Interfacial Charge Transfer for Enhancing Nonlinear Saturable Absorption in WS2/graphene Heterostructure

Abstract Interlayer charge‐transfer (CT) in 2D atomically thin vertical stacks heterostructures offers an unparalleled new approach to regulation of device performance in optoelectronic and photonics applications. Despite the fact that the saturable absorption (SA) in 2D heterostructures involves highly efficient optical modulation in the space and time domain, the lack of explicit SA regulation mechanism at the nanoscale prevents this feature from realizing nanophotonic modulation. Here, the enhancement of SA response via CT in WS2/graphene vertical heterostructure is proposed and the related mechanism is demonstrated through simulations and experiments. Leveraging this mechanism, CT‐induced SA enhancement can be expanded to a wide range of nonlinear optical modulation applications for 2D materials. The results suggest that CT between 2D heterostructures enables efficient nonlinear optical response regulation.


WS2/Graphene Heterostructure Construction
The fabrication of the WS2/Gr heterostructure used in this study can be found in our previous reports. 1It is produced by transferring a chemical vapor-deposited (CVD) WS2 monolayer onto a CVD graphene monolayer which was transferred on a sapphire substrate

Characterization
The optical transmission spectra were obtained with the UV-vis spectrophotometer (UV-2600, Shimadzu).Both the steady photoluminescence (PL) spectroscopy and Raman spectrum was collected by the Renishaw InVia Qontor confocal microsope system.The morphology was investigated by atomic force microscopy (Agilent) techniques.The detail of home-built Pumpprobe setup can be found in our previous work. 2,3

Micro OA Z-scan
The light source was the Ti:sapphire femtosecond laser system (Spitfire ACE, Spectra-Physics) with a central wavelength of 800 nm, a pulse duration of 40 fs, and a repetition rate of 2000 hz.The detail of home-built open-aperture Z-scan could be found in our previous work. 2In order to eliminate the influence of dust, wrinkles or uneven areas, based on the original Z-scan, the lens in front of the sample was replaced with a microscope objective (Magnification: 10X; Numerical aperture 0.30), and the detailed optical setup is shown in Figure S8.With the additional CCD camera and micro-objective (Magnification: 10X; Numerical aperture 0.30), a clean and wrinkle-free area with WS2/Gr heterostructures could be easily located for Z-scan test.
Prior to the sample measurement, we performed the Z-scan test on a clean transparent sapphire substrate to determine the optical intensity that the sapphire do not produce any NLO response.The WS2 and Gr samples were large-area CVD films uniformly covered on 1x1cm double-polished sapphire substrates.The laser beam waist radius was obtained by fitting the Zscan curve of the standard sample.The beam waist radius was about 3.5um-5um between 400nm-800nm.

Transient absorption spectra
The femtosecond TA spectra were taken using the Ultrafast System HELIOS TA spectrometer, where the laser source was a Coherent Astrella−1K-F Ultrafast Ti:Sapphire Amplifier (100 fs, 1 kHz, 800 nm) seeded by a Coherent Vitesse oscillator.The pump laser at 400 nm was generated by a BBO crystal.

DFT calculations
All calculations were carried out using the projector-augmented wave method in the framework of the density functional theory, as implemented in the Vienna ab initio Simulation Package (VASP). 4The generalized gradient approximation (GGA) and Perdew−Burke−Ernzerhof (PBE) exchange functional were used.The plane-wave energy cutoff was set to 500 eV, and the Monkhorst−Pack method 5 with a k-mesh of 6 × 6 × 1 was employed for the Brillouin zone sampling of the WS2/Gr structure.
The convergence criteria of energy and force calculations were set to 10 −6 eV/atom and 0.001 eV Å−1, respectively.A vacuum region of 15 Å is applied to avoid interactions between the neighboring configurations.The vdW interactions are described with Grimme's DFT-D3 approach. 6Figure S4a shows the optimized structure of WS2/Gr, which are constructed by the 2 2 1  supercell of WS2 matching the 7 7 1  supercell of graphene with the lattice mismatch of 1.1%. 7

Section S2. Calculation of PTE transferred carriers
According to the previous angle-resolved photoemission spectroscopy results, 8 the VBM of WS2 is 1.5 eV lower than the Dirac point of Gr, corresponding to a hole barrier.And the quasiparticle band gap of WS2 is 2.27 eV, 9 so the CBM of WS2 is 0.77 eV higher than the Dirac point, corresponding to an electron barrier.By the Z-scan curves, we can determine the beam waist at different wavelengths.The waist radius at 633 nm is determined to be 4.9 μm, while the waist radius at 800 nm is determined to be 5.4 μm.Based on the beam waist and the absorbed optical power density, we can determine the injected photon density at each point on the Z axis in the Z-scan.And according to the PTE model in Gr and the barrier height, we can calculate the number of carriers injected into WS2.As shown in Figure 3d, the calculation results of the PTE model agree well with the effect of saturation absorption enhancement, which shows the connection between carrier transfer and saturation absorption enhancement.
The electrons and holes in graphene that gains enough energy from carrier-carrier scattering could cross the electron barrier (   = 0.77 ) and hole barrier (  ℎ = −1.5), injecting into the conduction band and valence band of WS2 system, respectively.This part of carriers increased obviously with the excitation wavelength changed from 800 nm to 633 nm.As mentioned above, the modulation depth of the Gr/TMDs is negative correlated with the sum of the distribution function in

Section S3. The ab initio NAMD calculations
The ab initio NAMD calculations are performed using Hefei-NAMD code with phase correction version, 10 which augments the VASP with the NAMD capabilities within time-dependent density functional theory (TDDFT) similar to previous works. 11 perform different K points Hefei-NAMD calculation, 12 we use the hexagonal unit cell with 3 3 1  k-point grid which including K and Γ highly symmetric points of the WS2/Gr system.We use velocity rescaling to bring the temperature of the system to 300 K.Then, a 5 ps ab initio molecular dynamics trajectory is then generated from which the time-dependent KS wave functions can be obtained with the time intervals of 1.0 fs.After that, the surface hopping is applied on the basis of fewest switches surface hopping scheme using averaging over 50 different initial configurations and 20000 trajectories for each structure.
Figure S5a shows the optimized structure of WS2/Gr, which are constructed by the 2 2 1  supercell of WS2 matching the 7 7 1  supercell of graphene with the lattice mismatch of 1.1%.The band structure of heterostructure in Figure 4e demonstrated that the VBM and CBM of WS2 are on the either side of the Dirac cone of graphene, indicating a type-I band alignment.That is, the photo-generated electrons and holes in WS2 will transfer to graphene.According to the schematic diagram of the Brillouin zone in Figure S13b, the K@WS2 and K@Gr points of the Brillouin zones are folded to the K@HS (K point of the heterojunction), and the Γ@HS (Γ point of the heterojunction) point contains the Γ@WS2, Γ@Gr, M@WS2 and M@Gr.This is also evident from the band structure diagram in Figure 4e.We focused on the states near the Fermi level (~ -1 eV) by sampling at the Γ@HS and K@HS, and their energy evolution over time is depicted in Figure S14a and b.Within the given energy range (-3 ~ 0eV), the two red lines at the K point correspond to the CBM and VBM of WS2, and the two blue lines represent the Dirac cone states of Gr (See Figure S14a).The states evolution at the Γ point differs markedly from that at K point (See Figure S14b).The Gr state appears near -2.7 eV, indicating that the c arrier transfer at the Γ point is dominated by holes and occurs at a deeper energy level.

Figure S1 .
Figure S1.Schematic diagram of WS2/Gr in sapphire substrate and transmission spectrum of sapphire.

Figure S2 .
Figure S2.TA spectra of WS2 and WS2/Gr under 400 nm laser excitation Figure S3.TA spectra of Gr under 400 nm laser excitation Figure S4.Height profiles of AFM and schematic of the height of the WS2/Gr heterostructure in sapphire substrate.

Figure S5 .
Figure S5.Laser power-dependent Raman spectra Figure S6.TA spectra of WS2 under 800 nm laser excitation

Figure
Figure S1.(a) Schematic diagram of WS2/Gr in sapphire substrate.(b) Transmission spectrum of sapphire.

Figure S2 .
Figure S2.Color plot of TA spectra of (a) WS2 and (b) WS2/Gr heterostructure under 400 nm laser excitation.(c) TA spectrum of the WS2/Gr heterostructure and WS2 at a 400 fs time delay.

Figure S3 .
Figure S3.Color plot of TA spectra of (a) Gr under 400 nm laser excitation.(b) Normalized transient dynamics of the Gr probe at 700 nm.

Figure
Figure S4.(a) Height profiles, measured by atomic force microscopy, along the dashed white line in Figure 2e.(c) Schematic of the showing the WS2/Gr heterostructure in sapphire substrate.

Figure S5 .
Figure S5.Laser power-dependent Raman spectra of (a) Gr and (b) WS2/Gr heterostructure.(c) 2D peak position as a function of G-peak position.

Figure S6 .
Figure S6.Color plot of TA spectra of WS2 under 800 nm laser excitation.

Figure
Figure S9.Open-aperture (OA) Z-scan study of WS2 monolayers, Gr, and WS2/Gr heterostructure with the excitation wavelength of 700 nm.

Figure
Figure S11.(a) Color plot of TA spectra of WS2/h-BN/Gr, under 800 nm laser excitation.(b) TA spectrum of the WS2/h-BN/Gr, WS2/Gr, and WS2 at a 400 fs time delay.

Figure S12 .
Figure S12.Comparison of fitted (a) saturable intensity, (b) NLO absorption coefficients, (c) imaginary part of the third order of nonlinear optical susceptibility, and (d) figure of merit in different wavelength.

Figure S14 .
Figure S14.Time evolutions of the energy states in (a) K, and (b) Γ point of high symmetry of WS2/Gr heterostructure.

Table S1 .
Fitting results of lifetimes