# Observation of Moiré excitons in the WSe 2 / WS 2 heterostructure superlattice

A moire superlattice can form between two atomically thin materials with similar gratings, and its period varies continuously with the angle of torsion between the constituent layers. The periodic moire pattern introduces a new scale of length and energy, which is a powerful means of controlling quantum phenomena in 2D heterostructures.1,2,3,4,5,6,7,8,9,10,11,12. The most remarkable moiré super-lattice phenomena appear in the "strong coupling" regime, in which the periodic moiré potential dominates the kinetic energy in the mini-Brillouin zone and qualitatively modifies the structure of the electronic band and the electronic wave function in the heterostructure. Recently, it has been reported that high-coupling moiré superlattices can generate flat electronic bands, leading to exotic phases such as correlated insulative states and superconductivity in magical-torsion-layer bilayer graphs and insulating states. Mott adjustable in trilayer graphene / boron nitride heterostructures1,2,3,4,5,6.

Moiré supergrids also offer engineering possibilities for band structure of collective excitations, such as excitons in 2D semiconductor heterostructures. Monolayer transition metal dichalcogenides are direct bandgap semiconductors that exhibit strong light-exciton interactions and electron-electron interactions significantly improved over typical semiconductors such as silicon or arsenide. gallium. The exciton binding energies in monolayer transition metal dichalcogenides can be several hundred meV – orders of magnitude larger than those observed in typical semiconductors.16,17– which leads to well defined dispersive exciton bands in the Brillouin zone. It has recently been predicted that super moire networks in transition metal dichalcogenide heterostructures in the strong coupling regime could allow the formation of moire exciton minibands.13,14,15, which are distinguished from minibands separated electrons and holes due to the strong electron-hole correlation.

Here we report the first experimental observation, to our knowledge, of moiré excitons in closely aligned WSe.2/ WS2 heterostructures. The super moire network divides the WSe2 An exciton resonance in several peaks that all have comparable oscillator strengths in the spectrum of absorption. In addition, the peaks of emerging excitons show a doping dependence that is distinct from that of the exciton A in WSe.2 monolayers and that of WSe2/ WS2 heterostructures with a large torsion angle. This unusual behavior can be understood by using an empirical moiré exciton model with an exponential moiré potential of 250 mV. The periodic potential energy is much greater than the excitation kinetic energy of 8 meV in the first mini-Brillouin zone and it completely alters the dispersion of the excitation in the moiré superlattice, which leads to low energy flat exciton bands with a very localized exciton density. WSe closely aligned2/ WS2 The moiré super-network can therefore potentially host different excitonic states, such as topological exciton bands and a Hubbard model of strongly correlated excitons.13,14,15,18,19.

Figure 1a, b shows an optical microscopy image and a schematic view in side view of a representative sample.2/ WS2 heterostructure device (D1). The results measured from the D1 device were reproducible in all closely aligned heterostructures that we made (see Additional Information). The WSe2/ WS2 the heterostructure was encapsulated in thin hexagonal layers of boron nitride. Graphite flakes in a few layers were used for both the lower grid and the electrical contacts with the heterostructure. The concentration of the carrier in the heterostructure can be continuously regulated with the back gate voltage Vg. All 2D materials used were first exfoliated mechanically from bulk crystals, then stacked using a polyethylene terephthalate buffer according to a dry transfer method (see Methods). The entire battery was then transferred to silicon dioxide / silicon (SiO) at 90 nm.2/ Si) substrate. The relative torsion angle between the WSe2 and WS2 the layers were optically determined using measurements of the second harmonic generation dependent on the polarization. Characteristic patterns of second harmonic generation six times higher have been clearly observed for the WSe2 and WS2 layers (Fig. 1c), from which we determined that the relative torsion angle between the two layers was 0.5 ± 0.3 ° (see Additional Information).

For a heterostructure with a twist angle close to zero, the intrinsic lattice difference between the two layers is dominated by the intrinsic difference of the lattice constant of about 4% (ref. 20), which leads to a periodicity of moiré TheM about 8 nm (Figure 1d, see also additional information). Similar moiré superlattices have been observed experimentally using scanning tunneling microscopy in aligned WSe cells.2/ MoS2 heterostructures21,22, which have network constants almost identical to those of WSe2/ WS2 heterostructures. Confirm formation of the moiré super network in our WSE2/ WS2 heterostructure, we have prepared another device (D2) on a transmission electron microscopy grid and collected atomic resolution scanning transmission electron microscopy images of the device (methods), as shown in Figs. 1st, f. The images show a uniform triangular lattice pattern over the entire measured region (Figure 1e) with a well defined periodicity of about 8 nm (Figure 1f). This indicates that there is periodic network distortion with a periodicity of about 8 nm in the heterostructure in real space, which is consistent with strong layer-layer interactions and substantial network reconstruction in the super-lattice. moiré network that have been observed in previous scanning tunneling microscopy studies.21,22.

We then studied moiré excitons in WSe2 with optical spectroscopy at a temperature of 10 K. Figure 2a shows the photoluminescence spectra of the device D1 and a reference monolayer WSe2 sample on linear and logarithmic scales. The spectrum of the WSe2/ WS2 The heterostructure exhibits a single peak at 1.409 eV, which corresponds to the emission of the exciton exciton and shows no emission of the WSe.2 An exciton. This indicates efficient interlayer charge transfer over the entire measured region, leading to a strong deactivation of the WSe.2 photoluminescence23,24. The uptake of excitons in the same region of the heterostructure was directly measured using reflection contrast spectroscopy (Fig. 2b), in which a slowly varying background was subtracted so to better resolve the resonances (see Additional information). The absorption spectrum of the D1 device – a tightly aligned heterostructure – is distinctly different from that of a WSe at a large angle of torsion2/ WS2 heterostructure measured under the same conditions (lower panel of Fig. 2b). We focus on the WSe2 resonances in the spectral range between 1.6 and 1.8 eV, because they are well separated from all WS stations2 resonances. While the torsion angle heterostructure shows only one WSE2 An exciton peak at 1.715 eV, three important peaks emerge in the D1 device spectrum at 1.683, 1.739 and 1.776 eV (called resonances I, II and III, respectively). The three resonances show a strong absorption, the peak oscillator forces of peaks II and III reaching respectively 20% and 50% of the value of peak I. We systematically studied 18 different heterostructures covering a wide range of torsion angles. The three emerging peaks are present in the spectrum of all closely aligned devices for AA stack (0 ° torsion angle) and AB stack (60 ° torsion angle). These peaks weaken with the increasing twist angle between WSs2 and WSe2 and disappear completely when the torsion angle is greater than 3 ° (see Additional information for absorption spectra depending on the torsion angle of 18 heterostructures).

To better understand these exciton peaks, we measured the photoluminescence excitation spectrum of the D1 device (Fig. 2c) by monitoring the intensity of the exciton emission interchample. when the energy of the photons of excitation was scanned from 1.6 to 2.1 eV. The excitation spectrum corresponds very well to the results of the reflection spectroscopy (Fig. 2c). In particular, the excitation at the energies of each of the three new expon peaks between 1.6 and 1.8 eV resulted in a large increase in the excitation emission between layers at 1.409 eV, indicating that these peaks result from the strongly coupled WSe signal.2/ WS2 heterostructure rather than several separate domains.

To further investigate the nature of emerging exciton resonances, we measured their dependence on doping of the heterostructure (Fig. 3a). The three main summits of the WSe2 An exciton shows pronounced changes in both electron and hole doping. The strong gate dependence on electronic doping is particularly remarkable: because of the alignment of the type II band in WSe2/ WS2 heterostructures, the doped electrons mainly reside in the central layer2 layers and tend to have relatively weak effects on the intra-layer exciton resonance A in WSe2 (Ref. 25,26; see also additional information). WSe's previous studies2/ WS2 Heterostructures with large torsion angles have shown that the2 An exciton resonance only feels a slight shift toward red when the heterostructure is doped with electrons26. In contrast, exciton peaks in D1 – a heterostructure closely aligned with a large moire network – show unusual dependencies of electronic doping that vary for different peaks (Fig. 3b). Peaks I and III are substantially modified with the increase in electron concentration: peak I shows a strong blues shift and transfers the force of its oscillator to another emerging peak at lower energy (I), and peak III shows a strong blues shift with a diminished oscillator force. Conversely, Peak II remains largely unchanged, with the exception of a slight shift in energy.

The strong effect of electrons in WS2 on some exciton transitions in WSe2 indicates that the electron-exciton interlayer interactions are markedly improved by the moiré superlattice. In addition, the significantly different triggering behavior of exciton peaks can not be explained by established electron-exciton interactions in monolayers, such as dielectric filtering effects or trione formation, as these affect all the exciton peaks in a similar way.27,28,29. Instead, it indicates that the exciton peaks I, II, and III correspond to distinct exciton states in the moiré superlattice.

The emergence of several excitement peaks around the WSe2 An exciton resonance and the nature of their dependence on electron doping can be understood in the context of an empirical theory introducing a periodic moiré exciton potential in the strong coupling regime. We follow the theoretical model of ref. 13 and describe the movement of WSe's center of mass2 An excitons using the Hamiltonian

$$H = {H} _ {0} + sum _ {j = 1} ^ {6} {V} _ {j} { rm { exp}} left (i {{ boldsymbol {b} }} _ {{{ boldsymbol {j}} cdot { boldsymbol {r}} right)$$

(1)

in which H0 is the Hamiltonian with low energy consumption for exciton A 1s WSe monolayer state2. Vj describes the effective potential on the exciton generated by the moire pattern; its momentum is given by the reciprocal network vectors of the super moiré network, bj (Additional information). Due to the triple rotation symmetry and Hermitian requirement, a single component Vj is independent and can be defined as V1 = Vexp (I), in which V and ψ are the amplitude and the phase of the effective potential, respectively. We note that the peak-to-peak amplitude of moire potential Vpp can be much bigger than V after summarizing the contribution of the six components.

Exciton dispersion in the mini-Brillouin zone can be calculated directly from this model (Fig. 4a-c). γ, m and κ are the points of strong symmetry of the mini-Brillouin area, as shown in the box of Figure 4a. Without the moiré potential, the exciton shows two continuous low energy bands (Fig. 4a). These two bands are degenerate at the point γ and present respectively a parabolic dispersion and a linear dispersion, consequence of the interval interaction.13,30. Photons having a negligible momentum, only the exciton of lower energy can interact with light, thus giving a single powerful spike to E = E0 in the absorption spectrum (Fig. 4d). The moiré potential can mix exciton states with moments that differ by bjresulting in additional absorption peaks from the states of the γ points of the high energy minibands.

When the Moiré potential is low (V = 5 meV, FIG. 4b), the dispersion of the exciton remains largely unchanged. Consequently, the lateral peak emerging in absorption always appears about 30 meV higher in energy than the principal peak, whatever the exact form of the moiré potential (Fig. 4e). In addition, the amplitude of the lateral peak is several orders of magnitude lower than that of the main peak, due to the low mixing between states. These characteristics contrast strongly with the experimental absorption spectrum and can not explain our observations. Conversely, a greater moiré potential corresponding to the strong coupling regime considerably modifies the dispersion of the exciton (Figure 4c). Consequently, the energy of the exciting states moire in different mini-bands (labeled I to III in FIG. 4c), as well as the energy of the corresponding absorption peaks (peaks I to III in FIG. 4f), become strongly dependent moiré potential. Moreover, the strong mixture between the different exciton states makes their oscillator forces comparable to each other. If we put V = 25 meV and ψ = 15 °, the simulated absorption spectrum can reproduce our experimental observation (figure 4f, see also additional information). This moiré potential has peak to peak amplitude Vpp about 250 meV, which is much larger than the excitation kinetic energy in the first mini-Brillouin zone (see Background Information).

The substantial change in exciton dispersion in the kinetic space suggests that the exciton center-of-mass wave function is also strongly modified in real space. Figure 4g – i shows the distribution of the exciton probability density for states I to III in the moiré supergrid. The distribution of the wave functions, homogeneous origin, is significantly modified by the moiré potential. For example, the lowest energy state (state I) is concentrated around the minimum moire potential (called the α point) on a scale of much smaller length than the moiré superlattice ( Fig. 4g).

The unusual distribution of moire exciton wave functions in the strong coupling regime introduces a new degree of freedom which is determined by the location of the exciton in the moire superlattice. Notably, peaks I and III are centered around the same point, α, whereas peak II has its greatest amplitude at a different point, β (Fig. 4h, i). The difference in position in the real space between moire excitation states can explain their differences in doping dependence: the doped electrons will also have a density of states localized in a real space.21,22. If the electrons induced by the gate in WS2 are also localized at the point α in the superlattice of moiré, they will mainly modify the peaks of exciton I and III and the peak II will remain largely unaffected, as observed experimentally.

We note that a complete description of Moiré excitation spectra will require a much more sophisticated model taking full account of network relaxation and corrugation, as well as hybridization of interlayer electronic states. in the heterostructure moire superlattice this study. Experimental research of exciter states of interlayer moiré or obtaining spatially resolved optical measurements (such as near field nanoscopy) can provide additional information for such models. Nevertheless, our simple moire excitance model captures most of the salient features observed experimentally and shows that WS2/ WSe2 the heterostructures have interactions between layers strong enough to enter the strong coupling regime of the excitons, in which the Moiré excitons spatially concentrate at well separated points and form a quantum network in an extended moire network.13,14,15. The substantially reduced exciton bandwidth also makes this artificial exciton network a promising platform for the realization of exotic phases, such as a topological exciton isolator and a model. from Hubiton to excitons strongly correlated.