly related to the delocalization of the initial and final states between the donor and acceptor materials and to the frequency and range of phonon modes coupled to the electronic subsystem. Factors other than coherence, in particular, density of final states, NA coupling, and energy gap, also influence the time-scales of the processes under consideration. The charge transfer and vibrational relaxation are promoted primarily by the out-ofplane MoSe2 and MoS2 modes, because they influence the relative energies and localization of the donor and acceptor states and create the NA couplings. The current study demonstrates that light harvesting by both MoS2 and MoSe2 leads to efficient charge separation. The slow relaxation of the photogenerated hole indicates possibility of long-range band-like transport, favorable in applications. Charge separation at the MoS2/MoSe2 heterojunction reduces the electron−hole recombination rate, compared to the corresponding rates in isolated MoS2 and MoSe2 monolayers. Rapid charge transfer, combined with long electron−hole recombination times, indicates that MoS2/MoSe2 and similar metal dichalcogenides van der Waals heterojunctions constitute appealing candidates for photovoltaics and electronics applications. The reported simulations provide a detailed description of the complex quantum dynamics at the twodimensional transition metal dichalcogenide interface, generating important insights and suggesting design principles for operation of ultrathin devices under far-from-equilibrium conditions.

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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.nanolett.5b05264. Theoretical methodology and PDOS of the MoS2 and MoSe2 monolayers in small MoS2/MoSe2 heterojunction from DFT and GW calculations. (PDF)

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Letter

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. G

DOI: 10.1021/acs.nanolett.5b05264 Nano Lett. XXXX, XXX, XXX−XXX

Letter

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DOI: 10.1021/acs.nanolett.5b05264 Nano Lett. XXXX, XXX, XXX−XXX