Enhancing interlayer exciton dynamics by coupling with monolithic cavities through the field-induced Stark impact

Electrically tunable cavity-coupled IXs

A number of TMDC combos present type-II alignments with IXs^3,6. In our work, we selected MoSe₂/WSe₂ as an exemplary platform owing to the power and the low inhomogeneous broadening of its interlayer PL emission at cryogenic temperatures⁶, along with the ultra-long lifetimes of the hosted IXs³. This selection was additional motivated by the in depth literature on this platform, particularly regarding its angular emission sample³⁴ and optical transition dipoles^18,33. We word that layer-hybridized species in WSe₂ bilayers are additionally recognized to own environment friendly PL emission and tunable character¹¹, though their momentum-indirect nature might show difficult for the examine of tunable cavity coupling, which is out of the scope of this work. Different homobilayer TMDCs are characterised by momentum-direct hybrid species with excessive oscillator strengths^15,16, however these don’t represent the lowest-energy transition, leading to comparatively weak PL emission¹⁷. Moreover, owing to their intrinsic nature, the lifetimes of all these species are orders of magnitude decrease (<1 ns) than type-II IXs.

To use the quantum-confined Stark impact of IXs, we’ve got fabricated dual-gated MoSe₂/WSe₂ bilayer constructions absolutely encapsulated by hexagonal boron nitride (hBN), which we embedded in planar λ/2 cavities based mostly on DBR mirrors³⁵ (Strategies and Fig. 1a). We used the optical transfer-matrix technique to design the total stack and predict the vitality mode and the standard issue (Q) of our construction. In Supplementary Word 4, we current extra data on the chosen configuration of the DBR mirrors based mostly on the losses in our system. The optical micrograph of the principle construction used on this work (gadget A) is reported in Fig. 1c. We fabricated one other construction (gadget B) to verify our findings, and its optical micrographs are reported in Supplementary Word 1.

a, Schematic of the gadget construction, comprising a MoSe₂/WSe₂ heterobilayer encapsulated with hBN, with backside and high graphene (Gr) layers. Backside (V_BG) and high (V_TG) gate voltages are utilized to the graphene layers, respectively, whereas the TMDC flakes are grounded (GND). The cavity consists of the underside and high SiO₂ layers and the van der Waals heterostack. The underside DBR mirror contains 12 pairs of Ta₂O₅–SiO₂ layers, offering a large reflectance window within the 800–1,000 nm vary (Supplementary Fig. 2). The highest DBR mirror consists of six pairs of SiO₂–Si₃N₄ layers, every exactly matched on the optical path to correspond to half of the chosen wavelength (λ/2). b, Illustration of type-II IXs in MoSe₂/WSe₂ within the situation of weak coupling with an utilized electrical area. c, Optical micrograph of gadget A, with highlighted flakes of WSe₂ (blue), MoSe₂ (purple), backside graphene (white) and high graphene (black). Scale bar, 10 µm. d, PL spectra (backside) obtained from IXs at totally different electrical fields within the full-cavity gadget A, excited by a laser energy of fifty nW. Within the neighborhood of E_z ≃ −120 mV nm⁻¹, the exciton emission is aligned with the differential reflectance (DR) dip (high). A notable enhancement of the collected PL depth is current within the situation of exciton-cavity matching. This dataset is a subset of the total field-dependent spectra proven with a linear scale in Fig. 2a.

Earlier than rising the highest DBR pairs, we characterised the field-tunable emission of IXs and their dynamics in our platform (Supplementary Word 2). The lifetime of IXs on backside DBR substrates is monotonically tuned with respect to the electrical area E_z owing to the modulation of the electron–gap wavefunction overlap¹⁴. Then, we’ve got designed our cavity in order that its resonant vitality falls inside the similar vary because the tunable IX emission vitality. After the highest DBR deposition, we achieved a mean high quality issue of Q ~70 with variance ~30 inside the entire double-gated heterostack and a cavity peak mode centred round 1.389 eV (Supplementary Word 3). In Fig. 1d, we present the field-tunable PL spectra obtained by modulating the detuning between the exciton (E_IX) and cavity (E_C) modes. Particularly, from Fig. 1d, we extract an enhancement of the utmost IX peak depth of an element ~50 for cavity-coupled IXs (E_IX ≈ E_C) with respect to uncoupled ones (E_IX < E_C).

Tunable inhibition of IX spontaneous emission fee

Determine 2a exhibits the quantum-confined Stark impact of the IXs in our platform, excited by a pulsed picosecond diode laser (1.93 eV) with a mean energy of fifty nW and a repetition fee of 1 MHz. By becoming the Stark shift of the principle IX peak, we estimate a dipole size of 0.5 nm, in settlement with earlier studies^14,36. We observe a large enhancement of the recorded PL because the exciton-cavity detuning is decreased. Moreover, an obvious vitality leap might be noticed with the detuning at its minimal in Fig. 2b. For rising electrical area magnitudes with respect to the nominal resonance (E_z < −130 mV nm⁻¹), the utmost vitality peak place reverts again to the pattern dictated by the linear Stark impact. That is attributed to the field-dependent tuning of our IX emission from decrease to larger energies, inflicting the utmost PL peak to seem as shifted when the cavity transparency dip is reached (Supplementary Word 6).

a, IX PL spectra as a perform of the utilized vertical electrical area E_z, obtained by thrilling the construction with a 50 nW laser energy. The dashed line corresponds to the linear quantum-confined Stark impact of IXs. A area of upper depth is noticed on the neighborhood of 1.38 eV, similar to the cavity mode vitality (Fig. 1d). We additional present the field-dependent spectra in a waterfall plot in Supplementary Word 2, evaluating it with the half-cavity case to higher spotlight the behaviour of the IX peak when coming into the cavity transparency dip. b, Area-tunable place of the highest-emitting exciton peak vitality (purple). A shift of the brightest peak is discovered round –80 mV nm⁻¹ owing to entrance of the IX tail into the transparency window. The shift round –120 mV nm⁻¹ represents the primary exciton-cavity resonance situation. The cavity mode is highlighted by the differential reflectance dip (gray). c, Complete built-in IX PL depth (purple) and lifelong (blue) as a perform of E_z. Each depth and lifelong exhibit a gradual improve for E_z < −50 mV nm⁻¹, with a pointy peak at E_z ≃ −120 mV nm⁻¹ adopted by a gradual lower. At resonance, as indicated by the dashed gray line, a 50-fold enhancement is noticed for the built-in IX depth, along with a 5-fold improve in lifetime.

We’ll hereafter confer with the construction with out the highest SiO₂ and high DBR mirrors because the ‘half cavity’, and the whole gadget (Fig. 1a) because the ‘full cavity’ constructions. Determine 2c exhibits the field-dependent built-in PL depth and lifelong of the interlayer IX peaks within the full-cavity construction. As detailed in Supplementary Word 6, within the half-cavity construction, we observe a clean reducing PL depth pattern with respect to the utilized electrical area. Nevertheless, within the full-cavity construction, we measured an enhancement of depth for electrostatic fields that decrease exciton-cavity detuning. Particularly, a rise in PL emission is noticed for fields E_z ≤ −50 mV nm⁻¹, with a peak round E_z ≃ −120 mV nm⁻¹ adopted by a step by step reducing tail. To grasp the uneven pattern of the built-in PL depth recorded from our system, we used optical transfer-matrix technique simulations of the far-field emission of very best dipoles within the vitality vary of our IXs (Strategies). As additional mentioned within the following sections and in Supplementary Word 9, we ascribe such asymmetry to the angle-dependent emission of cavity-coupled in-plane IX optical transition dipoles.

Moreover, we measured the field-dependent dynamics of our interlayer ensembles by time-resolved PL, as proven in Fig. 2c. Earlier than the highest cavity progress, we recorded lifetimes within the vary of tens of nanoseconds. Particularly, the pattern of reducing lifetime with rising E_z within the half-cavity construction (Supplementary Fig. 2) is straight associated to the modulation of the electron–gap wavefunction overlap by the quantum-confined Stark impact, as in earlier studies^11,14,37. Within the full-cavity construction, we observe a pointy improve of the IX lifetime underneath the exciton-cavity matching situation, with a fourfold improve with respect to the half-cavity excitons (Supplementary Fig. 8d). Subsequently, our construction reveals a mixed enhancement of each the extracted PL depth and the lifetime of IX ensembles when tuned to the cavity resonance.

We clarify the obtained lifetime enhancement by a Purcell inhibition of the IX spontaneous emission fee (that’s, improve in IX lifetime). The primary components that may contribute to a large Purcell inhibition are spatial misalignment³⁸, spectral detuning³⁹ and the depletion of photonic states owing to the optical microcavity⁴⁰. Since we use a planar λ/2 cavity, the spatial detuning might be assumed to be negligible, whereas the quantum-confined Stark impact permits us to attenuate the spectral detuning. By evaluating with the half-cavity construction (Supplementary Fig. 8d), we verify that the noticed lifetime enhancement is a results of the modulation of the radiated photonic mode density, thus permitting a nontrivial simultaneous enhancement of the collected PL depth. Subsequently, we attribute the noticed lifetime pattern to the discontinuity of photonic mode density on the resonant situation for weakly coupled in-plane IX transition dipoles^41,42 (Supplementary Word 9).

Area-effect tuning of momentum-resolved IX emission

To analyze the radiation sample of cavity-coupled IXs in our monolithic DBR system in momentum area, we carried out Fourier imaging of the back-focal-plane (BFP) PL emission with respect to the utilized electrical area. Determine 3a–c exhibits the momentum-resolved emission of IXs at three totally different fields. okay_x and okay_y characterize the x and y elements of the in-plane photon wavevector okay₀ sin θ, the place θ is the emission angle and okay₀ is the photon wavevector in air.

a–c, Momentum-resolved IX emission obtained by BFP PL spectroscopy at electrical area strengths of E_z ≃ 100 mV nm⁻¹ (a), −120 mV nm⁻¹ (b) and −170 mV nm⁻¹ (c), respectively. All measurements have been obtained underneath a 50 nW laser excitation. Excessive-momentum elements dominate the sign for a and c, whereas low-momentum PL emission arises within the case of b. The whole field-dependent BFP dataset is proven in Supplementary Video 1. BFP photos are normalized at every electrical area to point out the totally different elements in momentum area in any respect exciton-cavity detuning situations. d,e, Area-dependent lifetime (d) and efficient IX diffusion space (e). The information in d are an extension of that proven in Fig. 2c. In settlement with earlier studies^11,13, we outline the IX efficient diffusion space because the area of the IX emission cloud in area with PL depth above 1/e of its most. The IX emission cloud is recorded by a CCD digital camera, as described in Strategies. The dashed purple strains point out the electrical area worth of lowest IX efficient diffusion space, in addition to highest PL depth and lifelong. f, Area-dependent angular emission is obtained by radially averaging the measured BFP photos at every electrical area. The recorded PL emission is normalized at every electrical area. The enhancement of the low-angle emission elements is noticed for electrical fields within the vary −130 mV nm⁻¹ < E_z < −50 mV nm⁻¹, similar to area (2).

We outline three most important areas of the utilized electrical area: (1) beneath resonance (E_z > −50 mV nm⁻¹), (2) low-angle resonance (−50 > E_z > −130 mV nm⁻¹) and (3) high-angle resonance (E_z ≤ −130 mV nm⁻¹). We observe a dominant high-angle emission within the momentum dispersion beneath cavity resonance (E_z ≈ 100 mV nm⁻¹; Fig. 3a). We word {that a} non-negligible sign round zero momentum can also be current. Furthermore, we observe a large enhancement of low-angle emission when within the exciton-cavity mode matching situation (E_z ≈ −120 mV nm⁻¹; Fig. 3b), concurrently with the recorded enhancement of each PL depth and lifelong (Fig. 3d). When additional rising the utilized electrical area magnitude, the emission sample reverts again to a state of affairs of dominant high-angle emission, as proven in Fig. 3c (E_z ≈ −170 mV nm⁻¹).

To additional spotlight the sector dependence of the momentum-resolved emission in our system, we calculate a radial common of the okay elements within the BFP photos with respect to E_z (Fig. 3f and Supplementary Video 1). These outcomes reveal a change within the angular emission of cavity-coupled IXs in correspondence with the enhancement of their emitted PL depth and lifelong. Furthermore, as the electrical area decreases from −50 mV nm⁻¹ to −130 mV nm⁻¹, time-integrated imaging of the spatial distribution of IX emission exhibits a notable discount within the IX diffusion space and simultaneous improve of IX lifetime, as illustrated in Fig. 3d–f. This coincides with a radiative enhancement of low-momentum IXs, suggesting a possible mechanism for photonic IX localization.

WSe₂/MoSe₂ heterobilayers are recognized to host a wealthy excitonic platform owing to the moiré potential arising from the atomic registry between the 2 layers^18,33,43,44. Particularly, the moiré superlattice in incommensurate WSe₂/MoSe₂ heterobilayers is anticipated to present rise to each in-plane and out-of-plane IX transition dipoles of comparable power¹⁸, the place solely the in-plane transition dipoles are anticipated to couple optimally with planar cavities³⁹. Thus, totally different IX species with totally different group velocities and emission profiles are anticipated to coexist. The exciton group velocity v_g might be outlined based mostly on the Wannier perform strategy for each monolayer TMDCs⁴⁵ in addition to for IXs in moiré heterobilayers⁴⁶. Thus, we clarify our outcomes by the enhancement of the emission of low-v_g IXs when in resonance, inducing an efficient IX cloud space discount with respect to off-resonance or high-angle resonance situations. The truth is, at resonance, the IX species with decrease group velocity should preferentially couple into low-angle (low-momentum) optical modes⁴⁵. When the electrical area is between −130 mV nm⁻¹ and −160 mV nm⁻¹, the visualized IX efficient diffusion space expands, corresponding with a rise in emission from higher-momentum IXs. Lastly, for E_z ≤ −160 mV nm⁻¹, the IX emission momentum stays dominated by high-momentum elements, whereas a pronounced lower in IX lifetime correlates with the noticed lower within the IX diffusion space.

IX transition dipoles and cavity coupling

To grasp the tunability of our cavity-coupled IX emission, in Fig. 4a–c, we present the energy-resolved PL of IXs in our platform with respect to their angular sample (Strategies), obtained from the okay_y element of the BFP knowledge. Particularly, Fig. 4a–c is consultant of areas (1) to (3), respectively. The whole energy-resolved field-dependent dataset is proven in Supplementary Video 2, reporting the linear Stark shift of the IX emission in vitality and the corresponding evolution of its angular sample. In area (1), we observe dominant emission at excessive angles for all IX energies, as beforehand proven by the corresponding BFP measurements (Fig. 3a). Nevertheless, for situations (2) and (3) in Fig. 4b,c, respectively, the emitted depth follows a quasi-parabolic pattern in the direction of larger angles.

a–c, Power-resolved IX emission obtained by the okay_y element of BFP PL spectroscopy at electrical fields E_z ≃ 100 mV nm⁻¹ (a), −120 mV nm⁻¹ (b) and −170 mV nm⁻¹ (c), respectively. All measurements have been obtained underneath 50 nW laser excitation. In a, high-angle emissions dominate the sign, with a non-negligible element at low angles. When approaching the resonant situation (b), low-angle emissions are enhanced, with residual elements nonetheless current at larger angles. Shifting in the direction of larger electrical fields (c), a progressive quasi-parabolic shift of the emitted PL is noticed in the direction of larger angles (Supplementary Video 2). The dashed white strains are guides to the attention following the field-dependent angular dispersion of the IX PL. d, Switch-matrix simulations of the angular emission sample of very best in-plane (g_//) and out-of-plane (g_⊥) dipoles inside our construction with respect to their emission vitality. The relative depth of the emission flux density is normalized for each dipolar species. No coupling situation is achieved for out-of-plane dipoles. As a substitute, a pointy rise within the in-plane dipole emission is current on the nominal cavity mode (1.38 eV). With rising energies, the cavity coupling situation remains to be obtained for larger angles of emission of the in-plane dipole, thus yielding a parabolic pattern at low angles, turning into linear at larger energies. e, Left: the emission within the below-resonance vary (E ≃ 1.26 eV), retrieved from a linecut in d, exhibits a non-negligible flux density at low angles (θ < 20°) for the in-plane dipole, adopted by a dominant sign at larger angles (θ > 40°). The emission from the out-of-plane dipole provides a large flux density at excessive angles. That is in settlement with the noticed emission in a. Proper: the emission at exciton-cavity resonance (E ≃ 1.38 eV) is robust within the neighborhood of 0° for the in-plane dipole owing to environment friendly cavity coupling. Against this, a high-angle sign remains to be current for the out-of-plane dipole. Thus, the sudden change to 0° emission within the exciton-cavity matching situation of b is expounded to the selective cavity coupling of in-plane IX transition dipoles. The pattern for E > 1.38 eV in d is according to the resonance noticed in c.

A notable enhancement within the low-angle emission in area (2), along with the quasi-parabolic pattern in (2) and (3), can also be reported in Supplementary Fig. 9 for one more place of the heterostructure in gadget A, in addition to in Supplementary Fig. 11 for gadget B. We word that no substantial distinction is noticed at totally different excitation powers, as proven by the characterization in Supplementary Fig. 9 performed at 0.9 mW. These outcomes present that the achieved area tunability of the IX angular emission sample is unbiased of intrinsic heterostructure region-to-region variations.

To grasp the noticed vitality dispersion of coupled IX emission, we have to take into account the presence of each in-plane and out-of-plane transition dipoles in our heterobilayer¹⁸, as talked about within the earlier part. Particularly, though the IX vitality of emission can range based mostly on the moiré periodicity, an emitting interlayer transition in a given TMDC heterobilayer with little atomic mismatch will characteristic a non-negligible coupling with in-plane and out-of-plane photon modes, with properties that modify throughout the moiré cell based mostly on the atomic registry. Within the case of WSe₂/MoSe₂, each spin-singlet and spin-triplet transitions are anticipated to own each in-plane and out-of-plane transition dipoles inside a moiré cell¹⁸. Subsequently, we’ve got carried out optical transfer-matrix simulations of very best emitters in our construction comprising each out-of-plane and in-plane optical dipoles as a perform of the optical dipole emission vitality. In Fig. 4d, we present the emitted depth flux obtained for a variety of emission energies, mimicking the vitality span coated by our field-tunable interlayer species. At energies decrease than the cavity mode (E < 1.38 eV), each in-plane and out-of-plane dipoles give emitted fluxes with maximal intensities at excessive angles (>30°), as additional highlighted in Fig. 4e. The presence of a large lobe of the flux density at low angles for the in-plane transition dipole is aligned with the non-negligible sign that we experimentally observe at low momentum off resonance (Fig. 4a). Thus, we attribute the noticed emission within the area (1) of the field-tunable BFP measurements to the superposition of each in-plane and out-of-plane IX transition dipoles of various native atomic registries³⁴. Against this, we observe a pointy improve of the in-plane dipole emission when reaching the cavity mode, as in area (2). Determine 4d exhibits that, for rising energies, cavity coupling is achieved for in-plane dipoles at larger angles, exhibiting a parabolic pattern within the vitality dependence of coupled emission, confirming our observations in area (3). We word that our assortment is restricted to a partial vary of angles (±40°; Strategies), which is nonetheless huge sufficient to be coated by our simulations. In Supplementary Word 8, we mimic the exciton emission vitality tunability by convoluting the simulated emission of an in-plane dipole in our construction with Lorentzian broadening. Consequently, Supplementary Fig. 14 provides a theoretical illustration of the tunable cavity coupling of in-plane IX transition dipoles in our construction.

We word that the big structural modifications owing to mesoscopic reconstruction have been proven to strongly influence the spectroscopic signatures of IXs⁴⁷. Whereas we acknowledge the likelihood that bubbles and morphological inhomogeneities might induce mesoscopic reconstructions in our samples, any arbitrary IX transition dipole can at all times be described as a superposition of two orthogonal transition dipoles⁴⁸ (Supplementary Word 9), thus additional motivating our theoretical therapy (Fig. 4d). That is corroborated by the qualitatively constant behaviour of cavity-coupled IXs between totally different positions inside the similar gadget and throughout totally different units (Supplementary Notes 6 and 7). Extra data on the spatial evaluation of the IX emissions in gadget A is offered in Supplementary Word 6.

On the idea of the earlier dialogue, we clarify the sharp improve in emission depth at exciton-cavity resonance based mostly on the change within the angular emission sample of weakly coupled in-plane IXs owing to cavity transparency. Against this, in any respect electrical area strengths, the out-of-plane IX dipoles don’t effectively couple to the cavity modes supported by our construction.