Quantum Coherence Facilitates Efficient Charge Separation at aMoS2/MoSe2 van der Waals JunctionRun Long*,†,‡ and Oleg V. Prezhdo*,§

†College of Chemistry, Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, 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 dichalcoge-nides (MX2, M = Mo, W; X = S, Se) hold great potential inoptoelectronics and photovoltaics. To achieve efficient light-to-electricity conversion, electron−hole pairs must dissociateinto free charges. Coulomb interaction in MX2 often exceedsthe charge transfer driving force, leading one to expectinefficient charge separation at a MX2 heterojunction.Experiments defy the expectation. Using time-domain densityfunctional theory and nonadiabatic (NA) molecular dynamics,we show that quantum coherence and donor−acceptordelocalization facilitate rapid charge transfer at a MoS2/MoSe2 interface. The delocalization is larger for electron thanhole, resulting in longer coherence and faster transfer. Stronger NA coupling and higher acceptor state density accelerate electrontransfer further. Both electron and hole transfers are subpicosecond, which is in agreement with experiments. The transfers arepromoted primarily by the out-of-plane Mo−X modes of the acceptors. Lighter S atoms, compared to Se, create larger NAcoupling 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 inisolated MoS2 and MoSe2, favoring long-lived charge separation. The atomistic, time-domain studies provide valuable insightsinto 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

Van der Waals heterojunctions constructed with two-dimensional (2D) transition metal dichalcogenides (MX2,

M = Mo, W; X = S, Se) have received broad interest inoptoelectronic and photovolatic applications.1,2 Many MX2monolayers are direct band gap semiconductors3,4 capable ofstrong light-matter interactions.5−7 It is particularly importantthat MX2 monolayers maintain their direct band structure in aheterojunction.8,9 This is possible because the layers couple byweak van der Waals interaction. Single-layer MX2 is oftenadvantageous over few-layer MX2, which undergoes direct-to-indirect band gap transition with increasing number of layers.The optical absorption of a MX2 heterojunction is expected tobe a sum of the absorptions of the individual components.10

Further, MX2 materials constitute promising candidate for Li−Sbatteries and efficient hydrogen production.11

First-principles calculations predict that most MX2 hetero-junctions have type-II band alignment, where the conductionband minimum (CBM) and the valence band maximum(VBM) reside in different monolayers.8,12,13 Such alignmentcan facilitate efficient separation of photoexcited electrons andholes,9,13 result in long photogenerated charge carrier lifetimes,

and reduce interfacial electron−hole recombination. Because oflow dielectric constants, the Coulomb interaction is poorlyscreened in the 2D MX2 materials. Theoretical studies havepredicted exciton binding energies ranging from 0.5 to 1.1 eVin MX2 monolayers.

14−16 For most MX2 heterojunctions, suchvalues are consistently larger than the charge separation drivingforce, determined by the offset between the donor and acceptorCBM for electron transfer, and the offset between the VBM forhole transfer. In particular, the CBM and VBM offsets in theMoS2/MoSe2 heterojunction are 0.37 and 0.63 eV, respec-tively.13,17 The corresponding offsets are 0.31 and 0.36 eV forthe MoS2/WS2 heterojunction.

17 The CBM and VBM offsets inthe MoS2/WSe2 heterojunction are 0.76 and 0.83 eV, asdetermined using the X-ray photoelectron spectroscopy andscanning tunneling spectroscopy.18 Comparison between theexciton binding energies and the charge transfer driving forces

Received: December 24, 2015Revised: February 13, 2016Published: February 16, 2016

Letter

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suggests that photoexcited electron−hole pairs should notdissociate effectively into free charge carriers in two separatelayers at a MX2 heterojunction. This is not the case, however,because many experiments demonstrate efficient chargeseparation at MX2 heterojunctions via photoinduced electronand/or hole transfer.19,20

Recent experiments reported quenching of photolumines-cence (PL) in the MoS2/WSe2 heterojunction,21 originatingfrom the photoinduced interlayer charge transfer. Applicationof the MoS2/WSe2 heterojunction in photovoltaic devices22

and field effect transistors23 were demonstrated. Otherexperiments showed that the ultrafast hole transfer fromMoS2 to WS2 occurred within 50 fs after photoexcitation20 andrevealed an extremely long time scale of electron−holerecombination in the MoSe2/WSe2 heterojunction.24 Morerecently, Zhao et al. investigated systematically in time-domainthe dynamics of electron and hole transfer, as well as electron−hole recombination in the MoS2/MoSe2 heterojunction usingtransient absorption measurements.19 The reported electronand hole transfer time-scales were subpicosecond. Oncetransferred, the electrons and holes formed spatially indirectexcitons, which had longer lifetimes (up to 240 ps)19 than theexcitons in individual MoS2 (∼100 ps)25,26 and MoSe2 (∼125ps).27 Little is known theoretically about the ultrafast chargetransfer dynamics in these 2D heterojunctions. For instance, itis not clear why excitons separate efficiently, and electrons andholes are transferred on ultrafast time scales. The mechanismsof the photoinduced charge transfer and electron−holerecombination across the interface and inside each materialare not established. The phonon modes promoting thesenonradiative processes are not identified. An atomisticunderstanding of the charge separation and energy relaxationdynamics is necessary for design of high-performance devicesbased on 2D transition metal dichalcogenides.The paper presents the first time-domain ab initio simulation

of the photoinduced charge separation and recombinationdynamics at a MoS2/MoSe2 heterojunction. It reveals thatquantum coherence at the interface, facilitated by significantdelocalization of photoexcited states between the donor andacceptor materials, helps to overcome the electron−hole pairattraction and leads to efficient charge separation. The obtainedsubpicosecond time scales for electron and hole transfers are inexcellent agreement with the available experimental observa-tions.19 The electron transfer is faster than the hole transfer dueto longer coherence, stronger nonadiabatic (NA) coupling,higher density of acceptor states, and interaction with higherfrequency vibrational modes. The same factors rationalize thedifferences in the electron and hole energy relaxations. Therelatively long lifetime of the “hot” hole facilitates long-distancebandlike transport observed in organic systems. Driven by out-of-plane S−Mo and Se−Mo motions, electrons recombine withholes in isolated MoS2 and MoSe2 within one hundredpicoseconds, which is in good agreement with experi-ments.26−28 The electron−hole recombination across theinterface is several times longer, also in excellent agreementwith the measurement.19 The rapid subpicosecond electron andhole transfer emphasizes the role of quantum coherence, andguarantees that both MoS2 and MoSe2 can be used as sun-lightabsorbers in solar energy harvesting. The long exciton lifetimeat the interface indicates that van der Waals heterojunctions canbe used to design efficient photovoltaic devices.NA molecular dynamics are simulated using fewest-switches

surface hopping29 implemented within the time-dependent

Kohn−Sham theory.30,31 Quantum decoherence effects aredescribed using the optical response theory32 and a semi-classical correction to the NA dynamics.33 The method wasproven reliable in application to photoinduced processes in avariety of materials,33−39 including TiO2 sensitized by asemiconducting39 and metallic37 nanoparticles, carbon nano-tubes,33 graphane,38 and a fullerene-quantum dot composite.34

A detailed description of the method is presented in ourprevious publications30,33,40−44 and in the Supporting Informa-tion. While it is desirable to incorporate explicit electron−holeinteraction, such as that described by the Bethe-Salpeter theory,calculations of this type are very expensive. Time-dependentBethe-Salpeter theory has been applied only to systems withfixed nuclei.45−47 The chosen approach incorporates electroncorrelation effects implicitly in the density functional.Currently, it is the most rigorous ab initio method availablefor modeling the processes under investigation.The present work is motivated by both recent experi-

ments19,20,24 and theoretical works9,13−17 showing that chargesundergo efficient separation at the MoS2/MoSe2 interface andother 2D MX2 heterojunctions, even though the driving force isconsistently weaker than electron−hole binding. The simu-lations relate most directly to the experimental work by Zhaoand co-workers,19 focusing on the electron transfer from MoSe2to MoS2, the hole transfer from MoS2 to MoSe2, and theelectron−hole recombination at the MoS2/MoSe2 interface andin isolated MoS2 and MoSe2 monolayers.Figure 1a demonstrates the energy levels involved in the

photoinduced charge separation and recombination dynamics

at the type-II MoS2/MoSe2 photovoltaic heterojunction.Excitation of MoSe2 leads to electron transfer, while MoS2excitation results in hole transfer, ①. Competing with theseparation, the electron and hole can recombine inside eithermaterial, ②. Following the separation, the charges canrecombine at the interface, ③. Electronic degrees of freedomcouple to vibrations, leading to loss of quantum coherence.

Figure 1. (a) Electronic energy levels involved in the photoinducedcharge separation and recombination dynamics at the MoSe2/MoS2interface. Absorption of a photon hv by either MoSe2 or the MoS2leads to charge separation ① due to electron or hole transfer,respectively. Competing with the separation, the weakly boundelectron 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 duringthe ultrafast electron and hole transfer at the interface between MoSe2and MoS2, processes 1 and 2, and during intraband charge relaxationinside MoSe2 or MoS2, process 3. The decoherence times are shown inTable 1. The relatively long coherence ensures rapid interfacial chargetransfer. Longer coherence results in faster transfer and faster relaxation of electrons compared to holes, Figure 4.

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Processes 1 and 2 shown in Figure 1b represent loss ofcoherence between pairs of states involved in electron and holetransfer between MoS2 and MoSe2. Process 3 in Figure 1brefers to decoherence between different electronic states withinthe same material. This process is relevant to electron and holeenergy relaxation. We also consider decoherence for the CBM−VBM state pairs of either the same or different materialsinvolved in electron−hole recombination.Electronic Structure of the MoS2/MoSe2 Heterojunc-

tion. Figure 2a shows the projected density of states (PDOS)

of the MoS2/MoSe2 heterojunction, separated into thecontributions from the MoS2 and MoSe2 monolayers (blackand red lines). The PDOS indicates formation of a type-IIheterojunction. The canonically averaged CBM and VBMoffsets are 0.06 and 0.50 eV. The lowest energy excited stateformed at the heterojunction is a charge transfer state with theelectron localized at the MoS2 CBM and the hole localized atthe MoSe2 VBM. Photoexcitation of MoSe2 results in electrontransfer to MoS2, while photoexcitation of MoS2 induces holetransfer to MoSe2. The energies lost to vibrational motionsduring the electron and hole transfers are 0.06 and 0.50 eV,respectively. A total of 8.5 times more energy is lost after MoS2excitation 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 theinterfacial interaction and dynamics. The average distancebetween the MoS2 and MoSe2 monolayers decreases from 3.10Å at 0 K to 2.79 Å at room temperature, indicating that thedonor−acceptor interaction is enhanced due to thermalfluctuations. Atomic motions at a finite temperature distortthe perfect geometries of the 2D materials, providing additionalinteraction opportunities.

The charge densities of the key electron and hole orbitals areshown in Figure 2b. The vertical arrows pointing from panel bto panel a indicate the energies of these states. Figure 2b showsthat both photoexcited states are delocalized between the twomaterials, indicating significant donor−acceptor coupling;consider the MoSe2 CBM shown in the right-most pictureand the MoS2 VBM shown in the left-most picture. Thesituation is different for the acceptor states. The electron finalstate, that is, the MoS2 CBM, is slightly delocalized ontoMoSe2, while the hole final state, that is, MoSe2 VBM, isstrongly localized on MoSe2. The difference arises due to thedifference in the band offsets: the MoSe2 VBM is isolatedenergetically from the MoS2 states, while the MoS2 CBM isenergetically close to the MoSe2 states.The mixing of the donor and acceptor states alone does not

guarantee ultrafast charge separation. Quantum dynamicsrequires formation of coherent superpositions of the states.Long lifetimes of quantum superpositions facilitate fastdynamics, while short coherence time slows dynamics down,resulting in the quantum Zeno effect in the limit of infinitelyfast decoherence.48−51 The mixing between the donor andacceptor states has a significant effect on quantum coherence,because decoherence time is directly related to fluctuations ofthe energy gaps between the initial and final states, and thefluctuations are determined by the corresponding wavefunctions.

Electronic Coherence. In order to characterize thephonon-induced loss of electronic coherence, we computedthe pure-dephasing functions for the dephasing processeslabeled by 1, 2, and 3 in Figure 1b. The time scales, obtained byGaussian fitting, f(t) = exp[−0.5(−t/τ)2], are summarized inTables 1 and 2 for electron−hole separation and recombina-

tion, respectively. Loss of coherence between states involvingtwo complementary materials occurs faster than between statesof the same material. This is true for both charge separation,compare processes 1 and 2 versus process 3 (Figure 1b andTable 1), and recombination, Table 2. States localized within

Figure 2. (a) PDOS of the MoS2 and MoSe2 monolayers in the MoS2/MoSe2 heterojunction. The driving force for the charge separation isdetermined by the donor−acceptor band edge energy offsets. (b)Charge densities of the donor and acceptor states for the electron andhole transfer. Both electron and hole donor states are significantlydelocalized between MoSe2 and MoS2, forming coherent super-positions between the two materials. The electron acceptor state isslightly delocalized onto the donor, due to a small donor−acceptorenergy offset in this case, panel a. On the contrary, the hole acceptorstate 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) forSuperpositions of States Involved in Electron and HoleTransfer (1 and 2) and Relaxation (3)a

electrons holes

1 25 10.42 30 10.53 37 20

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

Table 2. Non-Adiabatic Coupling, and Elastic(Decoherence) and Inelastic (Recombination) TimesCharacterizing Electron-Phonon Interactions duringElectron-Hole Recombination Insider Pure MoSe2, PureMoS2, and MoSe2/MoS2 Interface

a

NA coupling(meV)

decoherence(fs)

recombination(ps)

MoSe2 0.440 7.0 63MoS2 0.257 8.6 41MoS2/MoSe2 0.135 6.2 680

aRecombination across the interface is longest as a result of smallercoupling and shorter coherence.

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the same material oscillate more coherently, subject to the samephonon modes.Decoherence is slower for electron transfer than for hole

transfer, Table 1. This fact can be also rationalized by statelocalization. Both initial and final states for electron transfer aredelocalized between the two materials, while only the initialstate for hole transfer is delocalized, Figure 2b. The relativelylong coherence ensures rapid interfacial transfer52 rationalizingefficient charge separation at the MoS2/MoSe2 interface

19 andother MX2 heterojunctions.

20 Longer coherence results in fasterdynamics of electrons than holes, as discussed below. A similareffect of quantum coherence enhancement of charge separationwas reported in organic photovoltaic blends on the basis ofboth experimental and theoretical work.53,54

Coherences between the pairs of states involved in theelectron−hole recombination, Table 2, are shorter thancoherences formed during the charge separation, Table 1.Combined with the large energy gaps involved in therecombination processes, small coherence times rationalizelong 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 presentsthe spectral densities, computed by Fourier transforms (FT) ofthe energy offsets between the initial and final states for theelectron and hole transfer. Figure 3a shows FT of the gapbetween the MoS2 and MoSe2 CBMs, while Figure 3b depictsFT of the gap between the MoS2 and MoSe2 VBMs. The insetsin Figure 3a show the unnormalized autocorrelation functions(ACF) of the energy gaps. The ACF initial values give theenergy gap fluctuation squared. The magnitude of the gapfluctuation has a strong effect on coherence time.55 Thefluctuation is notably smaller for the electron transfer than forthe hole transfer, corresponding to slower dephasing, Table 1.The fluctuation magnitude is smaller for the electron transfer,

because both initial and final states are delocalized between thetwo 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 electrondynamics involves acceptor states localized inside MoS2,containing light S atoms, to be compared to the hole acceptorstates localized in MoSe2, with heavier Se atoms, Figure 2. Theelectron transfer couples primarily to the 400 cm−1 mode, whilethe hole transfer involves the 300 cm−1 mode. In addition, theelectron couples to several higher frequency phonons, while thehole couples to a lower frequency mode. Faster modes createlarger NA coupling, because at a given temperature they havelarger nuclear velocities, dR/dt, that enter the NA coupling

matrix element, ϕ ϕ− ℏ⟨ |∇ | ⟩it

Rk R m

dd.

The dominant 400 cm−1 peak for electron transfer can beassigned to the out-of-plane S−Mo A1g mode.

56−59 The peak at460 cm−1 can be attributed to either the double overtone of theA1g mode of MoSe2 or the MoS2 out-of-plane A1g

2 mode at463.84 cm−1.57 The very high-frequency mode at 850 cm−1 isthe overtone of these lower frequencies. For hole transfer, themajor peak at 300 cm−1 corresponds to the Raman-active Eg

1

mode of MoSe2 at 285.90 cm−1. It can also be assigned to thein-plane Eg

2 mode of MoS2 at 283.78 cm−1.57 The small peak at460 cm−1 corresponds to the 463.84 cm−1 out-of-plane A1g

2

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 initiallyphotoexcited states for both processes are delocalizedsignificantly between MoS2 and MoSe2, Figure 2b. The out-of-plane displacements of Mo, S, and Se have a strong effect onthe electron, hole, and energy relaxation dynamics, becausethese motions modulate the energies of the MoS2 and MoSe2electronic states and change the donor−acceptor coupling.

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 unnormalizedACF 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 energiesof the delocalized donor and acceptor states, resulting in a large gap fluctuation, Cun(0), which fluctuation favors faster decoherence, Table 1. High-frequency phonons have higher velocities and create larger nonadiabatic coupling, eq 5 of Supporting Information. Longer coherence and largercoupling lead to faster electron transfer, compared to hole transfer, Figure 4a,b, respectively.

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Charge Separation Dynamics at the MoS2/MoSe2Interface. The dynamics of the photoinduced chargeseparation and the subsequent intraband energy relaxation are

characterized in Figure 4. Parts a and b represent chargetransfer, while parts c and d give energy relaxation. The timeconstants reported in Figure 4a−c are obtained by exponential

Figure 4. Charge separation dynamics. Top panels (a,b) show decay of the population of the electron and hole donor states, due to charge transferto the corresponding acceptor. Bottom panels (c,d) show evolution of the electron and hole energies. The data shown in (a−c) are fitted by theexponential, 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. Itcannot be fitted by a simple function. The charge transfer is faster than the energy relaxation. Both electron and hole transfer occur on ultrafast timesscales due to high density of acceptor states compared to density of donor states, significant nonadiabatic coupling, and relatively long coherencetimes.

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

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fitting, f(t) = exp(−t/τ). The hole energy relaxation cannot befitted reliably by a function combining one or two exponents orGaussians. This is because the hole relaxation involveselectronic states with a relatively low density, extending overa significant energy range, Figure 2a. The initial Gaussian orcosine type dynamics, characteristic of a Rabi oscillation, slowlydevelop into Fermi golden rule type exponential decay, oncemultiple state become accessible.The subpicosecond electron and hole transfer time scale

agrees well with the experimental data.19 The electron transferoccurs faster than the hole transfer for several reasons.Quantum coherence persists for a longer time for electronsthan holes, Table 1. The density of MoS2 states accepting theelectron is higher than the density of MoSe2 states acceptingthe hole, Figure 2a. The donor−acceptor interaction is strongerfor the electron transfer than the hole transfer, as indicated bythe notable delocalization of the final state of the electron-transfer process, the third panel of Figure 2b. Finally, thecomputed average absolute value of the NA coupling is largerfor 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” holecan facilitate rapid, bandlike transport to long distances, knownin organic photovoltaic blends.53,54

Electron−Hole Recombination. In addition to chargeseparation and relaxation, solar cell performance is affected bycharge recombination. Figure 5 shows the electron−holerecombination dynamics in isolated MoS2 and MoSe2 and atthe MoS2/MoSe2 heterojunction. The times are obtained usingthe short-time linear approximation to the exponential decay,f(t) = exp(−t/τ) ≈ 1 − t/τ. The decoherence effects areparticularly important here because loss of coherence occursmuch faster than the corresponding quantum transition.40 Thetime scales of coherence loss, Table 2, also known as pure-dephasing in the optical response theory,32 determine thehomogeneous line widths of the corresponding opticaltransitions, which can be measured for isolated MoS2 andMoSe2 monolayers. The optical line width for light emissionfrom the interfacial charge transfer state is harder to detect,because the state has low optical activity due to weak overlap ofthe 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 ingood agreement with the available experimental data for MoS2(100 ps)25,26 and MoSe2 (125 ps).27 The discrepancy may beattributed to the small size of the simulation cell, possiblyoverestimating electron−phonon interactions. The 680 psnonradiative electron−hole recombination time for theinterfacial process also agrees well with the experimental 240ps time.19 The smaller experimental number may berationalized by interfacial defects expected in experimentalsamples. Defects create states inside the bandgap, acceleratingthe recombination.33,60

Panels c and d of Figure 5 depict spectral densities of theCBM-VBM energy gap for the MoS2, MoSe2, and MoS2/MoSe2systems, characterizing the phonon modes promoting therecombinations. The electronic subsystem of the MoSe2monolayer couples primarily to the 240 cm−1 out-of-planeSe−Mo vibrational mode.61,62 Both MoS2 and MoS2/MoSe2show a strong contribution at the higher frequency of 400cm−1, which can be assigned to the out-of-plane S−Mo A1gphonon mode.56,58,59 The weak 340 cm−1 peak seen with the

MoS2/MoSe2 heterojunction can be attributed to the out-of-plane A1g motion of MoSe2.

57

In order to test reliability of the present DFT calculationswith the more rigorous many-body GW method,63−65 wecomputed the PDOS of the small periodical 6-atom MoS2/MoSe2 unit cell using the DFT and GW methods with a dense20 × 20 × 1 Monkhorst−Pack k-point mesh,66 Figure S1. Asexpected, GW gives a larger bandgap than the DFTcalculations. At the same time, the PDOS obtained from GWshows similar behavior to the DFT results of both small andlarge cells, Figure S1a and Figure 2a, indicating our currentDFT calculation is suitable to describe the electronic bands andtheir relative alignment in the MoS2/MoSe2 van der Waalsheterojunction. More rigorous Bethe-Salpeter calculationssignificantly decrease the optical excitation energy in thesematerials, bringing it closer to the experiment and the DFTbandgaps.67,68 It should be emphasized that both GW andparticularly the Bethe-Salpeter theory are very computationallyexpensive and cannot be used for the present purpose ofinvestigation of phonon-driven electron dynamics in the time-domain.In order to test the sensitivity of the electron−hole

recombination times to the bandgap values, we scaled thegaps to experiment and repeated the NAMD calculations forMoSe2 and MoS2 monolayers and the MoS2/MoSe2 interface.The MoSe2 and MoS2 gaps were scaled to the experimentalvalues of 1.5569 and 1.85 eV,70 respectively. The bandgap of theheterojunction was scaled to match the experimental gap ofMoSe2. The resulting electron−hole recombination time scalesin MoSe2, MoS2, and MoS2/MoSe2 are 79, 58, and 830 ps.These results show similar trend to the original data shown inTable 2. The similarity of the shapes and offsets of the GW andDFT valence and conductions bands of the two materials in theheterojunction supports our findings on the photoinducedcharge separation. The moderate dependence of the electron−hole recombination dynamics on the bandgap, validates ourconclusions on the nonradiative charge losses.

Concluding Remarks. Many applications of van der Waalsheterojunctions were proposed under the assumption of weakcoupling at the interface. Large interfacial spacing between thematerials, compared to typical chemical bond distances, allowsone to assume that these materials maintain their individualproperties. As a result, one often invokes the traditionalincoherent mechanism of charge transfer. The ultrafast timescales measured for this process question the incoherentmechanism. Indeed, we find that the interfacial charge transferoccurs by a coherent mechanism. The incoherent and coherentcharge transfer mechanisms exhibit notably different properties,for instance, in excitation energy dependence,71 and insensitivity to defects72 and densities of donor and acceptorstates.73

Related discoveries have been made recently regardingphotoinduced charge transfer from metallic systems, such asgraphene and plasmonic nanoparticles, into semiconductors.Here, one wonders how photoinduced charge transfer canhappen despite rapid electron and holes recombination, typicalof metals. Experiments have shown that plasmon-driven chargetransfer from metallic particles into TiO2 cannot be explainedby the traditional incoherent mechanism.71 The correspondingtheoretical prediction was published a year earlier.37 A coherentmechanism was established for the photoinduced chargeinjection from graphene into TiO2.

72 The latter case differsqualitatively from the current van der Waals heterojunction,

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because graphene shows strong chemical-like interaction withTiO2. The importance of quantum coherence in charge andenergy transport has been demonstrated in a number of otherbiological74,75 and nanoscale76,77 systems.In summary, we have investigated the photoinduced electron

and hole transfer dynamics in a MoS2/MoSe2 van der Waalsheterojunction using time-domain density functional theorycombined with NA molecular dynamics. The simulations showthat longer quantum coherence favors more rapid chargeseparation. The importance of coherence in quantum dynamicshas been established in several biological57,78−81 and materi-als82−84 systems. We demonstrate that coherence is importantfor efficient and rapid charge separation in the van der Waalsheterojunction. Longer coherence leads to faster transfer ofelectron compared to hole. Electron−hole recombination ismuch slower than charge injection and is associated with fasterdecoherence. The coherence time is directly related to thedelocalization of the initial and final states between the donorand acceptor materials and to the frequency and range ofphonon modes coupled to the electronic subsystem. Factorsother than coherence, in particular, density of final states, NAcoupling, and energy gap, also influence the time-scales of theprocesses under consideration. The charge transfer andvibrational relaxation are promoted primarily by the out-of-plane MoSe2 and MoS2 modes, because they influence therelative energies and localization of the donor and acceptorstates and create the NA couplings.The current study demonstrates that light harvesting by both

MoS2 and MoSe2 leads to efficient charge separation. The slowrelaxation of the photogenerated hole indicates possibility oflong-range band-like transport, favorable in applications.Charge separation at the MoS2/MoSe2 heterojunction reducesthe electron−hole recombination rate, compared to thecorresponding rates in isolated MoS2 and MoSe2 monolayers.Rapid charge transfer, combined with long electron−holerecombination times, indicates that MoS2/MoSe2 and similarmetal dichalcogenides van der Waals heterojunctions constituteappealing candidates for photovoltaics and electronicsapplications. The reported simulations provide a detaileddescription of the complex quantum dynamics at the two-dimensional transition metal dichalcogenide interface, generat-ing important insights and suggesting design principles foroperation of ultrathin devices under far-from-equilibriumconditions.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.5b05264.

Theoretical methodology and PDOS of the MoS2 andMoSe2 monolayers in small MoS2/MoSe2 heterojunctionfrom DFT and GW calculations. (PDF)

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: runlong@bnu.edu.cn.*E-mail: prezhdo@usc.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

R.L. is grateful to the National Science Foundation of China(Grant 21573022) and the Science Foundation Ireland SIRGProgram (Grant 11/SIRG/E2172). O.V.P. acknowledgessupport from the U.S. Department of Energy (Grant DE-SC0014429).

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