Photoinduced Electron Transfer at the Interface between

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C: Physical Processes in Nanomaterials and Nanostructures

Photoinduced Electron Transfer at the Interface Between Heterogeneous Two-Dimensional Layered Materials Kenji Iida, Masashi Noda, and Katsuyuki Nobusada J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05684 • Publication Date (Web): 23 Aug 2018 Downloaded from http://pubs.acs.org on September 2, 2018

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The Journal of Physical Chemistry

Photoinduced Electron Transfer at the Interface Between Heterogeneous Two-Dimensional Layered Materials Kenji Iida,∗ Masashi Noda, and Katsuyuki Nobusada Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, 444-8585, Japan E-mail: [email protected]

∗

To whom correspondence should be addressed

1

ACS Paragon Plus Environment

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Abstract We study the optical response of a MoS2 –graphene heterostructure by carrying out first-principles calculations of electron dynamics in real-time and real space. Our attention is primarily focused on the effect of interfacial contact between MoS2 and graphene. The interfacial contact has a negligible influence on the optical absorption of the MoS2 –graphene heterostructure. However, the photoinduced electron dynamics of the heterostructure is crucially different from those of the isolated monolayers of MoS2 and graphene; electronic polarization perpendicular to the MoS2 –graphene interface is induced by a laser pulse polarized parallel to the interface. By analyzing the variation in the electron occupation number, we find that electronic transitions in graphene and MoS2 accompany the electron transfer from graphene to MoS2 . This is due to the difference in the magnitudes of the density of states of MoS2 and graphene. In other words, the photoinduced electron transfer is governed by the details of the electronic structure in the atomically thin interfacial region and thus cannot be explained with a conventional band model. Our first-principles results reveal the novel mechanism of the optical response inherent in atomically thin interfacial regions.

1

Introduction

The optical response of heterointerface systems consisting of two-dimensional (2D) layered materials has been extensively investigated in relation to the development of photodetectors, solar cells, and photocatalysis. 1–9 Various 2D materials such as semiconductors (e.g., transition metal dichalcogenides), insulators (e.g., hexagonal boron nitride), and semimetals (e.g., graphene and silicene) are now utilized to fabricate heterointerface systems. 5–8,10 It has 2


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been shown that the integration of heterogeneous 2D materials yields novel optoelectronic devices whose functions cannot be performed with only a homogeneous 2D material. 5,10–12 Furthermore, a van der Waals contact is formed between 2D materials owing to their chemical stability. Because the lattice matching condition is not imposed upon the creation of van der Waals structures, numerous combinations of 2D materials are potentially available for providing heterointerface systems. Thus, it is necessary to obtain fundamental insights into their optical responses to effectively develop optical functional materials. When heterointerface systems are constructed with heterogeneous 2D materials, it is assumed that each component independently performs optical and/or electronic functions. For example, photodetectors consisting of graphene and a transition metal dichalcogenide (MX2 ) are designed so as to efficiently utilize the strong optical response of MX2 and the high electronic conductivity of graphene. 5,12 However, it is gradually being realized that the optical response of heterointerface systems often cannot be rationalized on the basis of the optical properties of each component. It has been reported that carrier transfer rates between 2D materials strongly depend on defects and contaminants in the interfacial region. 13,14 Strong electronic coupling between 2D materials is induced by photoexcitation. 15–17 These studies indicate that the atomically thin interfacial region plays a crucial role in the optical response. In order to obtain atomic-scale insights, first-principles computational methods are increasingly applied to nanostructures including 2D materials. 18,19 First-principles calculations of optical response have been widely performed with linear response (LR) approaches owing to their low computational cost. However, it is still difficult to address the optical response of heterointerface systems using the first-principles methods mainly because of two problems. First, a sufficiently large unit cell is required to substantially reduce the effect of the 3



artificial geometrical distortion that is attributed to the difference in the unit cell sizes of the employed materials. Second, to investigate the optoelectronic functions of heterointerface systems, the photoinduced electron dynamics should be explicitly considered. It is wellknown that the optical response in the interfacial region does not terminate with electronic excitation, but excited electrons often dissociate from electron holes; therefore, a photocurrent is obtained. Furthermore, the optical and electronic properties of 2D materials can be considerably altered by photoinduced electron transfer because their density of states (DOS) is fairly low. 5,11,20 Such complex electron dynamics cannot be explained by the LR theory that describes a first-order perturbative change in the electronic state. Thus, theoretical insights into the optoelectronic functions of heterointerface systems have been severely limited. We have been developing a first-principles computational program named SALMON (Scalable Ab-initio Light-Matter simulator for Optics and Nanoscience) for electron dynamics in real-time and real-space. 21 In SALMON, time-dependent density functional theory (TD-DFT) calculations are performed at real-space grid points. 22,23 Thus, this program is highly suitable for performing massively parallel calculations and can be applied to nanostructures including heterointerface systems. Furthermore, because the electron dynamics is directly calculated in real-time, it is possible to investigate complex optical responses that cannot be addressed by conventional LR approaches. In other words, SALMON overcomes the above-noted two problems. With this program, we have elucidated various optical responses of isolated systems (e.g., a gold-thiolate nanocluster) and periodic systems (e.g., a metal-organic framework). 24,25 In this study, we clarify the mechanism of the optical response of a MoS2 –graphene 4


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heterostructure by using SALMON. This heterostructure is one of the most extensively investigated heterointerface systems consisting of heterogeneous 2D materials. 12–14,26,27 As experimental results have been accumulated for this system, the importance of the interfacial region in the optical response has been gradually demonstrated. For example, while the photoinduced electron transfer from MoS2 to graphene is controlled by an applied electrode bias, 13 that from graphene to MoS2 occurs by creating a clean MoS2 –graphene interface. 14 However, there are fewer theoretical insights into the relation between the interfacial electronic structure and the optical response. It has only been reported using an LR approach that the MoS2 –graphene interface has a negligible influence on optical absorption. 28 Here, we shed new light on the role of the interfacial region in the optical response by carrying out real-time and real-space electron dynamics simulations. It is revealed that photoexcitation of the MoS2 –graphene heterostructure causes the electron dynamics inherent in atomically thin interfacial regions.

2 2.1

Theory Time-Dependent Kohn–Sham Equation

In SALMON, the electron dynamics is calculated by the time-dependent Kohn–Sham equation for auxiliary electronic wave functions in the Coulomb gauge as follows: 21,29 [ ] ∫ ∂ 1 2 1 2 ρ(r′ , t) ′ i ψjk (r, t) = − ∇ − iA(t) · ∇ + A (t) + vnuc (r) + dr + vXC (r, t) ψjk (r, t) , ∂t 2 2 |r − r′ | (1)

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where A is the vector potential of an external field, vnuc is the nuclear attraction potential, vxc is the exchange correlation (XC) potential, and ρ is the electron density given as

ρ(r, t) =

2 ∑ fjk |ψjk (r, t)|2 . ktot j,k

(2)

In eq. (2), ktot is the number of k points, and fjk is the electron occupation probability, which is defined by the Fermi–Dirac distribution function. 30 The electric conductivity σ and dielectric function ϵ are given by ∫

dteiωt J(t) , dteiωt Eext (t) 4πiσ(ω) ϵ(ω) = 1 + , ω

σ(ω) = ∫

(3) (4)

where Eext (t) is the electric field of the laser pulse and J(t) is the electric current flowing the unit cell. 29 The electronic polarization density per unit area, P (t), is then given as ∫ P (t) =

t

J(t′ )dt′ .

(5)

0

This definition of the polarization is available independent of whether its direction is perpendicular or parallel to the interface. We also calculate the electron dynamics subject to a laser pulse whose electric field is given as

ˆ cos (ωt) sin2 (πt/τ ) , Eext (t) = E0 u

6


(6)

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ˆ is a unit vector along the Cartesian axis, ω is the laser frequency, E0 is the amplitude where u of the incident laser field, and τ is the pulse width. The laser intensity I (W cm−2 ) is related √ to E0 (V m−1 ) by E0 = 27.45 I. Since we consider a Coulomb gauge, the vector potential in eq. (1) is given as A(t) = −

2.2

∫t 0

Eext (t′ )dt′ . 29

Theoretical Formula for Analyzing Electronic Excitation

To analyze the photoexcitation dynamics induced by a laser pulse, we calculate the variation in the electron occupation number using the following equations:

cljk (t) = fjk (t = 0) |⟨ψjk (r, t)| ψlk (r, t = 0)⟩|2 , ∫ ∑ Dlk (E ≡ εlk , z, t) = cljk (t) |ψlk (r, t = 0)|2 dxdy,

(7) (8)

j

∆Dlk (E, z, t) = Dlk (E, z, t) − Dlk (E, z, t = 0),

(9)

where ε is a band energy in the ground state. In eq. (7), the time-evolved orbital ψjk (r, t) is projected onto the ground-state orbital ψlk (r, t = 0), 31 and fjk is introduced to deal with fractionally occupied orbitals. Using eq. (8), we spatially visualize an electronic excitation. Because the electron density |ψlk (r, t = 0)|2 is integrated over the x and y directions, the electronic excitation is depicted along the z direction perpendicular to the x–y plane. It is here assumed that the x and y directions are parallel to the interface of a hetero-interface system, and the z direction is perpendicular to the interface. In eq. (9), we calculate the difference in Dlk between the values at t ̸= 0 and t = 0. Lorentzian broadening is then applied to ∆Dlk , and the distributions of ∆Dlk are summed with respect to l and k. We thereby obtain the variation in the electron occupation number, ∆Dtot , induced by a laser 7



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pulse. The variation in the occupation number is further divided in terms of the band energy as follows:

Djk (E ≡ εjk , z, t) = −

∑

∫ cljk (t)

l(εlk ∈α)

Dlk (E ≡ εlk , z, t) =

∑

cljk (t)

|ψjk (r, t = 0)|2 dxdy,

(10)

∫ |ψlk (r, t = 0)|2 dxdy,

(11)

j(εjk ∈β)

where the minus sign is applied in eq. (10) to define Djk as the decrease in the electron occupation number, while Dlk in eq. (11) denotes the increase in the number. The summations in these equations are performed when the band energies satisfy the condition of εlk ∈ α ∩ εjk ∈ β. Thus, we can evaluate the variation in the occupation number due to specific electronic transitions from an energy range α to an energy range β (denoted as Dαβ ).

3

Computational Details

Geometry optimization was performed by using the Quantum Espresso program package. 32 The dispersion-corrected Perdew–Burke–Ernzerhof (PBE) functional was employed to calculate the exchange correlation potential to deal with van der Waals interactions. 33–36 The number of k points and the cutoff energy were set to 12×12×1 and 90 Ry, respectively. The optimized geometry is shown in Figure 1. The distance between the atomic layers of S and C is 3.3 ∼ 3.4 ˚ A, which is well in accordance with previous experimental and theoretical studies (3.4±0.1 ˚ A). 37–39 The optimized geometry was used to calculate the optical response with SALMON, in

8


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which the time-dependent Kohn–Sham equation is directly solved in real-time and realspace. The grid spacings were set to ∼0.22 ˚ A in accordance with the unit cell size. The supercell length along the direction perpendicular to the MoS2 –graphene interface was set to a sufficiently large size of 36 ˚ A. All electrons other than the Mo 4d5 5s1 , S 3s2 3p4 , and C 2s2 2p2 electrons were replaced with effective core potentials obtained by using the Troullier– Martins scheme implemented in the fhi98PP program. 40,41 Visualizations of the geometrical structure were performed with the VESTA program package. 42 The PBE functional 33,34 was mainly used in the calculations with SALMON. It is known that the generalized gradient approximation (and the local density approximation) functionals reproduce the band gap of MoS2 well. 43–46 Nevertheless, we also performed calculations using the Tran–Blaha modified Becke–Johnson meta-GGA (TB-mBJ) functional, which is available for improving the computational results of optical properties. 47 The TB-mBJ functional has been applied to not only bulk systems but also to various systems including interfacial and surface systems such as Si(111), and the validity has been well investigated. 48 We found that the difference between the TB-mBJ and PBE functionals has a qualitatively (b) Side view

(a) Top view

z x

y x

Figure 1: (a) Top and (b) side views of the optimized geometry of the MoS2 –graphene heterostructure. S, Mo, and C are colored yellow, purple, and brown, respectively.

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negligible influence, at least, on the photoinduced electron dynamics discussed in this study. The result of the TB-mBJ calculation is also briefly described in Section 4.2. Because of the difference in the unit cell sizes of graphene and MoS2 , their geometries are artificially distorted in the MoS2 –graphene heterostructure. To investigate this effect, we also performed geometry optimization of the isolated monolayers of MoS2 and graphene. It was confirmed that the optical absorption spectra were almost unchanged by geometrical distortion (Supporting Information, Section S.1).

4 4.1

Results and Discussion Electronic and Optical Properties

We first describe the fundamental electronic and optical properties of the MoS2 –graphene heterostructure, confirming the validity of the computational methods. Figure 2 shows a map of the 2D local density of states (LDOS) of the heterostructure. The horizontal axis is the z direction perpendicular to the MoS2 –graphene interface. The positions of the atomic layers are depicted below the 2D LDOS map; the atomic layers are located around 4.6 ˚ A (S), 3.1 ˚ A (Mo), 1.5 ˚ A (S), and −1.9 ˚ A (C). The vertical axis is the band energy E relative to the Fermi level. In the valence band from 0 eV to −1 eV (area I enclosed by the white dotted line), the distribution is discernible around the graphene monolayer whereas not found around the MoS2 monolayer at all. This is because graphene and MoS2 are semimetallic and semiconducting materials, respectively. In the conduction band at ∼ 1 eV (area II enclosed by the white dotted line), the distribution around MoS2 is much larger than that around

10


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MoS2

Graphene

LDOS

2 (eV-1·Å-1) 1

5

II 0

I

-1 -2

0 -3

7

6

5 4

S

3 2 1 0 -1 -2 -3 -4

Mo S

-4 E (eV)

C z (Å)

Figure 2: A 2D LDOS map of the MoS2 –graphene heterostructure. A distribution whose value is larger than the threshold value is set to the same color as the maximum value.

graphene. As shown in the next section, the photoinduced electron dynamics of the MoS2 – graphene heterostructure is governed by these differences in the magnitudes of the DOSs. In Figure 3, we plot the optical absorption spectra with the polarization parallel to the plane of the 2D materials. The quantity α2 is defined as α2 ≡ zs Im[ϵ]/(4π), where ϵ is the dielectric function and zs is the supercell length along the z direction. α2 has been used by Yang et al., 49 and is almost independent of the unit cell size. This is because ϵ is proportional to zs−1 when a large vacuum region is introduced. 28 Here, we primarily focus on the effect of the interfacial electronic interaction; thus, the geometrical structures of the isolated monolayers of MoS2 and graphene are fixed to that of the heterostructure for comparison. The isolated graphene monolayer has a broad absorption with a small peak around 4 eV. The spectrum of the isolated MoS2 monolayer begins to rise at 1.5 eV, and peaks are found around 2 eV and 3 eV. These spectral profiles are qualitatively in accordance with previous experimental and theoretical results. 13,28,50,51 Figure 3 also shows the sum of

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2.5 MoS2-Graphene Sum (MoS2 + Graphene) 2.0

α2 (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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MoS2 Graphene

1.5

1.0

0.5

0.0 1.5

2.0

2.5

3.0

3.5

4.0

4.5

Energy (eV)

Figure 3: Optical absorption spectra with the polarization parallel to the plane of the 2D materials. “MoS2 –Graphene” denotes the MoS2 –graphene heterostructure, and “Sum” means the sum of the spectra of the isolated monolayers of graphene and MoS2 . “Graphene” and “MoS2 ” denote the isolated monolayers of graphene and MoS2 , respectively.

the absorption spectra of the isolated monolayers. The sum is almost superposed with the spectrum of the MoS2 –graphene heterostructure. This result means that the interfacial contact between MoS2 and graphene has a negligible influence on the optical absorption of the heterostructure, as reported in the previous theoretical study. 28 However, in the following, it is clarified that the interfacial contact causes photoinduced electron dynamics that cannot be explained by the LR theory; therefore, the optical response of the heterostructure becomes significantly different from those of the isolated monolayers of graphene and MoS2 .

4.2

Photoinduced Electron Dynamics

Figure 4 shows the z component of the time-dependent electronic polarization, P (t), induced by a laser pulse polarized along the x direction parallel to the 2D material layer. The laser intensity and energy are 109 W cm−2 and 2 eV, respectively, and the pulse duration is 20 fs. Then, the power spectrum of the incident laser, |Eext (ω)|2 , has the half width of half maxi12


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3.0E-6

Induced polarization (a.u.)

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MoS2-Graphene (I = 109 W cm-2) MoS2 (I = 109 W cm-2) Graphene (I = 109 W cm-2) MoS2-Graphene (㽢1/10; I = 1010 W cm-2)

2.5E-6 2.0E-6 1.5E-6 1.0E-6 5.0E-7 0.0E+0 -5.0E-7 0

5

10

15

20

Time (fs)

Figure 4: Time-dependent polarizations along the z direction induced by an x-polarized laser field. The results for the 1010 W cm−2 laser are divided by 10. The notation in the figures is the same as that in Figure 3.

mum of 0.17 eV, which is sufficiently small, at least, to well distinguish electronic transitions discussed in this study. The laser excitation of the MoS2 –graphene heterostructure causes electronic polarization perpendicular to the interface as time evolves, while such electronic polarization is not induced in the isolated monolayers of graphene and MoS2 because of their geometrical symmetry. Thus, this electronic polarization in the heterostructure is attributed to the interfacial contact. Electronic polarization partly analogous to the present result has been found in a previous study on an isolated organic donor–acceptor pair using a real-time first-principles approach. 52 In Figure 4, we also show the result for the heterostructure irradiated by a 1010 W cm−2 laser pulse, where the magnitude of the polarization is divided by 10 for comparison. The polarizations due to the 109 and 1010 W cm−2 lasers are almost superposed with each other, that is, the magnitude of the polarization is proportional to the square of the electric field of the incident laser pulse. LR approaches are available only for describing an electronic

13



polarization linearly depending on an external electric field; thus, the present electronic polarization is not a simple electronic excitation process that can be adequately investigated by LR approaches but a more complex optical process. To clarify the origin of the electronic polarization along the z direction, we show in Figure 5 the variation in the electron occupation number (i.e., ∆Dtot defined with eqs. (7)–(9)) at t = 20 fs induced by the laser pulse. The definitions of the horizontal and vertical axes are the same as those in Figure 2. The red and blue distributions indicate that the electron occupation number becomes larger and smaller than that in the ground state, respectively; that is, electrons are excited from the blue areas to the red areas. Figure 5(a) shows the result for the MoS2 -graphene heterostructure. The distributions are found in areas A (−1.7 to −1.3 eV), B (−1.3 to −0.8 eV), C (0.2 to 0.8 eV), and D (0.8 to 1.3 eV), whose borders are drawn by white dotted lines. The write arrows depict an energy gap of 2 eV, i.e., the incident laser energy. 2-eV electronic transitions take place in both of the moieties of MoS2 (A→C) and graphene (B→D), and are also found in the isolated monolayers of MoS2 and graphene, as shown in Figures 5(b) and 5(c), respectively. Electronic transitions characteristic to the heterostructure are enclosed with black dotted circles in Figure 5(a). The circled distributions indicate that electrons transfer from graphene (blue) to MoS2 (red). This electron transfer is the origin of the electronic polarization along the z direction shown in Figure 4. The electron transfer from graphene to MoS2 is also yielded by the calculation with the TB-mBJ functional, as well as the present PBE calculation (see Supporting Information, Section S.2). It is further noted that an experimental study has recently reported remarkable photoinduced electron transfer from graphene to MoS2 by creating a clean MoS2 –graphene interface. 14 The electronic excitation of this heterostructure consists of numerous electronic transi14


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(a) MoS2-Graphene MoS2

2

(eV-1·Å-1)

4·10-3

Graphene

D

1

0

0

-4·10-3

C

-1

B

E (eV)

A -2 7 6 5 4 3 2 1 0 -1 -2 -3 -4

(b) MoS2

2

(c) Graphene

z (Å) 2

1

1

0

0

-1

-1

-2

-2 0 -1 -2 -3 -4

7 6 5 4 3 2 1 0

Figure 5: Variations in the electron occupation number due to the photoexcitation of (a) the MoS2 –graphene heterostructure and the isolated monolayers of (b) MoS2 and (c) graphene. A distribution whose value is larger (smaller) than the threshold value is set to the same color as the maximum (minimum) value.

tions from valence band states to conduction band states; thus, to analyze the photoinduced electron transfer, the electronic transitions are further divided into groups of electronic transitions from A or B to C or D. Figure 6 shows the variation in the electron occupation number due to the A→C and B→D transitions (i.e., DAC and DBD defined with eqs. (10) and (11)) at t = 20 fs. The sum of these variations reproduces the overall picture shown in Figure 5(a) well, and the other transitions, A→D and B→C, are negligibly small. This is because only the transition energies of A→C and B→D are the same as the incident laser energy of 2 eV. The A→C and B→D transitions mainly occur in the moieties of MoS2 and graphene,

15



(a) A→C

2 1

C 0

(eV-1·Å-1) 4·10-3 -1

A 7 6 5 4 3 2 1 0 -1 -2 -3 -4

(b) B→D

-2

0 2 1

D

-4·10-3

0

-1

B

-2

E (eV)

7 6 5 4 3 2 1 0 -1 -2 -3 -4

z (Å)

Figure 6: Variations in the electron occupation number due to the (a) A→C and (b) B→D transitions. A distribution whose value is larger (smaller) than the threshold value is set to the same color as the maximum (minimum) value.

respectively, and accompany the electron transfer between MoS2 and graphene at A and D. Indeed, a close relation between the electronic transitions and the electronic transfer is found in Figure 4. Since the probability of an electronic transition is proportional to the laser intensity, the results for the 109 and 1010 W cm−2 lasers indicate that the magnitude of the electron transfer is determined by the strength of the electronic transitions. From the above results, the electron transfer is attributed to interference between one-photon excitations of frequencies 2 eV/h and −2 eV/h (h: Planck’s constant), which causes the electron dynamics within the same energy level (i.e., 2 eV − 2 eV). 53,54 In fact, the power spectrum

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of electric current has a large peak around 0 eV due to the monotonic electronic polarization (see Supporting Information, Section S.3). Analogous monotonic photoinduced electronic polarizations, or steady photocurrents, have been intensively investigated for bulk materials lacking inversion symmetry. 54 Table 1 summarizes the numbers of excited electrons belonging to the moieties of MoS2 and graphene due to the A→C and B→D transitions. The results for the isolated monolayers are also listed for comparison. Here, to evaluate the number of excited electrons, the distributions of the transitions are spatially separated by a bisecting plane between the atomic layers of graphene and S (z = −0.2 ˚ A). We then sum the densities belonging to the separated distributions. The total number of transferred electrons from graphene to MoS2 is given as 2.6 × 10−3 , while the number directly evaluated from the variation in the electron density (i.e., ρ(r, t) − ρ(r, t = 0)) is 2.7 × 10−3 . The difference between these numbers is sufficiently small for verifying the validity of the present analysis based on the projection method given by eqs. (7)-(11). The total numbers of exited electrons belonging to the A→C (12.7 × 10−3 ) and B→D (7.0 × 10−3 ) transitions are almost the same as those of MoS2 (12.8 × 10−3 ) and graphene (6.9 × 10−3 ), respectively. This accordance means that the electronic transitions in the respective moieties of MoS2 and graphene are almost independent of the interfacial Table 1: Numbers of excited electrons (10−3 ) in the moieties of MoS2 and graphene. Conduction band Valence band MoS2 Graphene MoS2 Graphene A→C 11.6 1.1 12.6 0.1 B→D 0.1 6.9 1.7 5.3 MoS2 12.8 – 12.8 – Graphene – 6.9 – 6.9

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contact but accompany the electron transfer from graphene to MoS2 . On the basis of the above-noted results, the mechanism of the electron transfer is schematically illustrated in Figure 7, where the band states with a low density are depicted as dashed bars in accordance with Figure 2. It is noted that the magnitude of the DOS is not taken into account in conventional band models. In the A→C transition (Figure 7 (a)), electrons are excited in MoS2 . Since the electron population in valence band A of MoS2 decreases owing to electronic excitation, electrons transfer from graphene to MoS2 . This electron transfer by the A→C transition is described also as the hole transfer from MoS2 to graphene due to the creation of holes in MoS2 . In conduction band C, excited electrons cannot transfer to graphene because the DOS is significantly low in the graphene moiety. The inhibition of electron transfer in C indirectly contributes to the hole transfer. In the B→D transition (Figure 7(b)), electronic excitation takes place in graphene. In valence band B, the DOS is not found in the MoS2 moiety at all; thus, electrons do not transfer from MoS2 to graphene. Although the excitation of graphene is weaker than that of MoS2 , the excited electrons in D readily transfer to MoS2 . In fact, Table 1 indicates that the ratio of transferred electrons to excited electrons in graphene, (6.9 − 5.3)/6.9, is fairly larger than that in MoS2 , (12.6 − 11.6)/12.6. This is because the DOS of graphene is much lower than that of MoS2 in A, C, and D. The B→D transition largely increases the electron density per band states in D of graphene with the low DOS, and strongly induces the electron transfer from graphene to MoS2 with the higher DOS. In contrast, in the A→C transition, the hole transfer from MoS2 to graphene in A readily reduces the difference in the hole density per band states between the MoS2 and graphene moieties while the electron transfer from MoS2 to graphene in C is significantly inhibited; therefore the relatively small hole transfer is induced. In other words, both of the 18


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(a) A→C

e-

C

A

e-

e-

e-

MoS2 Graphene

e-

MoS2 Graphene

(b) B→D

e-

D

B

e-

e-

eMoS2 Graphene

MoS2 Graphene

Figure 7: Schematic of photoinduced electron transfer. The yellow circles and black arrows denote electrons and the directions of electron transfer, respectively.

A→C and B→D transitions accompany the electron transfer from graphene to MoS2 owing to the difference in the magnitudes of the DOSs of graphene and MoS2 . In experimental studies, photoinduced electron transfer in MoS2 –graphene heterostructures has been phenomenologically explained using conventional band models, which are widely applied to heterostructures consisting of bulk materials. It has been considered that photoexcited electrons in MoS2 are transported owing to the internal built-in electric field and hence electrons are transferred between MoS2 and graphene. 13,14 The mechanism of the present electron transfer is significantly different from that considered in the experimental studies. First, our first-principles results show that the electronic excitation of graphene substantially contributes to the electron transfer. This is because, as seen from Table 1, the excited electrons in graphene readily transfer to MoS2 , even though the number of excited electrons in graphene is smaller than that in MoS2 . Second, this electron transfer is not

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related to the internal electric field. In the present system, the MoS2 and graphene moieties are negatively and positively charged in the ground state, respectively, owing to the interfacial contact between them (see Supporting Information, Section S.4) as well as previous computational results. 39,55 Thus, the electron transfer from graphene to MoS2 is not induced by the internal electric field. The notable feature of this electron transfer is its strong dependence on the details of the electronic structure. Indeed, an experimental study has reported that photocurrents in the MoS2 –graphene heterostructure crucially depend on the numbers of contaminants and defects. 14 Meanwhile, this electron transfer is considered to be negligible when an optoelectronic function is performed in a bulk region. This is because the magnitudes of the DOS should have a minor influence on the optical response when the DOS is sufficiently high. In fact, electron transfer in heterostructures consisting of bulk materials has been widely rationalized using the conventional band models. In other words, the present photoinduced electron transfer can remarkably take place in atomically thin interfacial regions with a low DOS. Here, we have revealed a novel mechanism for the optical response of heterointerface systems precisely designed at the atomic scale.

5

Concluding Remarks

We have studied the optical response of a MoS2 –graphene heterostructure by carrying out real-time and real-space electron dynamics calculations. The interfacial contact between MoS2 and graphene has a negligible influence on the optical absorption. However, laser excitation of the heterostructure causes characteristic electron dynamics that does not occur

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in the isolated monolayers of graphene and MoS2 . By analyzing the variation in the electron occupation number, we clarified that the electronic transitions in MoS2 and graphene accompany the electron transfer from graphene to MoS2 because of the difference in the magnitudes of the DOSs between MoS2 and graphene. Experimental studies have extensively investigated the optical response of atomically thin layered materials, while its mechanism has been phenomenologically explained with conventional band models. In this context, the present first-principles study reveals a novel mechanism for photoinduced electron transfer, which is different from those considered in experimental studies. This electron transfer is mainly characterized by its strong dependence on the electronic structure in the atomically thin interfacial region. Heterointerface systems have been extensively designed on the basis of the assumption that the optoelectronic functions are independently performed in each component. However, it is found that the variation in the optoelectronic function depending on the combination of employed materials can become larger than that estimated on the basis of previous theoretical considerations. The insights obtained in this study are expected to contribute to the development of optoelectronic devices consisting of heterogeneous atomically thin layered materials.

Associated Content Supporting information available: the effects of artificial geometrical distortion on optical absorption, the variation in the electron occupation number of the MoS2 –graphene heterostructure induced by the laser pulse using the TB-mBJ functional, the power spectrum of the electric current perpendicular to the interface of the MoS2 –graphene heterostructure,

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the variation in the electron density due to the contact between MoS2 and graphene in the ground state.

Acknowledgments This research was supported by JSPS KAKENHI (Grant No. 25288012), MEXT as a social and scientific priority issue (Creation of new functional devices and high-performance materials to support next-generation industries) to be tackled by using the post-K computer (ID: hp170074, hp170250) and the JSPS Core-to-Core Program, A. Advanced Research Networks. This work mainly used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (ID: hp170074, hp170250). Computations were also partly performed at the Research Center for Computational Science, Okazaki, Japan.

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TOC Graphic

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Photoinduced Electron Transfer at the Interface between

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