Introduction

In two-dimensional (2D) materials, Coulomb-induced electronic states of excitons have been examined as a platform to understand many-body carrier–carrier interactions. These excitonic interactions dominate in layered materials due to quantum confinement and reduced dielectric screening. 2D atomic crystals of transition metal dichalcogenides (TMDs) have provided new opportunities in the studies of single-exciton single-photon interactions, spin–orbit coupling, ultrafast dynamics, and nanoelectronic devices.1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 Layer-by-layer stacking of TMDs-based van der Waals (vdWs) heterostructures has recently captured the attention of the scientific community where the tailored band alignment with diverse 2D materials can be achieved via advanced 2D growth and transfer techniques.23,24,25,26,27,28 This has allowed the extension of indirect excitons with spatially separated electrons and holes from, for example, coupled quantum wells in GaAs/AlGaAs29,30 to TMD vdW heterostructure bilayers, where they are referred to as interlayer excitons. These interlayer excitons exhibit rich physics in TMDs-based vdWs heterostructures due to the novel atomic granularity control through layer-by-layer stacking and the chiral properties of quantum electronic states.8,31,32 Recently several studies observed that heterostructure interlayer excitons feature long lifetimes, spin-valley polarization by circularly-polarized pumping, near-unity valley polarization via large magnetic splitting, and charge transfer at the heterogeneous interfaces.32,33,34,35,36,37,38,39,40,41,42,43,44,45

Here, we demonstrate TMDs-based vdWs heterostructures composed of a three-layer WSe2–MoSe2–WSe2 stack to achieve unique band alignment that promotes efficient interlayer radiative recombination. We first design the heterostructure through pseudopotential calculations based on spin-polarized density functional theory (DFT), with the exchange-correlation potential estimated via the Perdew–Burke–Ernzerhof functional. Optimizing the designed heterostructure band structure through conjugate gradients, we include the effects of spin–orbit coupling through non-collinear computations. We correlate the obtained real-space pseudo-wavefunctions with lattice points in reciprocal space to understand the carrier localization, the type-II optical transition oscillator strength, and potential asymmetries in the electron and hole band profiles towards neutral interlayer excitons and three-body trion complexes. Enabled by the first-principle computations, we fabricate the trilayer heterostructure stack through hexagonal boron nitride-assisted transfer. Our dry transfer process allows a relatively undoped heterostructure and atomic smoothness at the interfaces. We perform cryogenic photoluminescence on the designed trilayer heterostructure along with time-resolved pulsed measurements via time-correlated single-photon counting, mapping the spectral, pump fluence, and bath temperature dependence of the interlayer excitons. We observe an order-of-magnitude larger photoluminescence in the trilayer compared to bilayer heterostructures, due to the more distributed hybridized valance band state in the trilayer for increased oscillator strength, along with the formation of the neutral interlayer exciton. The additional WSe2 layer absorbance in the trilayer also contributes to the stronger photoluminescence compared with the bilayer. At 4 K, we observe a spectrally-distinguishable trion formation. We determine that the energy splitting between the neutral exciton and trion is largely dependent on the pump fluence and photocarrier densities instead of the bath temperature. We observe that the trion mostly red-shifts while the neutral exciton stays consistent and extract a trion binding energy of approximately 27 meV in our trilayer heterostructure. This result is close to the interlayer negative charged exciton binding energy of 28 meV as predicted by the recent theoretical study on the vertical stack MoS2/WS2 heterostructures.46 With increasing photocarrier injection and decreasing bath temperatures, the trion-to-neutral intensity ratio is also increased. Radiative lifetimes of the interlayer excitons are measured up to ≈2.54 ns at 4 K. We examine the radiative lifetimes for different bath temperatures, pump fluences, and excitation wavelengths, with observed stronger dependences on the bath temperature. Our study enables the engineering of indirect neutral excitons and charged trions with spatially separated electron and hole wavefunctions, towards control of the oscillator strengths and excitonic character with designed atomic granularity.

Results

Theoretical analysis

Here, we introduce the concept towards the enhancement of the exciton recombination rate of the trilayer heterostructure illustrated in Fig. 1a, b. The trilayer heterostructure consists of a single-layer (SL) MoSe2 sandwiched between two SLs of WSe2. The anticipated type-II band alignment, depicted in Fig. 1b, supports excitons with the electron and hole residing respectively in the conduction band of MoSe2 and valence band of WSe2. This resembles the situation for excitons in heterostructure bilayers, where the electron and hole are strongly localized to the different layers by the large band offsets.47,48,49 This is indeed the case for the electron in the conduction band of the trilayer structure, which is strongly localized in the central MoSe2 layer due to a weak interlayer coupling.50 However, in our case, the valence band states are subject to a stronger interlayer coupling.50 Consequently, the valence band states in our two outer WSe2 layers hybridize with the state in the central MoSe2 layer. Accordingly, the delocalization of the valence band state over the entire trilayer enables the strong overlap of the electron–hole in the trilayer, compared to the prior bilayer counterparts.

Fig. 1
figure 1

Excitonic states of TMDs-based trilayer heterostructure, interlayer excitons model, and computed band structure and wavefunction distribution comparisons between the bilayer and trilayer heterostructures. a Illustration of WSe2–MoSe2–WSe2 trilayer heterostructure with a sandwiched single layer (SL) MoSe2 between two SLs WSe2. b Schematic summary of the interlayer exciton radiative recombination predicted by type-II heterojunction. εX, εopt, and εg represent the exciton binding energy, optical gap, and electronic gap, respectively. c Computed band structure of the WSe2–MoSe2 bilayer heterostructure. d Computed band structure of the WSe2–MoSe2–WSe2 trilayer heterostructure. e Computed orbital wavefunction of the WSe2–MoSe2 bilayer heterostructure valence band maximum (VBM) and conduction band minimum (CBM) at k-point as a function of the interlayer distance z. f Computed orbital wavefunction of the WSe2–MoSe2–WSe2 trilayer heterostructure

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To support this physical picture, we carried out first-principles DFT calculations including the spin–orbit interaction of the bilayer and trilayer band structures and wavefunctions, with the computational details described in the Methods. The results are summarized in Fig. 1c, d. (Band structures of SL MoSe2 and SL WSe2 are shown in Supplementary Section S1.) While the bilayer heterostructure shows a ≈1.22 eV bandgap, the trilayer heterostructure has a slightly smaller ≈1.21 eV bandgap, both at the K-point. In both the bilayer and trilayer structures, our calculations predict states which are predominantly localized in either WSe2 (blue) or MoSe2 (red) layers, in agreement with the band alignment illustrated in Fig. 1b. Figure 1e, f shows the spatial distribution profile of the electron and hole probability densities in the out-of-plane direction, for the states at the valence and conduction band edges. In the bilayer, the electron and hole states hardly overlap, hence the long lifetime,31,32,51,52 and our weaker PL is shown in Figure S3. On the other hand, in the trilayer structure the valence band state shows the expected delocalization with a large center-layer component and thus a significant overlap with the localized conduction band state.

In our proposed scheme as shown in Fig. 1b, the type-II staggered heterojunction leads to energetically lower excitonic states due to the band offset between MoSe2 and WSe2. Furthermore, with the trilayer heterostructure, the strong asymmetry between the electron and hole band profile promotes excitons complexes such as trions.2,16,33,39,53 Unlike bilayer TMD heterostructures, a metallic state through biasing the Fermi level in the conduction or valence band is required in the trilayers to produce imbalance in electron and hole populations and hence increase the likelihood of trions formation.33,39 The interlayer trions can be achieved, for example, with two electrons in the MoSe2 layers and one hole in the WSe2 layer. A description of the radiative recombination pathways in the trilayer and the trions is shown in Supplementary Section S2.

Trilayer sample preparation and cryogenic photoluminescence spectroscopy

We fabricate the WSe2–MoSe2–WSe2 trilayer heterostructure on a SiO2/Si substrate by dry transfer with a hexagonal boron nitride (h-BN) flake of 20 nm thickness as shown in Fig. 2a. Both SL WSe2 and SL MoSe2 are mechanically exfoliated from bulk crystals and identified with optical microscopy, PL, and Raman spectra. Before the stacking process, the sample thickness is further confirmed independently via atomic force microscopy (AFM) as shown in Fig. 2b. Raman spectroscopy is conducted on the SL MoSe2, SL WSe2, 20 nm-thick h-BN as well as TMDs trilayer heterostructures as illustrated in Fig. 2c. In the inset of Fig. 2c, we observe two distinguishable modes at 243 cm−1 (MoSe2) and 247 cm−1 (WSe2). 20 nm-thick h-BN is used as an encapsulating layer due to its atomic smoothness and relative absence of charge traps and dangling bonds.54 Raman shift of h-BN shows up in the TMDs-based trilayer heterostructure. The completed h-BN/WSe2/MoSe2/WSe2 stacked structure is on a 290 nm SiO2 substrate. To avoid undesired doping, we do not use any chemicals. With regards to the stacking geometry, we randomly stack our TMDs-based vdWs heterostructure since interlayer excitons can potentially be formed regardless of the layer orientation in vertically stacked heterostructures.8 As shown in Fig. 2d, PL spectroscopy is performed on our SL MoSe2 and SL WSe2 before and after transfer at varying temperatures, with the 1.88 eV pump excitation at ≈2 mW and with an ≈1 μm beam spot size. PL spectra show each peak of the SL MoSe2 (≈1.57 eV) and SL WSe2 (≈1.64 eV) are obtained with high quantum efficiency; our trilayer shows two PL peaks captured by a Si detector. With decreasing temperature, both MoSe2 and WSe2 peaks are blue-shifted, consistent with prior studies.20,55,56,57,58 The interlayer optical transition from the type-II heterojunction becomes dominant at low temperatures. We noticed from the 77 and 4 K trilayer PL curves in Fig. 2d that when the interlayer PL is more dominated, the intralayer PL is more quenched suggesting an efficient ultrafast charge transfer in the trilayer heterostructure, which agrees with previous ultrafast charge transfer studies of the bilayer heterostructure.48,59,60 As shown in the light brown line of Fig. 2d, we observe that the PL intensities of the interlayer excitons can be larger even compared to those of intralayer excitons. (An example comparison of the trilayer to the bilayer is shown in Supplementary Section S3.) It is interesting to note that the addition of a WSe2 layer to the MoSe2–WSe2 bilayer can result in higher PL quantum yields of both intralayer and interlayer excitons at room temperature and cryogenic temperatures. The reason, as noted in the “Introduction” and “Theoretical analysis” sections, is from the strong wavefunction overlap in the trilayer and additional exciton formation from the extra WSe2 layer absorbance. We note that the PL enhancement due to absorbance from the extra layer is not more than a factor of 2, while the enhancement measured is an order-of-magnitude larger. This additional enhancement is the contribution of the increased wavefunction overlap.

Fig. 2
figure 2

TMDs-based trilayer van der Waals (vdWs) heterostructure fabrication and characterization. a Microscopic images of the exfoliated transition metal dichalcogenides monolayers [i–iii] and trilayer vdWs heterostructure [iv] on SiO2 substrate. The dashed red and blue lines in the lower panels denote the atomic force microscopy (AFM) regions. The area enclosed by dashed yellow line indicates the trilayer heterostructure region. Scale bar: 5 μm. b AFM cross-sectional profiles, where each atomic single-layer (SL) is ≈7 Å. WSe2 and MoSe2 are the blue and red lines, respectively. c Raman spectra of the trilayer heterostructure versus each SL (MoSe2, WSe2, h-BN) decomposition, pumped with a 532 nm laser. Inset: zoom-in of the Raman shift around 245 cm−1. d Room-temperature PL spectra for the SL WSe2, SL MoSe2, and the trilayer heterostructure, together with the low-temperature PL spectra from the trilayer heterostructure at 77 and 4 K. The excitation is via a 632 nm HeNe laser. Dotted lines under the trilayer heterostructure PL spectra are the bilayer heterostructure PL spectra, with especially large enhancement of the lower-energy interlayer exciton transition

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Interlayer excitons in coupled quantum wells have previously been studied at low temperature in order to avoid thermal quenching of the PL due to nonradiative processes and electron–hole pairs excited to energies outside the light cone.29,30 In Fig. 3, we illustrate the temperature-dependent PL measurements from 4 to 245 K of our trilayer atomic crystal, in order to examine the interlayer many-body excitonic transitions. Here, we use a liquid-nitrogen-cooled InGaAs photodetector with high responsivity from 900 to 1600 nm. In our trilayer heterostructure, a long lower-energy spectral tail can be observed in the main interlayer exciton PL peak and becomes spectrally distinguishable from the neutral interlayer exciton (IEX1) peak at 4 K as shown in Fig. 3a (1.96 eV pump excitation). We consequently deconvolved our trilayer interlayer lineshape into two peaks with Lorentzian lineshapes. The higher energy (black line fit) and lower energy (red line fit) peaks are denoted as IEX1 and IEX2, respectively, which we will subsequently attribute to the interlayer neutral excitons and trions (charged exciton) respectively as we will further elaborate below. The inset of Fig. 3a shows the spectroscopy with our one-dimensional focal plane array InGaAs detector, with the horizontal axis the spectra and the vertical axis the spatial position across the sample via a scanning mirror.

Fig. 3
figure 3

Temperature-dependent PL intensities and spectral lineshapes of the interlayer excitons in the trilayer heterostructure. a Indirect excitons PL spectra at 4 K, fitted with a blue line. Both IEX1: neutral exciton (black) and IEX2: trion (red) lines are fitted with Lorentzian lineshapes. Inset image shows PL spectrum captured by a focal plane array detector with horizontal axis the spectra and the vertical axis the spatial position across the sample in one direction. b Temperature-dependent indirect PL spectra in trilayer heterostructure with pump excitation at 1.96 eV and ≈1.2 mW reaching sample. The black and red lines denote the respective peaks, with the dashed black and red curves at the 4 K spectra illustrating the Lorentzian lineshape decomposition. The data were obtained from the same spot on the sample. The spectra are offset for clarity. c PL peak shifts of the neutral exciton (IEX1) and trion (IEX2) deduced from the main panel and fitted with semiconductor bandgap temperature-dependence model. The phonon-induced bandgap renormalization is described in Supplementary Section S5. d PL peak intensities at different cryogenic temperatures. Black and red dots indicate the PL intensities of neutral exciton and trion, respectively. e The ratio of neutral exciton (IEX1) to trion (IEX2) peak intensities in the trilayer heterostructure are illustrated as a function of bath temperature

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Figure 3b shows the interlayer exciton spectra at different bath temperature, with the black (IEX1) and red (IEX2) lines tracking the spectral decomposition. It is worth noting that IEX2 becomes distinguishable only at fairly low temperatures in the interlayer exciton lineshape. As shown in Fig. 3b, both peaks are blue-shifted and broadened as the temperature increases and become undetectable above 245 K. Figure 3c summarizes the measured temperature dependence of their peak positions, quantified by the bandgap variation with temperature.58 Linewidth temperature dependence and the phonon-induced bandgap renormalization model is described in Supplementary Sections S4 and S5, respectively. Under the same pump fluence and as shown in Fig. 3c, we note that the energy difference between IEX1 and IEX2 does not change as temperature increases up to 126 K, the temperature after which the IEX2 peak is too weak to distinguish with certainty. This is consistent with the fact that peak splitting of exciton and trion depends on the pumping fluence,16,61 further supported by our power-dependent PL spectra results later in this study.

Figure 3d, e shows the neutral exciton and trion PL peak intensities and their ratio as a function of temperature. The PL peak intensities decrease with increasing temperature because in, for example, SL MoS2 it is attributed to thermally excited excitons which escape the light cone.62 Our reduced PL intensity with increasing temperature is attributed to the band structure of our trilayer heterostructure, which resembles that of SL MoSe2 near the band edges despite the existence of two WSe2 layers. In addition, we note that the phonon-assisted transitions move the weight from the main PL peak to lower energies and thereby reduce the PL peak intensities. Furthermore, since the promoted nonradiative process competes readily with radiative recombination of the interlayer excitons, the interlayer radiative recombination is not observed at room temperature. In Fig. 3e, we plot the ratio of PL peak intensities, IIEX2/IIEX1, which increases from ≈0.13 at 96 K to ≈0.28 at 4 K due to suppressed nonradiative recombination and high carrier densities. An abrupt rise around 10 K is typically induced by a rapidly increasing lifetime of trions and is a key feature of trions.20 Discussion about the abrupt rise using mass-action model is detailed in the Supplementary S9. We note that the interlayer radiative recombination channels—in both the neutral exciton and trion—may involve the processes of optical phonons in order to conserve momentum in the band-to-band transition by optical phonon absorption and phonon emission. This is especially the case for the trion which has approximately two times larger full-width half-maximum (FWHM) than the neutral exciton (detailed in Supplementary Figure S4) and has a stronger thermal dependence.

In our experimental measurements, we have assigned the two distinct interlayer PL emission peaks IEX1 and IEX2 to the neutral exciton and the three-body trion, respectively. More details on the interlayer excitonic radiative recombination pathways are described in Supplementary Section 2 and Figure S2. For the lower energy (IEX2) interlayer peak, we have also considered two other scenarios but both are unlikely. The first is a phonon-assisted indirect radiative recombination between valence band maximum (VBM) of WSe2 at K-point and conduction band minimum (CBM) of MoSe2 at Σ-point, per the band diagram of Fig. 1c, d. However, based on our DFT calculations, the second valley at Σ-point of MoSe2 CBM is located at ≈200 meV higher than K-point of MoSe2 CBM. This large energy requirement makes it hard for the carriers to thermalize in this phonon-assisted transition, even at room temperature (≈25.7 meV). The second considered scenario is that of a potential sub-band above the K-point of MoSe2 CBM. However, in our DFT calculations, we could not find the sub-band or energy splitting at MoSe2 CBM nor the WSe2 VBM. This further supports that the IEX2 transition arises from the interlayer trions.

In Fig. 4, we summarize the pump fluence dependence of the two interlayer excitons in our trilayer heterostructure by tuning the optical injection of the carriers. While the spectral shift of interlayer neutral exciton under increasing pump fluence has only a slight blue-shift, the spectral position of the trion is significantly more red-shifted with increasing pump fluence. This is illustrated in Fig. 4a. Figure 4b summarizes the extracted energy difference between the peaks of the two electronic states for increasing photocarrier injection, illustrating a resulting linear dependence. A description of the two peak energy difference and the trion binding energy, in the presence of carrier screening, is detailed in Supplementary Section S2. Based on this energy splitting, we extract the trion binding energy of ≈27 meV from Fig. 4b,19 which is higher than the thermal activation energy at room temperature and even comparable with intralayer trion binding energy of SL TMDs,16,19,20,21,58,63 and ≈28 meV negative charged interlayer exciton binding energy in vertical stack MoS2/WS2 heterostructures.46 This increasing spectral shift and binding energy with photocarrier density is another evidence for the interlayer trions.19,39 This is because, with increasing photocarrier injection, free charge requires more energy to occupy the three-body trion excitonic states. In turn, we plot the PL spectral weights of the neutral exciton and trion in Fig. 4c for increasing excitation fluence. With increasing photocarrier injection, the spectral weight and the ratio of the trion to the neutral exciton increases, which is supporting evidence of the interlayer trions existence.39

Fig. 4
figure 4

Power-dependent PL spectra in the trilayer heterostructure at 4 K. a Power-dependent PL spectra with Lorentzian-fitted neutral exciton (black curve) and trion (red curve) at 4 K. b Energy splitting (trion binding energy: EIEX1−EIEX2) between two interlayer optical transition peaks as a function of excitation power (log scale). c PL spectral weight of neutral exciton (black dots) and trion (red dots), and the ratio of trion to neutral exciton (blue dots), as a function of pump excitation power

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Discussion

We further investigate the lifetimes of the interlayer neutral exciton and trion, to help elucidate the many-body process. We build the time-resolved photoluminescence (TRPL) setup by means of a time-correlated single-photon counting (TCSPC) system and conduct temperature-, pump fluence-, and pump wavelength-dependent TRPL experiments. All results are fitted biexponentially to the experimental data. Radiative recombination of excitons is difficult to obtain at room temperature because nonradiative recombination is dominant. Accordingly we perform lifetime measurements at cryogenic temperatures, with ≈9 μJ/cm2 pump fluence and 1.88 eV (660 nm) pump wavelength, above both the SL MoSe2 and SL WSe2 direct gaps. Figure 5a, b summarizes the recombination lifetimes of interlayer neutral exciton and trion at various cryogenic temperatures. We note that, in the measurement of the IEX2 lifetimes, we band-pass filter the spectrum with center wavelength around 990 ± 2 nm and FWHM of 10 ± 2 nm, to select the PL centered ≈985 nm in order to exclude the dynamics of the interlayer neutral exciton. As shown in Fig. 5a, the lifetimes of our trilayer heterostructure interlayer exciton (IEX1) are ≈2.54 ns (4 K), 2.47 ns (40 K), 1.84 ns (80 K), and 0.41 ns (120 K), on the same order-of-magnitude as prior bilayer heterostructure studies47 and theoretical calculations.32 For our trilayer heterostructure interlayer trion (IEX2), they are ≈1.24 ns (4 K) and 0.47 ns (20 K). At higher bath temperatures, nonradiative recombination (including phonon-assisted processes) is faster, resulting in the shorter effective lifetimes observed.

Fig. 5
figure 5

Interlayer excitons lifetime and its dependence on temperature and photocarrier injection in the trilayer heterostructure. a, b Temperature-dependent carrier lifetimes of interlayer neutral exciton (IEX1) and trion (IEX2) in trilayer heterostructure. Samples are excited with ≈9 μJ/cm2 power fluence at 1.88 eV (660 nm). c Carrier lifetimes of IEX1 and IEX2 with different temperatures at pump fluence of ≈9 μJ/cm2. The carrier relaxations are fitted with exponentials to extract the carrier lifetimes. d Time-resolved radiative recombination of IEX1 under different pump fluences at 4 K. e Carrier lifetimes of IEX1 under different pump fluences at 4 K

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Figure 5c summarizes the extracted lifetimes from Fig. 5a, b. Although the data points are sparse, we note that the lifetime of the interlayer excitons decreases linearly with increasing temperature and the interlayer trions decreases faster than interlayer excitons. This also correlates with the observed faster trion lifetimes in the finite bath temperature TRPL and the broader linewidths of the trions. We note that the lifetime of the interlayer trion is not observable above 20 K due to the low photon counts. To further explore the properties of interlayer exciton, we turn our attention to the interlayer exciton lifetimes under various pump fluences and pump wavelengths. As shown in Fig. 5d, e, the lifetime of interlayer exciton (IEX1) is weakly dependent on carrier injection compared to the bath temperature. As the pump fluence increases, the lifetime only decreases slightly from ≈2.72 ns (1.6 μJ/cm2) to ≈2.53 ns (8.1 μJ/cm2). With increasing pump fluence, the interlayer exciton density increases which cause a blue-shift. The dipolar exciton–exciton interaction may lead to the change of peak positions and the decrease of lifetime.64 The decrease of lifetime with increasing excitation fluence indicates that residual defect states are involved, as shown in Fig. 5d for the IEX1 interlayer lifetime (lifetime of IEX2 with increasing excitation fluence is not distinctly resolvable). The presence of residual defects also explains why the PL intensities of interlayer exciton and trion decrease as temperature increases. We also conduct pump wavelength-resolved TRPL experiment, which is detailed in Supplementary Section S6. There is no correlation between the pump wavelength and the lifetimes of the interlayer exciton. This is because the electron–phonon decay dynamics to the band edge in TMDs is on the order of picoseconds, much shorter than the radiative recombination of interlayer excitons.65,66,67

In this study, we demonstrated the enhanced Coulomb interactions in WSe2–MoSe2–WSe2 trilayer vdWs heterostructures, through interlayer radiative recombination of the neutral and charge excitonic states. Designed through spin-polarized DFT with exchange correlation and spin–orbit coupling, we examined type-II heterostructures with increased optical transition oscillator strengths. Fabricated via h-BN enabled dry transfer, the trilayer heterostructure exhibits an ≈3× (at 77 K) and 5× (at lower temperature) stronger photoluminescence in our measurements. This arises from the more spatially distributed hybridized valence band state across the trilayer which, while the conduction band is localized only at the MoSe2 layer, enables larger overlap and oscillator strengths. Our cryogenic steady-state and time-resolved photoluminescence measurements elucidate the additional presence of a three-body excitonic state in the interlayer radiative recombination, with the trion binding at ≈27 meV and largely dependent on the pump fluence and carrier densities instead of the bath temperature. Conversely, the trilayer interlayer radiative lifetimes are largely dependent on the bath temperature instead of the pump fluence and exciton wavelengths, promoted by phonon-assisted transitions. The relatively long radiative lifetimes measured up to 2.54 ns at 4 K enables next-generation excitonic devices.68 Future experiments include gating the heterostructures with controlled carrier densities and spectrally separated excitonic resonances to further clarify their roles in exciton dephasing and population relaxation.17,69 Also, previous studies about the ultrafast charge transfer between layers within the MoS2/WS2 heterostructures reveal the fs scale dynamics which can be tuned significantly by changing stacking configuration.53,63,64 So future ultrafast pump-probe spectroscopy experiment on our trilayer compared with the bilayer heterostructure can be an interesting topic about the effect of extra WSe2 layer, inducing its stacking configuration, on the charge transfer dynamics. With advanced 2D material growth techniques and computational methods,27,70 we believe our trilayer heterostructures support the understanding of interlayer light–matter interactions with facilitated carrier transfer and type-II heterojunctions, paving new ways to tailor the electronic and optoelectronic character of vdWs heterostructures.

Methods

Computational method

In the computational modeling of the MoSe2 and WSe2 based heterostructures, the atomic structure of monolayer MoSe2 and WSe2 are first optimized using first-principles pseudopotential calculations based on the spin-polarized DFT within the generalized gradient approximation (GGA). The optimized monolayers are placed on top of each other with proper interlayer distances that correspond to the ground state energy for each heterostructure. During this process, van der Waals corrections are implemented following the DFT-D2 method of Grimme.71 Projector-augmented wave potentials (PAW) are used in the calculations and the exchange-correlation potential is approximated with Perdew–Burke–Ernzerhof functional.72,73 During the geometrical optimization steps, the Brillouin zone (BZ) is sampled in the Monkhorst–Pack scheme, where the convergence in energy as a function of the number of k-points is tested. The k-point sampling of (21 × 21 × 1) is found to be suitable for the BZ corresponding to the primitive MoSe2 and WSe2 unit cells. The heterostructures are optimized using the conjugate gradient method, where the total energy and atomic forces are minimized. The energy convergence value between two consecutive steps is chosen as 10−5 eV. A maximum force of 0.01 eV/Å is allowed on each atom. In order to avoid interactions between periodic unit cells, a supercell with 20 Å vacuum is used. The optimized heterostructures are then used for the electronic band structure calculations. The band diagrams are obtained by calculating the energies at 150 k-points between the Γ–M–K–Γ high symmetry points in the BZ. The effects of spin–orbit coupling on the electronic structures are calculated by performing non-collinear computations as implemented in VASP.74 The real-space wavefunctions are obtained from the DFT calculations using the binary wavefunction file that is produced by VASP. The binary WAVECAR file that is produced after a series of DFT calculations at the K-point is then mapped by WaveTrans, which correlates the binary wavefunctions with the corresponding lattice points in the reciprocal space and their associated planewave coefficients. The real-space pseudo-wavefunction is constructed again using WaveTrans.75

Sample preparation and characterization

SL MoSe2 and SL WSe2 flakes are separately prepared by mechanical exfoliation on clean 290 nm SiO2/Si substrates. A thin layer of hexagonal boron nitride is first exfoliated on a PMMA/PPC stack, which is then used for layer-by-layer picking up of the prepared WSe2 and MoSe2 in order. The picked up MoSe2/WSe2/h-BN/polymer stack is finally transferred on a WSe2/SiO2/Si substrate.25,26 During the entire dry transfer process, no solvent is involved to ensure the atomically clean interface between the 2D materials. Raman measurement (Renishaw, inVia basis) is conducted using a 532 nm laser to map out the sample quality.

Cryogenic micro-photoluminescence and time-resolved photoluminescence

We use an optical cryostat (Janis Research ST-100) to measure the cryogenic photoluminescence at 4 K. Measurements are carried out using a Si detector (Newport Model 2151) for the shorter wavelength regime (400–1000 nm) with a continuous-wave He–Ne 632.8 nm pump laser. For the longer wavelengths (900–1600 nm) where interlayer exciton and trion can exist, an InGaAs focal plane array detector with liquid nitrogen cooling system (Princeton Instruments 2D-OMA) is used with high responsitivity. The detector signal is improved by using a lock-in amplifier and selectively filtered by a spectrometer (Princeton Instruments SpectraPro 2500i). TRPL measurements are performed using a TCSPC system with PicoQuant. The sample is excited with a 30 ps 39/78 MHz tunable pulse laser system (NKT Photonics SuperK EXTREME EXW-12) and detected with a single-photon counting module (SPCM-AQR-16) attached to a monochromator and processed by a PicoHarp 300 correlating system with ≈300 ps resolution. The TRPL measurements are conducted at low temperature with optical filters in an enclosed optical setup to prevent pump and stray ambient light from affecting the detectors.