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Long-lived direct and indirect interlayer excitons in van der Waals heterostructures Bastian Miller, Alexander Steinhoff, Borja Pano, Julian Klein, Frank Jahnke, Alexander Holleitner, and Ursula Wurstbauer Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b01304 • Publication Date (Web): 25 Jul 2017 Downloaded from http://pubs.acs.org on July 25, 2017

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Long-lived direct and indirect interlayer excitons in van der Waals heterostructures Bastian Miller,1,2 Alexander Steinhoff,3 Borja Pano,1 Julian Klein,1,2 Frank Jahnke,3 Alexander Holleitner,1,2* Ursula Wurstbauer1,2* 1

Walter Schottky Institut and Physics-Department, Technical University of Munich,

Am Coulombwall 4a, 85748 Garching, Germany. 2

Nanosystems Initiative Munich (NIM), Schellingstr. 4, 80799 München, Germany.

3

Institut für Theoretische Physik, Universität Bremen, P.O. Box 330 440, 28334

Bremen, Germany

Abstract We report the observation of a doublet structure in the low-temperature photoluminescence of interlayer excitons in heterostructures consisting of monolayer MoSe2 and WSe2. Both peaks exhibit long photoluminescence lifetimes of several ten nanoseconds up to 100 ns verifying the interlayer nature of the excitons. The energy and linewidth of both peaks show unusual temperature and power dependences. While the low-energy peak dominates the spectra at low power and low temperatures, the high-energy peak dominates for high power and temperature. We explain the findings by two kinds of interlayer excitons being either indirect or quasi-direct in reciprocal space. Our results provide fundamental insights into long-lived interlayer states in van der Waals heterostructures with possible bosonic manybody interactions.

Keywords: van der Waals heterostructure, indirect excitons, interlayer exciton, photoluminescence, exciton lifetime, transition metal dichalcogenides;

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Semiconductor heterostructures (HS) very often lay the foundation for the observation of novel phenomena in fundamental science and applications. The electrical and optical properties of such HS can be engineered over a wide range resulting in precisely tailored functionalities. Of particular interest are optically active HS that facilitate device applications like photodetectors, solar cells, light-emitting diodes or lasers and that support the observation of many-body driven quantum phenomena. Excitons are electron-hole pairs coupled by attractive Coulomb interaction, which results in a ground state with a reduced energy compared to the corresponding single-particle energies. Exciton ensembles exhibit an intriguing interaction-driven phase diagram with classical and quantum phases including quantum liquids and solids 1–3. The bosonic nature of excitons enables these composite particles to condensate into macroscopic ground state wave functions forming a BoseEinstein condensate (BEC) 4. The reduced overlap of the electron and hole wave functions enlarges the radiative lifetime, and therefore makes ensembles of indirect a.k.a. interlayer excitons (IXs) cooled to lattice temperature promising systems to explore those phases. Besides IX ensembles in III-V HS 5–15 , hetero-bilayers prepared from semiconducting transition metal dichalcogenides (TMDs) exhibit superior potential for studying interacting IX ensembles 3,16–25 with intriguing spinand valley-properties 26–28. At the same time, TMDs are truly two-dimensional (2D) crystals coupled to each other or to substrates by van der Waals forces. In this respect, 2D materials provide a unique platform to stack them into HS without the limitations of lattice mismatch like in conventional crystals such as GaAs and InAs. TMDs excel by strong light-matter interaction 20 resulting e.g. in an absorbance of up to 15% of visible light for a monolayer 29– 31 . Reduced screening leads to strong exciton binding energies of up to 0.5 eV 32,33 that are one order of magnitude larger than in conventional III-V materials systems. The electronic band structure of TMDs can be controlled by the number of layers 34–36 and by doping and strain 37–40. In particular, increasing the electron density results in a reduction of the electronic band gaps at the K- and K’-points in reciprocal space 37,38,40,39,41. An even larger renormalization effect of the conduction band occurs for the Σ-point between the Γand the K-points, such that the monolayer system can turn into an indirect semiconductor 38,39 . The doping-induced lowering in the band gap and the corresponding reduction of exciton binding energies nearly cancel out each other, so that the energy of the neutral exciton in photoluminescence (PL) experiments remains almost unaffected by doping. However, the PL intensity is reduced by doping until the exciton Mott transition is achieved e.g. by high illumination intensities 40,41. Another aspect of van der Waals HS prepared from semiconducting TMDs is a type-II band alignment 24,16,19,42 driving an efficient transfer of photo-generated charge carriers, such that the electrons accumulate in one layer and the holes in the other layer 43,22,27, forming IXs with enhanced lifetime and density 21,26,25. While intralayer excitons in TMD monolayers are perfect in-plane dipoles fostering Förster-type energy transfer between hetero-bilayers 44, interlayer excitons possess a permanent out of plain dipole component. This alters the coupling to light and enables the tuning of exciton properties by static electric fields perpendicular to the layers. The exciton binding energies of IXs in such HS are reduced to about 0.2 eV 24, but they are still one order of magnitude larger compared to those of IXs in III-V HS.


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In TMD-based HS, the mismatch in the lattice constants of the two constituting monolayers gives rise to a Moiré pattern, which can impact the electronic band structure 45. For MoS2/WSe2 HS, a lateral modulation of the interlayer bandgap of up to ~150 meV was reported 45. In particular, the difference of MoS2-CB minima at the σ- and the K-points is sizably modulated. In addition, the lattice mismatch between the two layers of the HS causes a displacement of the conduction band minimum and valence band maximum at K and K’, resulting in bright IX with finite center of mass velocities 26,46, but it also affects other high symmetry points 46. Moreover, for a MoSe2/WSe2 HS it is even theoretically predicted that the Σ- point is below the K-points 47. Here, we investigate the optical properties of dense and diluted IX ensembles in a van der Waals HS prepared from monolayers of MoSe2 and WSe2. We characterize the power-, temperature-, and polarization-dependent photoluminescence (PL) in time-integrated and time-resolved experiments. In the HS region only, we observe an additional red-shifted luminescence signal that has a significantly increased lifetime in the order of several tens of ns indicating the formation of IXs in the HS. We find that this IX emission is composed of two peaks with different lifetimes and contrasting power- and temperature-dependences. We assign one transition to be indirect in real space yet direct in momentum space and the second one to be indirect in both momentum and real space. The observed homogenous filling of large lateral areas of the van der Waals HS together with the long IX lifetimes and interesting polarization behavior makes van der Waals HS highly attractive to study correlated quantum phases in these ensembles of composite bosons, but also for the design of novel optoelectronic device architectures. The investigated HS is a hetero-bilayer, which is prepared by micromechanical exfoliation from bulk crystals. The top monolayer of WSe2 is stacked onto the bottom monolayer MoSe2 using a viscoelastic dry stamping method 48,49, such that the crystal axes are rotationally aligned to 0° or 60° with a precision of about ± 2°. A reduction of the second harmonic generation on the HS with respect to the individual layers suggests AB stacking order 50 with a tilt of about 60° ± 2.4° (Figure S6). The HS are heated in vacuum ( 1 µW) considering only one emission peak. We observe an energy difference between the two peaks of about 30-50 meV [Figures 2(d) and 2(g)]. In our experiment, the linewidth of the luminescence is generally larger for the IX∇ peak compared to the one of the IX▼ peak [Figures 2(e) and 2(h)]. In first order, the FWHM of the IX∇ peak has a value of ~50 meV for most of the investigated laser powers at 3K, while it increases monotonously to a value of ~60 meV at 30K for the highest laser powers. In contrast, the FWHM of the IX▼ seems to increase for both temperatures as a function of laser powers with maximum values of ~45 meV for the investigated range of laser powers. In addition, several rather narrow emission peaks with a FWHM of about 3 meV appear in the spectral range of the IX▼ exclusively for an excitation power below P ≤ 200 nW and low


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temperatures T < 30 K [arrows in Figure 2(a)]. We ascribe them to local minima in the potential landscape, as will be discussed below. Figure 3 gives insight into the temperature dependence of the IX emission for an intermediate laser power of P = 200 nW. Figure 3(a) shows the original data in logarithmic waterfall plots, and figures 3(b)-(d) summarize the corresponding temperature dependence of the intensity, the emission energy, and the FWHM of the peaks IX∇ and IX▼. Again, all extracted values are deduced from Gaussian fits to the data. Overall, the intensity of both emission peaks IX∇ and IX▼ decreases with increasing temperatures. However, for this intermediate power of P = 200 nW, the IX▼ peak loses intensity at a lower temperature than the IX∇ peak. Only for the highest laser powers, the IX▼ peak dominates for all temperatures. The emission energy of the IX∇ peak decreases for Tbath > 20 K, while the one of the the IX▼ peak increases causing an increase of the energy difference with increasing temperature. Moreover, there seems to be no simple trend in the FWHM vs temperature for both peaks at this power [cf. Figure 3(d)]. In our understanding, this reflects the occurrence of different regimes of the PL emission vs temperature, as is obvious in the original data of Figure 3(a) and as it will be discussed below. We now turn to time- and polarization-resolved PL measurements for both IX∇ and IX▼ peaks. The HS is excited using laser pulses with σ+-polarization, a pulse duration of 85 ps and a repetition rate of 5MHz. The emitted light is then passed through analyzer optics to detect either σ+-polarized or σ--polarized light. The polarization-resolved PL is recorded by a time correlated avalanche photodiode (APD). The spectral resolution is achieved by two sets of filters adjusted such that either PL from the IX▼ or from the IX∇ emission is recorded by the APD (cf. SI for details). Figure 4 shows the time-resolved PL signal for a circular-co-(σ++) and circular-cross-(σ+-) polarization configuration for low and high excitation power (P = 100 nW and P = 10 µW). In particular, Figures 4(a) and (b) display the polarization-resolved temporal evolution of the IX PL signal for low excitation power, while the panels (c) and (d) show corresponding measurements for high excitation power. The lifetime of the IX ensembles extracted from bi-exponential fits to the data constitutes several ten ns up to ~100 ns [cf. Figures 4(e) and 4(f)]. For all investigated experimental parameters, the found values are significantly larger compared to the lifetime of intralayer excitons. This observation verifies the interlayer nature of the IX∇ and IX▼ peaks. The observed lifetimes are in the range reported in literature spreading from less than 2 ns 21 to more than 180 ns 25 . Figure 5 shows the spatial distribution of the PL measured at the emission energy of the IX∇and IX▼ peaks, respectively. The area coincides with the one of the HS, which is highlighted by the dashed square in Figure 1(a). Figures 5(a) and 5(b) depict corresponding intensity maps for a low excitation power (P = 200 nW), while Figures (c) and (d) present equivalent maps for a rather high power (P = 100 µW). For the latter, the PL is spatially homogeneous for both IX∇and IX▼ peaks [cf. (c) and (d)], which is consistent with a homogenously filled dense ensemble of long-living interlayer excitons spread over the whole area of the HS. For the low excitation power, the emission from the energetically higher IX▼ shows a more inhomogeneous spatial distribution of the PL intensity [Figure 5(b)]. This is the regime, in which we also observe spikes in the PL spectra [cf. arrows in Figure 2(a)]. In contrast, the emission of the energetically lower IX∇ is spatially homogeneous also for this low-power regime [Figure 5(a)] indicating that the potential landscape of the HS is rather 6 ACS Paragon Plus Environment

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smooth or smoothed out on the level of the low-energy IX∇, whereas there are lateral fluctuations in the potential landscape for the emission from the high-energy IX▼ peak. We note that for temperatures higher than Tbath > 30 K, the PL maps are spatially homogeneous for low and high excitation powers for both IX∇and IX▼ peaks (cf. SI Figure S2). To start the discussion, the different behaviors of the lateral homogeneity of the low-energy IX∇ and the high-energy IX▼ peak at a low laser power and low temperatures indicates that the two emission peaks stem from two interlayer excitons of different nature. Moreover, the IX∇ peak shows longer lifetimes and a distinctively broader linewidth than the IX▼ peak throughout the examined range of parameters. Moreover, the IX∇ dominates the luminescence at low power and low temperature, whereas the IX▼ does so at high power and high temperatures. In general, neglecting attractive Coulomb interaction between electrons and holes in adjacent layers, the single-particle band diagrams of MoSe2 and WSe2 [Figure 1(c)] already suggest two different kinds of interlayer excitons, that are either indirect or direct in momentum space with the holes located at the KWSe2-point of the WSe2-VB and the electrons either at the ΣMoSe2-point or the K(’)MoSe2-points of the MoSe2-CB. We note that our argumentation holds for HS with AB stacking (60° twist angle) and AA stacking (0° twist angle) due to spin-conserving interlayer hopping together with the existence of light cones at small kinematic momenta around K (K’) in which radiative recombination of the direct IX▼ is allowed 26,46. In the case of AB stacking, electrons in the MoSe2-CB reside in the K’(K)point and holes in the WSe2-VB at the K(K’)-point. For such an alignment three pathways for radiative recombination through virtual intermediate states exist, that are still consistent with overall circularly polarized emission 26. Similar arguments hold for the ΣMoSe2 – K’WSe2 and ΣMoSe2 – KWSe2 recombination paths. In the above drawn scenario with near AB stacking of the HS with the ΣMoSe2 – K’MoSe2 points occupied by electrons and the KWSe2 point occupied by holes, the lowest energy transitions of the HS would be (1) a momentum indirect interlayer transition between ΣMoSe2 – KWSe2 or Σ ’MoSe2 – KWSe2 and (2) a momentum direct interlayer transition between K’MoSe2 – KWSe2. Analog arguments can be drawn for a twist angel near 0° 46,26 . Moreover, the single-particle band diagrams of Figure 1(c) predict that the momentum indirect transition ΣMoSe2 – KWSe2 (analog for Σ ’MoSe2 – KWSe2 transition) is lower in energy than the one at K’MoSe2 – KWSe2, in agreement with our experimental findings. However, the calculations do not consider excitonic effects that might result in a competition between the two minima in the MoSe2-CB to exhibit the lowest energy. Yet, for the HS, the charge transfer across the heterojunction sustains a significant doping level of excess electrons in the MoSe2-CB as well as holes in the WSe2-VB. The electron density ne in the MoSe2-CB is estimated from the intensity ratio of the MoSe2 intralayer neutral exciton (X) and trion (T) to be about ne ≈ 31011cm-2 (cf. SI). Therefore the quasi Fermi level is expected to be high enough, such that electrons populate both, the minima at the Σand at the K point. As a direct consequence, we can indeed expect the two anticipated transitions for interlayer excitons. Although the single particle band structure calculations are done for the individual monolayers, the correct trends should be captured since hybridization effects in van der Waals HS are known to affect predominantly the electronic bands at the Γ point and only minor at the Σ-point, while the K- and K’-points are almost unaffected 24. The lattice constants of MoSe2 and WSe2 are aMoSe2 = 3.288 A and aWSe2 = 3.280 A, respectively 57. This mismatch gives rise to a Moiré pattern, which can impact the electronic 7 ACS Paragon Plus Environment

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band structure 32,45. However, the reported band gap modulation of ~150 meV by the formation of Moiré pattern in vdW HS 45 is too large to serve as an alternative interpretation for the observed doublet structure in the IX emission with an energy difference of about 40 meV. Still, the lattice mismatch between MoSe2 and WSe2 and/or a small twist angle between the two monolayers shifts the corners of the Brillouin zone away from each other. Consequently, Coulomb-coupled electron-hole pairs located exactly at the CB minimum at KMoSe2 and the VB maximum (i.e. at KWSe2) are situated out of the light cone as well. In other words, the transition at KMoSe2 – KWSe2 is also slightly indirect in momentum space but less than the one at ΣMoSe2 – KWSe2. Similar arguments hold for the K’MoSe2 – KWSe2 transition 26,46. In turn, such bound electron-hole pairs or excitons cannot recombine radiatively in a direct optical transition. They can only recombine if their momentum sum equals the displacement vector between the KMoSe2 and the KWSe2 corners, as recently proposed in 46. A direct fascinating consequence of this scenario are interlayer excitons with a finite kinematic momentum 46. Due to the small twist angle of about ±2° in the investigated AB stacked HS, the displacement vector is expected to be small but finite. As a result, increasing moderately the doping by photoexcitation lifts the quasi Fermi level for electrons EeFermi and holes EhFermi, so that the sum of the quasi Fermi momenta (keFermi + khFermi) can get larger than the displacement vector between the KMoSe2 and KWSe2 corners 46. In this way, we interpret that the more direct transition K’MoSe2 – KWSe2 can be activated as a function of doping by filling the electron-hole states such that states with sufficiently large kinematic momentum are occupied. This state filling argument is consistent with the observed laser power dependence [cf. Figure 2]. Furthermore, the transition can get bright by increasing the temperature resulting in a thermal broadening of the quasi Fermi momenta ∆(keFermi + khFermi), so that again electron-hole states with sufficiently large kinematic momentum are occupied. To be more quantitative, the emission from the direct IX▼ significantly contributes to the spectra for temperatures above 20 K corresponding to a thermal energy of 4 meV that is required to broaden the Fermi momentum such that the radiative recombination of electronhole pairs is momentum-allowed. Consequently, the transition can also be enabled by lifting the Fermi energy, i.e. by increasing the two-dimensional electron (hole) density by about 41011 cm -2 assuming parabolic bands (see SI). An excitation power larger than 100 nW is required to achieve similar photo-generated carrier densities (see SI), what is in agreement ▼ with the power dependence of the IX emission shown in Figure 2 (c, d). As mentioned, the second transition ΣMoSe2 - KWSe2 is significantly more indirect in momentum space. There, radiative recombination is mediated by the interaction with phonons to fulfill momentum conservation. A suitable phonon branch of the MoSe2 lattice for phonon assisted recombination would be given e.g. by LA phonons particularly at the M point, coupling to electronic states at the Σ- and K-points in reciprocal space 39. In particular, the LA(M) phonon with an energy of around ℏωphonon ≈ 15 meV has a high density of states with strong electron phonon coupling 39. We would like to note that phonons are optically excited even at the lowest investigated temperature and can therefore mediate the momentum indirect transition even at low temperatures. The assignment of the IXs is supported by the dominance of the IX∇ peak at low laser power, while the more direct transition IX▼ dominates the high power regime. Equally, it is consistent with the generally larger FWHM for the IX∇ peak compared to the IX▼ peak due to the required electron-phonon scattering to conserve the overall momentum within the indirect IX∇ transition. The power and temperature for which the PL intensities from IX∇ and IX▼ cross result from a non-trivial interplay between increase and/or broadening of the quasi Fermi-momentum at the K, K’- points, thermal 8 ACS Paragon Plus Environment

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excitations of phonons and carrier dependent increase of the electron-phonon interaction. We note that the FWHM for the IX∇ peak seems to be largely independent from the laser power at 3 K [cf. Figure 2(e)]. Generally, the FWHM of both intralayer as well as interlayer excitons of the investigated device are inhomogenously broadened and not lifetime limited 58,59 . An underlying electron-phonon interaction for the IX∇ transition further explains that the spatial distribution of the IX∇ peak seems to be somewhat smoothed out even at the lowest temperatures, while the spatial distribution of the energetically higher IX▼ peak shows inhomogeneities (cf. Figure 5). We point out that this low-temperature and low-power regime also exhibits the additional narrow emission peaks in the spectral range of the IX▼ [arrows in Figure 2(a)]. Intriguingly, the narrow peaks do not occur at the absolute lowest energy transitions of the excitonic system. In turn, we interpret the peaks to be induced by intrinsic or extrinsic modulations of the potential landscape, i.e. either by a Moiré pattern 45 or by trapped molecules and residues at the hetero-interface 25. For large excitation densities, such potential minima would be smoothed out by an increasing exciton density, which is consistent with our experimental observations. The dependence of the emission energy on power and temperature is a complex interplay between dipolar repulsion, exciton diffusion to potential minima 25 and doping-dependent renormalization of the electronic bands that particularly effects the CB minima at the Σ-, K’and K-points with a different strength 37, as already demonstrated in Figure 1(c). In addition, temperature affects the single-particle bands, and also an altered strength of the Coulomb interaction can play an important role for different charge carrier and exciton densities as well as temperature regimes. In first order, the temperature and power dependence of IX▼ is interpreted as an interplay between the dipolar repulsion of the IX ensemble, an exciton diffusion and increasing kinematic momentum with increasing temperature and doping. This interplay already results in a blue-shift of the emission energy with increasing exciton density, as is consistent with our data and equally suggested in 25. In agreement with having indirect IX∇ and a more direct IX▼, both the time-resolved and time-integrated data show only a weak polarization dependence (cf. Figures 4 and S2). In particular, the involved scattering processes with phonons and other charge carriers explain that the transitions IX∇ and IX▼ show a rather low polarization dependence. Intriguingly, we observe that the PL lifetimes of the IX∇ get shorter for higher powers, while the ones for IX▼ stay the same [cf. Figures 4(e) and 4(f)]. In our understanding, this observation is consistent with an incrementally heated phonon bath, which is involved in the IX∇ transition. Finally yet importantly, the fact that the lifetimes of IX∇ are significantly longer than the ones of IX▼ indicates that the wave function overlap is reduced for the IX∇, as expected for an indirect IX∇ compared to a more direct IX▼. There are two further possible explanations for the observed splitting of the IX PL that are less likely as we will explain in the following. A first alternative interpretation for the observed splitting of the IX PL is the formation and dominance of charged excitons, such as trions, with excess charge carriers in the MoSe2-CB or WSe2-VB. A comparison of the power- and temperature-dependent emission intensity and energy for single TMD monolayers 60 and a MoS2 bilayer separated by hexagonal boron nitride as tunnel barrier 17 and also for a gated overall n-type doped MoS2/MoSe2 HS 52, reveals significant differences to the observations shown in Figures 2 and 3. Particularly, the power-dependent emission energy is reported to be opposite for trions and neutral excitons for a MoS2 HS with two monolayers of MoS2 separated by hexagonal boron nitride. Moreover in both studies on n-doped HS 17,52 the 9 ACS Paragon Plus Environment

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high-energy neutral exciton emission drops in intensity with increasing excitation power, whereas the trion emission increases in intensity with increasing excitation power. As shown in Figure 2, both PL peaks IX▼ and IX∇ increase with increasing power density with a change of the dominance of the lower energy IX∇ peak at low power to a dominance of the IX▼ emission. This behavior disagrees with a trion interpretation since the lower energy peak should be assigned to the trion whose intensity is expected to increase with increasing doping density as realized e.g. by increasing excitation power. In addition, the observed emission energies of both peaks IX▼ and IX∇ increase concurrently. However, the energy separation between trion and exciton is expected to change for varying the doping level and hence, excitation power 60. As a result, the interpretation of the IX splitting due to the formation of intralayer trions is unlikely. Another possible explanation of the observed doublet splitting would be the emission from SOC-induced spin-split conduction bands at the K- and K’-points. In this scenario, the lower energy IX would stem from the forbidden (dark) transition from the lowest MoSe2-CB state at the K’ point to the highest WSe2-VB state at the K point with opposite spin direction in our AB stacked HS 55. We would expect such dark IX to become bright with increasing temperature as already experimentally observed for such dark intralayer excitons in WX2 (X = S, Se) 61,62 in disagreement with the temperature dependent evolution of the IX▼ and IX∇ PL intensities. The spin-splitting of the MoSe2 CB is expected to be minor dependent on the temperature in disagreement with the observed increase of the energy separation between IX▼ and IX∇ of about 30 meV at 10 K to about 80 meV at 70 K [cf. Figure 3(c)]. In addition, the measured PL lifetimes are almost identical for co- and cross-polarization [Figures 5(e) and 5(f)]. Only in time-integrated measurements, IX▼ shows a polarization of about 15% at the lowest temperatures, while IX∇ seems to be much less polarized within the given experimental error (see Figure S2). For the above reason also the interpretation of the IX doublet in terms of emission from SOC-induced spin-split MoSe2-CB is very unlikely. We note that in the high-power regime, also non-radiative recombination due to Auger processes might occur, and we cannot exclude that the IXs dissociate and undergo an exciton Mott transition 41. However, we do not recognize signatures in our data pointing towards an unbound electron and hole plasma in the adjacent layers. Instead, the homogenous filling and lateral distribution of the IXs for high excitation intensities makes the system promising to study the manifold phase diagram of interacting composite bosons that are very stable even at rather high temperatures due to the strong Coulomb interaction of about 200 meV reported for IX in such HS 24. Finally, we would like to point out that the general dependences and signatures of the IX emission are taken from different spots on the HS. The measurement series is conducted from various cool downs with the HS warmed up to room temperature in between, establishing the robustness of the observed signatures. Moreover, a very similar behavior is observed for a second AB stacked HS (twist angle 60° ± 1°) with low intrinsic electron density of about ne ≈ 6 1010 cm-2 in the MoSe2-CB further supporting the exclusion of the trion interpretation (data shown in the SI Figures S6 – S8 and table S2). The reduced twist angle mismatch might account for the fact the direct K’MoSe2 – KWSe2 transition is activated for a smaller kinematic momentum of the IX provided by the smaller quasi-Fermi level compared to the higher doped HS with a twist angel of twist angle 60° ± 2.4°. The energy difference between the two emission lines constitute ~40 meV for the higher doped HS structure with larger twist angel, while ~60 meV for the lower doped HS with a smaller twist angle. Charge carrier dependent band structure calculations cannot 10 ACS Paragon Plus Environment

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explain this difference. A more probable reason is the different twist angle, and especially a different interlayer coupling in the two samples, as it is already evident from a reduced bleaching of the intralayer exciton in this HS [c.f. S1]. To conclude, we show a detailed photoluminescence study of interlayer excitons in a MoSe2/WSe2 heterostructure as a function of temperature, excitation power, light polarization, and spatial coordinates. We find two emission peaks with a linewidth of about 50 meV and 40 meV, which are separated by some 30-50 meV in energy. The emission energy of both is ~300 meV below that of the intralayer excitons in MoSe2- and WSe2monolayers. For both peaks, we find long lifetimes of several tens of nanoseconds up to 100 ns at 3K. The lifetimes are getting shorter for an increasing bath temperature. The energetically higher peak of the two shows several spikes in the photoluminescence spectrum for a low excitation power and low temperatures. Corresponding spatial maps of the photoluminescence intensity show distinct emission centers at the position of the heterostructure. The spatial and spectral inhomogeneities disappear for higher excitation powers and temperatures. We compare our experimental results to GW-based singleparticle band structure calculations of MoSe2- and WSe2-monolayers which are doped due to optical excitation. We conclude that there are two sorts of interlayer excitons. The lowenergy interlayer exciton is indirect both in real and reciprocal space, while the high-energy interlayer exciton is only indirect in real space. While writing this manuscript, we got aware of a related work 25. However, the authors discuss data only for larger laser powers and without mentioning any doublet structure of the interlayer excitons.


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ASSOCIATED CONTENT Supporting Information. PL of monolayer regions. Estimation of the electron density in MoSe2. Degree of polarization of the IX emission. Spatial maps of the PL at 60K. Raman and AFM measurements. Verification of the crystal axes by second harmonic generation. Data of a second sample. Details of the optical measurements. Estimation of the photo excited carrier density.

AUTHOR INFORMATION Corresponding Authors *(U.W.) E-Mail: [email protected] *(A.W.H.) E-Mail: [email protected] The authors declare no competing financial interest. ACKNOWLEDGMENTS We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) via excellence cluster ‘Nanosystems Initiative Munich’ as well as DFG projects WU 637/4-1 and HO3324/9-1 and the Munich Quantum Center (MQC). A.S. and F.J. acknowledge financial support by the DFG (JA 14-1). The band-structure calculations shown in this publication are directly based on ab initio calculations by G. Schönhoff, M. Rösner and T.O.Wehling (University of Bremen).


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Figure 1. Interlayer excitons (IXs) in a MoSe2/WSe2 heterostructure (HS). (a) Optical microscope image of the heterostructure made from monolayers (1L) of MoSe2 and WSe2. (b) Photoluminescence (PL) spectrum taken from the heterostructure area within the dashed square in (a) at a bath temperature of Tbath = 3 K for P = 140 µW. At low emission energy, there are two peaks which we define as IX∇ and IX▼. Their energy is lower than the ones for the intralayer excitons in MoSe2 and WSe2. (c) Left panel: computed conduction band of MoSe2 with a charge carrier density of 3 1011 cm-2 (green) and without doping. Middle panel: sketch of the type-II band alignment of the MoSe2/WSe2 heterostructure with the IX having the electron and the hole located in MoSe2 and WSe2, respectively. Right panel: computed valence band of WSe2 with a charge carrier density of 3 1011 cm-2 (green) and without doping. The calculations are performed at a bath temperature of Tbath = 30 K.


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Figure 2. Excitation power dependence of the interlayer exciton emission. (a) and (b) Logarithmical waterfall presentation of the PL spectra with the emission peaks IX∇and IX▼ vs laser power in the range of 2 nW ≤ P ≤ 140 µW for a bath temperature of Tbath = 3K (a) and 30K (b). For low P and 3K, we detect emission spikes in the spectral range of the energetically higher IX▼ (arrows), which are not present for the energetically lower IX∇. They equally disappear for high temperatures. (c) to (e) Power-dependence at 3K of the corresponding PL intensity (c), the emission energy (d) and the FWHM (e) with open (filled) triangles representing the data for the IX∇ (IX▼). (f) to (h) equivalent data for 30K. Lines are guides to the eye. [The laser repetition rate is 10 MHz except for the highest power spectra shown in panels (a – b), where 80 MHz repetition rate is used. We therefore exclude this data from the evaluation in panels (c-h)].


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Figure 3. Temperature dependence of the interlayer exciton emission. (a) Logarithmical waterfall presentation of PL spectra with the emission peaks IX∇ and IX▼ vs temperature in the range of 3K ≤ Tbath ≤ 70 K for a fixed laser power P = 200 nW. (b) to (d) Temperature dependence of the corresponding PL intensity (b), emission energy (c), and FWHM (d) with open (filled) triangles representing the data for the IX∇ (IX▼). [The laser excitation rate is 10 MHz].


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Figure 4. Polarized photoluminescence lifetimes of the interlayer excitons. (a) PL signal of the IX∇ vs time delay for a co-polarization (σ++) and cross-polarization (σ+-) of the excitation and detection, respectively. The data are taken for a low excitation power (P = 100 nW) at 10 K, and they are offset for clarity. (b) Equivalent data for IX▼. (c) and (d): Corresponding data for IX∇ (c) and IX▼ (d) for high excitation power (P = 10 µW). Lines are biexponential fits as described in the text. (e) and (f) Temperature dependence of the PL lifetimes at a laser power of P = 100 nW with open (filled) triangles representing the data for the IX∇ (IX▼) for co-polarization (e) and cross-polarization (f). Panels (g) and (h) represent equivalent data for P = 10 µW. Lines are linear fits.


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Figure 5. Spatial distribution of the IXs’ emission signal at low and high excitation power. (a) Spatial PL map of the IX∇ within the area marked with a dashed square in Figure 1(a). The map is taken at a power of P = 200 nW. (b) Similar map for the IX▼. (c) and (d): PL map for IX∇ (c) and IX▼ (d) for a high excitation power (P = 100 µW). All intensities are given in counts per second (counts/s). The data are measured at 3 K.


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