The recent advances in fabrication and character ization of twodimensional (2D) materials and heterostructures present new opportunities for engineering ultrathin synthetic quantum materials with unique physical properties [1,2]. Among the many recently developed heterostructures, heterobilayers comprised of different monolayer transition metal dichalcogenides (TMDs) have attracted intense research efforts [3]. These composite materials host an atomically sharp typeII electronic interface [4,5] (figure 1(A)), which results in the formation of an interlayer exciton (IX) [6,7]-the Coulomb bound state composed of electron and hole localized in different layers (figure 1(B)). This system has emerged as a promising platform for optoelectronic devices with valleytronic functionality [8] and for explorations of the fundamental physics of excitons [3].

The interlayer exciton is the lowest lying optical excitation in TMD heterobilayers, and the spatial sepa ration of the constituent charges results in a number of advantageous properties. In particular, the IX exhibits enhanced exciton population [6,9] and valley lifetimes [10][11][12], compared to its monolayer TMD counter parts. Moreover, the intrinsic electric dipole moment of the IX allows for modulation of the exciton energy [6,13], as well as control of exciton flux [14] by patterned electrodes and gates. However, theoretical [15,16] and experimental [17] works have revealed small opti cal dipole moment for IX, with oscillator strength about 2 orders of magnitude lower than that of a sin gle monolayer TMD. This limitation has made optical studies of the IX properties challenging.

On the other hand, the high sensitivity of 2D mat erials to their dielectric environment makes them suitable for coupling to planar photonic devices. This presents an opportunity to not only overcome the weak optical emission, but also new scientific oppor tunities, such as exploring excitonpolaritons with val ley degrees of freedom at room temperature. Already, monolayer TMDs embedded within distributed Bragg reflector microcavities have demonstrated the forma tion of valley excitonpolaritons [18,19]. Moreover, the surface coupling of monolayer TMDs with pho tonic crystal nanocavities has given rise to ultralow threshold nanoscale lasers [24], cavity enhanced light emitting diodes [20], and enhanced second harmonic generation [21][22][23]. Here, we show that the placement of the TMD heterobilayer on top of a gallium phos phide photonic crystal (PhC) linear threehole defect cavity results in IXcavity coupling in the weak regime, with a significant enhancement of the photolumines cence (PL) resulting from the Purcell enhancement of the IX in resonance with the PhC cavity modes.

The sample in our study consists of a MoSe 2 -WSe 2 heterobilayer placed on top of a gallium phosphide (GaP) linear threehole defect (L3) photonic crystal cavity, as illustrated in figure 1(C). Photonic crystal cavity is chosen because of the small modevolume and highquality factor of the cavities, which give rise to a strong light-matter interaction. The L3 cavity was fabricated by defining an etchmask on top of a 125 nm GaP thin film on sacrificial layer of InGaP substrate, using electron beam lithography, followed by reactive ion etching, and subsequent removal of the sacrificial layer, as described in our previous work [24]. The photonic crystal cavity was first characterized by cross polarized reflectivity measurements [25] at 300 K, prior to fabrication and transfer of the heterobilayer. The monolayers of MoSe 2 and WSe 2 were mechanically exfoliated from bulk materials and assembled into the heterobilayer using topdown viscoelastic stamping techniques [26]. The straight edges of the monolayer flakes of WSe 2 and MoSe 2 were carefully aligned during the fabrication, and the final transfer was directed onto the photonic crystal cavity. We note that aligning the edges is a common technique to achieve samples that are bright, which requires a small twist angle, since the cleaved monolayer WSe 2 and MoSe 2 crystals favor zigzag edges. The brightness of the sample is a reliable indicator that the sample is aligned within about 5 • , as we have experienced before in experiments. A scanning electron micrograph of the completed device is shown in figure 1(D), with the different layers of the heterobilayer highlighted in false color for clarity. For further details on the sample fabrication, see methods.

Crosspolarized reflectivity measurements of the bare cavity revealed resonances at ω 1 = 1.37 eV and ω 2 = 1.33 eV, with quality factors of Q 1 = 1370 ± 140 and Q 2 = 780 ± 50, respectively (figure S1). The quality factors are estimated by fitting a single Lorentzian function to the peaks observed in the cavity transmission spectrum. This particular cavity was chosen because the higher energy resonance is wellmatched to the PL energy of IX in the MoSe 2 -WSe 2 heterobilayer [3]. The optical response of the TMD heterobilayer on the PhC was then char acterized using confocal PL spectroscopy in reflection geometry, normal to the plane of the heterobilayer, at a temperature of 5 K. A continuous wave (cw) laser (λ = 532 nm) was used to excite the sample. The PL spectrum of the heterobilayer consists of emission from intralayer excitons in the energy region of ~1.6-1.72 eV, as well as IXs with lower energy of ~1.3-1.4 eV (figure S2). As we focus the laser spot on the PhC cavity (the area from where the holes are removed), a strik ing difference emerges in the PL response of the low energy spectrum: two narrow peaks are observed in the PL spectrum on the cavity, that are absent off of the cavity (see figure 2(A)). To measure the emission off the cavity, we focus our aboveband laser away from the defect region, but still on the photonic crystal. The energies of these peaks are very close to the cavity resonances measured via transmission. By fitting the two narrow peaks in the PL, we found that the cavity Qfactor exhibited minimal degradation due to the heterobilayer transfer (see figure S3). By comparing the emission intensity on and off the cavity, we esti mate the enhancement of the photon emission to be ~15 at the first resonance(∼ 1.37 eV) .

To confirm the assignment of the low energy PL as originating from interlayer excitons, we performed PL excitation spectroscopy (PLE) on the heterobilayer region on the PhC cavity. Using a frequency tunable Ti:Sapphire cw laser (M 2 SolsTiS), we tuned the exci tation energy across the excitonic manifolds of the isolated TMD monolayers (1.61 to 1.75 eV) while col lecting the low energy PL. The PLE response, shown in figure 2(B), displays two broad resonances for the narrow peaks in the PL spectrum. Figure 2(C) presents the integrated PL spectrally degenerate with the cavity mode as a function of laser energy, which shows that the PLE resonances appear at the energetic positions of intralayer excitons in monolayer WSe 2 (1.72 eV) and monolayer MoSe 2 (1.64 eV). This result indicates that the PL comes from interlayer excitons [6,9], which are excited through photon absorption in the monolayer WSe 2 (MoSe 2 ), followed by ultrafast interlayer charge transfer of the electron (hole), and subsequent forma tion of interlayer exciton, as illustrated in the insets of figure 2(C).

The polarization of the interlayer exciton PL on the cavity was then analyzed in the linear basis. The polarizationresolved PL measurements, shown in figure 3(A), reveal strong linear polarization of the narrow PL peaks. The integrated PL from the higher energy resonance (black arrows denote the integration region in figure 3(A)) is plotted as a function of the axis of linear polarization in figure 3(B). Compariso n of the major axis of this linearly polarized PL with the orientation of the photonic crystal shows that it is directed along the ŷ axis of the L3 cavity, which corre sponds to a transverse electric polarized cavity mode, with only inplane electric field components (see fig ure S4 in supplementary materials (stacks.iop.org/ TDM/7/015027/mmedia)).

Under the electric dipole approximation, this implies that the optical coupling of the interlayer exci ton has significant component in the plane of the het erobilayer, which is consistent with recent theoretical predictions [15,16,27,28]. By scanning the objective lens, we also performed confocal spatial mapping of the polarization dependence of the PL across the entire PhC. The resulting spatial maps reveal a sharp peak in the intensity of ŷ polarized interlayer exciton PL from the region on the cavity (I y , figure 3(C)) that is absent from the spatial map of the xpolarized inter layer exciton PL intensity (x, figure 3(D)). The spa tial map of the cavityenhanced PL defined herein as I PhC ≡ I ŷ -I x , illustrates that it is spatially localized to the cavity (figure 3(E)). We note that there is another polarizationsensitive bright spot, which we attribute to the fabrication imperfections. New cavity designs supporting both transverse electric and transverse magnetic modes could provide more information on the inplane and outofplane dipole of the interlayer exciton.

The dynamics of the cavityenhanced PL were then characterized through time resolved PL measure ments. A pulsed laser (1 MHz repetition rate, ~10 ps pulse duration) resonant with the A exciton of the WSe 2 monolayer (1.72 eV) was focused on the region of the heterobilayer on the cavity. The light is primar ily collected from the bright spot in the spatial map of I ŷ -I x in figure 3(E). The polarization of the PL was analyzed along the x and ŷ axes before being directed into a timecorrelated single photon counting system. The narrow peak of cavityenhanced PL was spectrally filtered to isolate the dynamic response of the PL reso nant with the PhC cavity mode. The timeintegrated cavityenhanced PL under pulsed excitation is shown in figure 4(A). The dynamics of the PL resonant with the higher energy cavity mode (denoted by arrows on top of figure 4(A)) is shown in figure 4(B). We observe a significant difference in the decay of the interlayer exciton PL linearly polarized along the x and ŷ axes of the PhC for the first ~200 ns, after which, the enhance ment of the PL is diminished. The cavityenhanced PL dynamics calculated via I ŷ -I x and shown in fig ure 4(C), are fit well by a triple exponential decay, with decay times of 1.3 ns, 20 ns, and 80 ns. Meanwhile, the PL after the first 200 ns is well fit by a double expo nential with decay constants of about 116 and 670 ns. However, no appreciable lifetime reduction is observed in the exciton emission. We note that, as such, we do not have a clear explanation of the multiexponential decays, and more studies are warranted.

The obtained spectroscopic results support the coupling of the interlayer exciton in the MoSe 2 -WSe 2 heterobilayer to the PhC L3 cavity. The energetic positions of the narrow peaks in the PL, 1.32 eV and 1.36 eV, closely match the energies of the bare photonic crystal cavity modes, measured at room temperature. Moreover, the narrow resonances measured in PL have similar quality factors as the bare cavities (measured via reflection, see figure S2), indicating low absorptive loss from the IX. The slight redshift of the cavity modes with the heterobilayer on top is expected, as the TMDs have higher refractive index than air. The PLE results clearly indicate that this PL stems from the interlayer exciton, rather than intralayer excitons confined in deep potentials. This assignment is further supported by the long decay dynamics of the PL, which are several orders of magnitude longer than ~ps lifetimes of intralayer excitons [29].

The total decay rate of the exciton population is given by the sum of the radiative and nonradiative recombination pathways, Γ = Γ rad + Γ nrad , and the cavity enhances only the radiative part. Hence, an emit ter with large nonradiative decay rate (Γ nrad Γ rad ) cannot exhibit Purcell enhancement. The ground state of interlayer exciton has finite velocity, which implies vanishing oscillator strength. The interlayer exciton momentum relaxation therefore manifests itself as a fast nonradiative decay channel as the interlayer exciton transitions from a bright state to a dark state. Together with the large inhomogeneous broadening, this precludes conclusive determination of the lifetime reduction in this system (see supplementary discus sion), although the enhancement of the PL intensity is evident. This enhancement of the PL intensity can origi nate from two effects: enhancement of the spontaneous emission rate and the cavity antenna effect. In most cav ity quantum electrodynamic (cQED) systems involving solidstate emitters, the emitter is embedded inside the semiconductor, and thus already confined in the slab via total internal reflection. A cavity can redistribute the momentum vectors of the emission and provide bet ter collection. In our system, however, the emitters are located on top of the semiconductor slab, and numeri cal simulation shows that the integration with the cavity reduces the collection efficiency: only ~8% of the light emitted from the heterobilayer on the cavity is collected by the objective lens, whereas we expect to collect almost ~32% of the light emitted from a heterobilayer placed on an unpatterned semiconducting substrate. This implies the radiative rate is actually enhanced by ~60 times (see supplementary discussion).

We can calculate the Purcell factor theor etically to be ~65, with a Q of 1370, mode volume of ~0.7 λ n 3 , and emitter's position at the cavity surface E 2 surface E 2 center = 0.44 . We emphasize that, if a cQED sys tem operates in the 'good cavity' regime, i.e. the cavity has smaller linewidth compared to the emitter, the Q used in calculation of the Purcell factor should be the Q of the emitter [30,31]. However, our experimental results indicate that the cQED system is actually oper ating under the 'bad cavity' regime, which implies the homogeneous radiative linewidth of the emitter is nar rower than the cavity, and the Q used in the Purcell fac tor calculation is that of the cavity. Our results laid a solid foundation in exploring more cQED effects in the nanocavity integrated 2D heterostructure photonics.

The cavity was fabricated from a 125 nm thick GaP membrane, grown via molecular beam epitaxy, on 1 µm thick sacrificial Al 0.8 Ga 0.2 P layer on a GaP wafer. The patterns were first defined in ZEP520A resist by electronbeam lithography (JEOL JBX6300FS, 100 keV) and then transferred to the GaP membrane by Argon and chlorinebased reactive ion etch. Excess resist was removed with dichloromethane. The sacrificial layer was undercut with hydrofluoric acid to yield suspended membrane structures with high index contrast, followed by cleaning in dilute KOH to remove any byproducts of the undercut. The photonic crystal used in the experiment has a periodicity of a = 264 nm and radius of r = 65 nm. The cavity is created by removing three holes from a line, which is why the cavity is called linear threehole (L3) defect cavity. The holes at the end of the cavity are shifted by 0.176a, and the radius of those two holes are changed to 0.9r, to increase the quality factor. These geometric parameters of the cavity are optimized via finite difference time domain (FDTD) simulations using Lumerical FDTD solutions.

For PL measurements, a diodepumped solid state laser was used to excite the sample at 532 nm.

The PL from the sample was collected in reflection geometry, normal to the plane of the heterobilayer and photonic crystal, using a 40× objective lens (0.6 NA). Cryogenic measurements were performed in a Montana Instruments Cryostation, in vacuum.

The PL was dispersed by a 0.5 m monochromator equipped with a 600 line mm -1 groove density diffraction grating and a thermoelectrically cooled chargecoupled device (Andor Shamrock + Newton CCD) for timeintegrated measurements. Polarization specific detection was accomplished by a combination of achromatic λ/2 waveplates and a linear polarizer.

For PLE measurements, the excitation source was a power stabilized, frequency tunable cw Ti:Sapphire laser (M 2 SolsTiS). For timeresolved measurements, the excitation source was spectrally filtered output (~3 nm FWHM) from a supercontinuum laser with ~6 ps pulse duration and 1 MHz repetition rate. The PL was spectrally filtered (~2 nm FWHM) using a slit assembly mounted at the side port output of the monochromator before being directed onto a single photon detector (Excelitas SPCM) connected to a timecorrelated counting system (PicoHarp 300), with an overall instrument response time of ~450 ps. In all PL measurements, the excitation beam was spectrally filtered from the signal using a combination of dichroic beam splitters and longpass filters.