Abstract
The rise of quantum science and technologies motivates photonics research to seek new platforms with strong lightmatter interactions to facilitate quantum behaviors at moderate light intensities. Topological polaritons (TPs) offer an ideal platform in this context, with unique properties stemming from resilient topological states of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) as a promising platform for topological polaritonics. We show that the strong coupling between topological photonic modes of the metasurface and excitons in TMDs yields a topological polaritonic Z_{2} phase. We experimentally confirm the emergence of oneway spinpolarized edge TPs in metasurfaces integrating MoSe_{2} and WSe_{2}. Combined with the valley polarization in TMD monolayers, the proposed system enables an approach to engage the photonic angular momentum and valley and spin of excitons, offering a promising platform for photonic/solidstate interfaces for valleytronics and spintronics.
Introduction
Topological photonics^{1,2,3} has seen a tremendous progress in the past years with numerous topological phases implemented in a variety of platforms, from microwave to optical frequencies^{4,5,6,7,8,9,10,11,12,13,14,15}. Enriching topological photonics by mixing light with condensed matter provides even more exciting avenues for controlling exotic states of light and matter. Indeed, integrating topological photonic systems with quantum wells and quantum dots has already led to major breakthroughs, such as topological lasers^{16,17,18,19}, topological polaritonic phases^{20,21,22,23,24}, active^{25,26} and nonlinear^{27,28,29} topological photonic devices. Consistent with their nontopological cousins, TPs^{20,21,30,31} represent “halflight and halfmatter” excitations emerging as the result of strong coupling^{32,33,34,35,36} between electromagnetic and solidstate degrees of freedom. In addition, they are enriched by topological features. The combination of photonic topological properties (oneway pseudospinpolarized transport, topological protection against scattering) and strong interactions arising from lightmatter hybridization, may support phenomena such as topological solitons, modulation instability, and generation of squeezed topological light^{12,27,29,30,37,38,39,40,41,42,43,44}. Moreover, TPs pave the way towards the development of active topological nanophotonic devices with giant optical nonlinearity^{45,46} enabling control of light by light at small intensities, down to the singlephoton level^{47,48,49,50}. Overall, polaritonic systems^{51,52,53} serve as an ideal interface between photonics and solidstate systems, facilitating control of spin and valleydegrees of freedom^{54,55,56,57,58,59,60,61,62} in future quantum devices. TPs, enriched with additional degrees of freedom, inherited from nanoscale structured photonic materials thus offer uniquely versatile control of quantum states with photons.
In this context, TPs have been an active subject of research with several recent theoretical and experimental findings, in particular in systems based on quantum wells integrated into photonic nanostructures^{16,20,21,23,24,26}. However, the topological polaritonic systems reported so far have been mostly limited to 1D systems, and a 2D system characterized by 1D topological invariants^{16,24}. The only TP system characterized by a 2D topological invariant^{21}, the Chern number, has been demonstrated recently by Klembt et al.^{22} for the case of broken timereversal (TR) symmetry. Specifically, 2D TPs have been realized in Bragg micropillar lattices based on GaAs quantum wells under the application of a strong external magnetic field. On the other hand, spinHall TPs, a different 2D topological polaritonic phase that does not require magnetic field and therefore has significantly more opportunities for broad applicability and integration in nanophotonic systems, has so far evaded experimental realization.
In this work we put forward an approach to spinHall topological polaritonics based on the versatile platform of polaritonic metasurfaces containing monolayer transition metal dichalcogenides (TMDs). Our approach leverages the large exciton dipole moment in a monolayer semiconductor and the remarkable compatibility of 2D materials with various photonic structures to realize strong coupling between light and matter. We show that the strong coupling regime between a topological spinHall photonic metasurface and a TMD monolayer featuring a pair of degenerate TR partner excitons gives rise to a topological transition and the formation of a topological polaritonic phase characterized by nonvanishing spinChern numbers. Introduction of domain walls separating topological and trivial phases is then shown to produce spinpolarized polaritonic boundary modes. Spinlocking of these modes and their selective coupling to circularly polarized light of opposite handedness enables unique polaritonic spinHall phenomena that we demonstrate experimentally. In addition, by studying photoluminescence of WSe_{2} topological metasurface, we confirm valley polarization of edge polaritons.
Results
Topological polaritonic metasurface
The structure we consider here is schematically shown in Fig. 1a and represents a Si photonic metasurface^{12,63} supporting photonic topological spinHalllike phase^{64} with MoSe_{2} and WSe_{2} TMD monolayer placed on top of it. The leaky character of the modes allows a direct excitation and probing both photonic and polaritonic modes supported by such a metasurface^{65,66}. A TMD monolayer encapsulated with a thin hBN layer is placed on top of the metasurface which was adjusted to hold topological modes near the exciton frequencies. Apart from the general purpose of enhancing the quality of the exciton in the monolayer, the hBN layer enables tuning of the parameters of our system (see Supplementary Note 7).
In order to induce a topological transition in the structure^{63,64,67}, its symmetry is reduced by shrinking (Fig. 1a, blue unit cells) or expanding the six nearest triangular holes (Fig. 1a, red unit cells), which leads to the opening of trivial and topological photonic band gaps, respectively^{12,66,67,68}. It is important to mention that the topological polaritonic phase reported here is enabled by the structure of the modes of the metasurface. Thus, the pairs of upper and lower cones in unperturbed structure correspond to the clockwise and counterclockwise s = ±1 circularly polarized dipolar \({p}_{\pm }={p}_{x}\pm i{p}_{y}\)(\(l=\pm 1=1\times s\)) and quadrupolar \({d}_{\pm }={d}_{xy}\pm i{d}_{{x}^{2}{y}^{2}}\) (\(l=\pm 2=2\times s\)) modes, where the polarization handedness s takes the role of a photonic pseudospin, essential for the spinHall phase^{64}.
By adding a TMD monolayer on top of this photonic structure we introduce excitonic degrees of freedom^{67,69}. It is important to stress that excitons in TMDs (MoSe_{2} and WSe_{2} in our case) are (i) characterized by nonzero angular momentum (the spin of sexcitons) of m = +1 and m = −1 (at K and K’ valleys, respectively), and thus form TR partners essential for the topological polaritonic spinHall phase engineered here, and (ii) polarized in the plane of the monolayer, which allows to efficiently couple the inplane electric field of the modes of the metasurfaces to the excitons^{65}. We note that the characteristic size of excitons (~1 nm) and the scale of spatial variation of the photonic modes are orders of magnitude apart, which implies that excitons can interact with both dipolar and quadrupolar photonic modes, and there are no selection rules with respect to the orbital momentum of photonic modes. Nonetheless, the selection rules with respect to the photon pseudospin \(s\) do apply to interactions of optical and excitonic modes due to the conservation of angular momentum (see discussion in Supplementary Note 4).
Theoretical description
The topological polaritonic system under study can be described by an effective Hamiltonian of the form
where the photonic Hamiltonian \({\widehat{ {\mathcal{H}} }}_{ph}\) is obtained from electromagnetic theory (detailed in Supplementary Note 2) and it assumes the form of the wellknown Bernevig–Hughes–Zhang (BHZ) Hamiltonian^{70} of the twodimensional Z_{2} topological insulator
Here, an energy shift \({\omega }_{0}\), equal to the frequency of the Dirac point for the unperturbed lattice, was introduced so that the Dirac point arises at zero energy. In what follows we express frequency in electronvolt units. In Eqs. (1–3) \({\hat{a}}_{{\bf{k}},l}\) and \({\hat{b}}_{{\bf{k}},l}\) (\({\hat{a}}_{{\bf{k}},l}^{+}\) and \({\hat{b}}_{{\bf{k}},l}^{+}\)) are the annihilation (creation) operators for photons and excitons, respectively, and the label k corresponds to the Bloch momentum of photonic modes, \({\tilde{\omega }}_{ex}={\omega }_{ex}{\omega }_{0}\) is the exciton frequency shifted by \({\omega }_{0}\), and \({g}_{({\bf{k}},l,m,s)}\) describes the coupling between photonic and excitonic degrees of freedom in our system. We note that the subscript m = ±1 simultaneously describes the orbital momentum of excitons and their valley degree of freedom (K or K’) due to the valley polarization in the TMD monolayer. As described in Supplementary Notes 1 and 2, the 4 × 4 structure of the photonic Hamiltonian Eq. (4) incorporates both pseudospin s and orbital momentum l degrees of freedom of photonic modes, while the mass term M reflects the band inversion.
The excitonphoton coupling and its form are crucial for generating the TPs reported here, as it induces the topological charge transfer from a photonic to a polaritonic band. In our case, this coupling, described by the 2 × 4 matrix
ensures that angular momentum is conserved, which is also reflected by the \({\delta }_{s,m}\) factors in Eqs. (1–3), and \({q}_{{p}_{+}}={q}_{{p}_{}}\), \({q}_{{d}_{+}}={q}_{d}\) (when the TR symmetry is preserved). This ensures that the spinorbital coupling in the original photonic system is effectively transferred to excitonpolaritons once the hybrid system is in the strong coupling regime.
The form of coupling in Eq. (5) ensures preservation of the two TR partners for excitons and photons, and it also ensures that the coupling takes place only between pseudospinup (down) photons and spinup (down) excitons. Consequently, the presence of spinorbital coupling in the photonic metasurface leads the indirect coupling between the orbital momentum of photons and the spin of excitons. This indirect spinorbital coupling represents the main mechanism behind the topological polaritonic Z_{2} phase^{70,71} observed here. Thus, the form of coupling described by Eq. (5) can be shown to yield an effective phase winding in the interaction between topological photons and excitons. This winding leads to the transfer of topological invariant from the bulk photonic bands to the bulk polaritonic bands (see Supplementary Note 2 for details).
As a confirmation, in Fig. 1c we show the band structure calculated for the spinup domain of the effective Hamiltonian Eq. (1) for the case of the (m = 1) exciton crossing lower dipolar photonic (s = 1) band. For the case of expanded (topological) photonic lattice, without coupling to excitons, the photonic bands are known to possess a spinChern numbers \({C}_{ph}=+1\) and \({C}_{ph}=1\) for the lower and upper bands, respectively. Turning on the excitonphoton coupling leads to a transition to the topological polaritonic phase. Thus, we observe that the strong coupling gives rise to avoided crossing of excitonic and photonic bands, and the formation of lower and upper polaritons. Calculation of the spinChern numbers for the upper polaritonic band yields nonzero values identical to those of the crossed photonic bands before coupling (as in Fig. 1c for the spinup upper polariton). Inspection of the Berry curvature in momentum space confirms that the topological transition arises due to exciton photon coupling since the main contribution comes from the region of avoided crossing (Fig.1c and Supplementary Note 2). Similar calculations for the spindown upper polaritons yield opposite sign of the Berry curvature and of the spinChern number, as expected for the Z_{2} phase.
Band structure calculated for the supercell with two domains, topological and trivial, obtained with the tightbinding model (TBM) (described in Supplementary Note 1) is shown in Fig. 1d, where the degree of the excitonic component of the modes is encoded in the color of the bands. As expected for this scenario, the flat section of the upper polariton (the remnant of the excitonic flat bands) is close to 100% excitonic, and the excitonic fraction fades away as we move into the parabolic portion of the band (having an increasing photonic fraction of the band). For the special case of the excitonic bands touching the tip of the photonic bands (\({\omega }_{ph}({\bf{k}}=0)={\omega }_{ex}\)) allows for an exact analytical treatment which shows that both upper and lower polaritonic bands appear to be ~50% excitonic at Γ point (k = 0). Remarkably, this scenario also yields topological boundary states with largest excitonic component. Indeed, as can be seen from Fig. 1d, the topological polaritonic boundary modes appear to be highly excitonic in a wide range of wavenumbers and energies below the midgap frequency, and even have a significant excitonic fraction in the midgap and at higher frequencies.
Below we focus on the experimental observation of these phenomena in two scenarios: when such crossing occurs (i) between the lower (dipolar) photonic band and excitons in MoSe_{2}, and (ii) between the upper (quadrupolar) photonic band and excitons in WSe_{2}.
Experimental results
The designs of our topological photonic metasurfaces were optimized to exhibit band crossing of the exciton resonances in MoSe_{2} with lower photonic band and in WSe_{2} with upper photonic band near the Γpoint. The final designs were fabricated by patterning Silicon on Insulator (SOI) substrates with the use of ebeam lithography followed by reactive ion etching. The details of the fabrication techniques used can be found in Methods. The fabricated samples consist of shrunken and expanded regions forming an array of armchairshaped domain walls^{67}. The bulk regions of at least 10 periods were confirmed to be wide enough to eliminate possible coupling between the edge states confined at the domain walls. One of such domain walls separating topological and trivial regions is shown in an SEM image in Fig. 2a.
Optical microscope images of the samples prepared for lower and upper band crossing scenarios are shown in Fig. 2b and c, and correspond respectively to (i) the case of the MoSe_{2} monolayer on top of the metasurface with subsequent transfer of a 12 nm hBN layer and (ii) the case of a WSe_{2} monolayer incapsulated by a 10 nm (bottom) and 30 nm (top) hBN layers. The boundaries of both TMD monolayers and hBN flakes on top of the metasurfaces are indicated by color lines in Fig. 2b, c. The leaky character of the photonic and polaritonic bands allows their optical characterization by the back focal (Fourier) plane imaging in our custombuilt experimental setup, which enables the extraction of the band diagrams in frequencymomentum space in a range from cryogenic to room temperatures (see Methods for details on the experimental techniques used).
We observe the formation of TPs by comparing the angleresolved differential reflectivity spectra from different domain walls of our metasurface (Fig. 3). The data from a domain wall without MoSe_{2} (Fig. 3a) reveal the photonic bandgap of the metasurface (~1.65–1.77 eV, see Supplementary Note 6 for details on experimental data processing) with two gapless modes inside the bulk bandgap, which correspond to the pseudospinup and pseudospindown topological photonic edge states propagating along the domain wall in the opposite directions. In this case, no polaritonic bands appear, yielding purely photonic topological edge states. In contrast, the spectra measured at 7 K from the domain wall covered by MoSe_{2} (Fig. 3b) demonstrate strong coupling between the lower energy photonic band of the topological metasurface and the exciton, which crosses it close to the band edge (1.65 eV) and gives rise to the transition to the topological polaritonic phase. The experimental spectra reveal the formation of polaritonic bands with Rabi frequency of Ω_{R} = 27.3 meV (exact value obtained by fitting the PL data as shown further). This is corroborated by the crosspolarized reflectivity data (Fig. 3c) which has greatly enhanced contrast due to suppression of the background Fabry–Perot interference from the oxide layer. These data confirm the formation of TP bulk states as well as topological edge polaritons. As an important indication of the polaritonic nature of the edge states at 7 K in Fig. 3b, c, we notice that the respective bands asymptotically approach the polaritonic bulk band. The dispersions of the edge modes extracted from the measured crosspolarized reflectivity maps fit well with the dispersion calculated via TBM (Fig. 3d). In agreement with theory (Fig. 1b) and the bulk boundary correspondence^{71,72}, this confirms that the topological invariants, i.e., the spinChern numbers, were transferred to the respective upper polaritonic bands from the former photonic band due to the strong coupling. Accordingly, the lack of edge states within the bandgap between upper and lower polariton branches further evidences that the spinChern number of the lower polariton band is zero due to this transfer. Notably, the transition from topological photonic to topological polaritonic spinHall effects can also be observed by changing the temperature, which influences the spectral position and oscillator strength of the exciton (see Supplementary Fig. 8).
We also note that for some experimental spectra the presence of a small gap between forward and backward edge states is evident at normal incidence (e.g., Supplementary Fig. 6). While the presence of such a gap is known from the original theoretical study^{64}, here, the variation of the gap width between different samples allows us to conclude that the primary mechanism of its formation is backscattering due to defects in the structure causing the coupling between backward and forward edge modes. At the same time, the narrow width of the gap (which varies across different samples, but generally does not exceed 5 meV) shows that this backscattering is very weak, and the presence of the defects does not affect the observed topological polaritonic phase.
We further study the TPs via angleresolved photoluminescence (PL) at 7 K. In the experiment, the sample was excited by HeNe continuouswave laser (1.96 eV). The spectra shown in Fig. 4a, b reveal the emission from both polariton branches as well as from uncoupled neutral exciton at 1.65 eV and charged exciton (trion) at 1.62 eV. We analyze the data by fitting it with the coupled oscillator model using the spectral position and linewidth of uncoupled exciton (\({\tilde{\omega }}_{ex}={\omega }_{ex}+i{\gamma }_{ex}\), \({\gamma }_{ex}=12\) meV) and photonic mode (\({\tilde{\omega }}_{ph}={\omega }_{ph}+i{\gamma }_{ph}\), \(\,{\gamma }_{ph}=\) 10 meV) that we extract from PL data at large kvectors and from reflectivity data with no strong coupling, respectively. The resulting spectral positions of the upper and lower polariton bands are given by the equations^{73}
From data fitting for both TE and TM polarized PL using Eqs. (6) and (7), we extract a coupling strength κ of 13.7 meV, which corresponds to a Rabi splitting Ω_{R} of 27.3 meV consistent with the strong coupling criterion.
The most important property of spinHall topological systems is the oneway spinpolarized character of their topological boundary states. While it was observed experimentally in photonic structures^{74}, a similar effect should also emerge in spinpolarized topological polaritonic boundary modes. We demonstrate this experimentally for TPs through circularly polarized reflectivity measurements, where only one of the edge states emerges for circularly polarized excitation of the structure. Figure 4c (left, central panel) shows the oneway edge state in the angleresolved differential reflectivity map for σ^{−} polarization (see also Supplementary Fig. 7a, b). Using the numerical model of the metasurface supercell with 10 topological and 10 trivial unit cells separated by the domain wall based on TBM/CMT modes, we calculate the excitonic and photonic fractions of the edge mode (shown in Fig. 4c as well). As expected, it has a strong excitonic component, which reaches nearly 100% near the exciton resonance (1.65 eV) and gradually fades away at higher energies where the photonic component starts to dominate. Due to the very low signaltonoise ratio of PL at the edge modes in this configuration, it was impossible to visualize the propagation of edge topological polaritons for nonresonant excitations. Instead, we corroborate the angleresolved data with differential real space images of the domain wall of topological polaritonic metasurface excited resonantly by focused circularly polarized laser pulses of the opposite helicity (Fig. 4c, right). As expected, towards the center of the topological gap (1.7–1.72 eV, cf. 1.65 eV), where the contribution of bulk TPs vanishes, the images show clear asymmetry, which indicates oneway propagation of edge TPs along the domain wall. The calculation indicates that at these frequencies the edge modes have considerable excitonic fraction (0.05 and 0.11 at 1.72 and 1.7 eV, respectively).
Finally, we demonstrate the possibility of polarization conservation and selective coupling of valley polarization to the edge modes. To this aim, we fabricate another topological polaritonic metasurface optimized for strong coupling between the upper photonic band and the exciton in WSe_{2}. The change of material is stipulated by much superior valley depolarization properties of WSe_{2}^{74} compared to MoSe_{2}^{75}. To characterize the valley polarization conservation in edge TPs, we transfer an hBNincapsulated WSe_{2} monolayer on top of the topological metasurface (Fig. 2c) with design optimized for the intersection of WSe_{2} exciton with the upper photonic band. First, we characterize the sample by measuring the angleresolved differential reflectivity and PL which confirm the formation of upper and lower TP bands (Fig. 5a, b). As WSe_{2} emission spectra are dominated by localized excitonic states at low temperature, for the strong coupling characterization we use a temperature of 100 K, for which the polaritonic branches become more pronounced for the PL signal (Fig. 5b). For excitation, we use a 1.96 eV HeNe CW laser. Similarly to MoSe_{2} sample, we fit the PL data with coupled oscillator model that yields slightly lower coupling strength (κ = 11 meV) and Rabi splitting (Ω_{R} = 22 meV) with \({\gamma }_{ex}=13\) meV and \({\gamma }_{ph}=12\) meV, which can be explained by the presence of an additional hBN layer between the monolayer and metasurface. Next, for the measurements of polarization conservation of TMD emission and its selective coupling to edge states, we employ resonant excitation at the WSe_{2} exciton frequency (1.74 eV) and decrease the temperature back to 7 K (Fig. 5c, d). Emission from TMD monolayer below the exciton energy (1.68 eV and below, also visible in PL map in Fig. 5b) in such configuration partially retains valley polarization^{76}, which provides the opportunity to observe the selective coupling of PL to the edge modes. Figure 5c,d show the maps of angleresolved differential reflectivity and circular polarization degree (CPD) of emission from edge states of topological polaritonic metasurface with WSe_{2} measured at 7 K. We define the circular polarization degree as CPD = \((I({\sigma }^{+})I({\sigma }^{}))/(I({\sigma }^{+})+I({\sigma }^{}))\), where \(I({\sigma }^{+})\) and \(I({\sigma }^{})\) are the PL emission intensity recorded for \({\sigma }^{+}\) or \({\sigma }^{}\) circularly polarized pump, respectively, without any polarization selective optics in the detection channel. Due to the polarization conservation of WSe_{2} PL and the spinmomentum locking of the edge modes, the emission is predominantly coupled to one of the counterpropagating edge modes depending on the helicity of the excitation, which leads to the opposite signs of CPD at the edge modes. Figure 5d reveals up to 20% CPD of the emission at the TP edge states, which suggests the possibility of valley transport with topological edge polaritons formed due to the transfer of topological invariant from photonic to polaritonic bulk modes.
Discussion
To summarize, here we have introduced an approach to engineer Z_{2} topological polaritonic phase with preserved TR symmetry by strongly coupling a topological photonic system with excitons in 2D materials. The strong polarizability and the presence of two TR partner exciton states in 2D semiconductors, leads to strong coupling and avoided crossing behavior accompanied by the emergence of effective winding and topological transition to the topological polaritonic spinHall phase. TR symmetry and conservation of angular momentum in the system ensures that the excitons with opposite orbital momenta couple with photons of respective pseudospins, thus ensuring the formation of two TR partner topological polaritonic bulk bands carrying nonzero spinChern numbers. This gives rise to the emergence of spinpolarized oneway edge TPs, which may carry valleypolarized polaritonic component.
Our work demonstrates Z_{2} 2D topological polaritonic phase which does not require magnetic field and exhibits a large topological bandgap hosting oneway topological polaritonic boundary modes. In our work the topological bandgap amounts to 20–30 meV, which is especially important for potential applications leveraging topological polariton nonlinearities, e.g., for generation of topological solitons which require a broad range of frequencies.
We note that in a recent work the formation of edge exciton polaritons has been reported^{77} due to hybridization of WS_{2} excitons with the topological photonic states of a SiN metasurface. In our work we focus on a different scenario of strong coupling with bulk photonic modes, which gives rise to a transfer of topological invariant to bulk polaritonic states. The resultant Z_{2} type topological polaritonic phase gives rise to the formation of topological edge polaritons, whose dispersion asymptotically approaches bulk polaritonic bands. Interestingly, in the case of the interaction between photonic edge states and excitons^{77}, the bulk states remain photonic, and the mechanism of edge polariton formation is different as it gives rise to the gapped character of edge polariton dispersion, with edge polaritons exhibiting oneway spinpolarized propagation. In the scenario considered here, we confirmed that for the case of hybridization of excitons with bulk photons, the edge polaritons emerge from the bulk upper polaritonic bands, in agreement with the bulkboundary correspondence, which directly evidences the Z_{2} topological polaritonic phase.
Our work paves the way to engineering topological phases in hybrid photonicexcitonic structures by enriching these systems with additional degrees of freedom inherited from their solidstate component, such as valley degree of freedom in TMDs. Our results thus envision an original platform that can be employed as a resilient topological interface between photonic and electronic components in future valleytronic devices. This platform also has clear advantages over the conventional approach based on semiconductor heterostructures since 2D materials support a broad range of excitations with a variety of internal degrees of freedom and are easy to integrate into topological photonic systems. Thus, this concept can be extended to a wide range of solidstate systems hosting different excitation, including phonons, polarons, magnons and spinwaves, which can be devised to interact with various topological photonic systems, e.g., regular and higherorder topological insulators, yielding topological phases and ways to control matter with light in a robust and a resilient manner. Strong and resilient lightmatter interactions in such systems will facilitate enhanced nonlinear effects and novel quantum effects involving halflight and halfmater excitations, which can be of immense value for various classical and emerging quantum applications.
Methods
Sample fabrication
A triangular lattice formed by the hexamers of triangularshaped holes was fabricated on the SilicononInsulator substrates (75 nm of Si, 2 μm of SiO_{2}) with the use of Ebeam lithography (Elionix ELSG100). First, the substrates were spincoated with ebeam resist ZEP520A of ~170 nm thickness and then baked for 4 min at 180 °C. Next, gold film 15 nm thick was sputtered on top of resist. Ebeam lithography exposure was followed by gold etch and the development process in nAmyl Acetate cooled to 0 °C for ~35 s. Then, anisotropic plasma etching of silicon was conducted in The Oxford PlasmaPro System ICP by a recipe based on C4F8/SF6 gases. Triangular shaped holes were etched to the depth of about 75 nm at temperature 5 °С etching with rate about 1.5 nm/s. Finally, the residue of resist was removed by sample immersion into NMP heated to 60 °С.
Monolayers of TMD materials (MoSe_{2}, WSe_{2}) were exfoliated onto a thick PDMS stamp using standard tape technique and transferred to the substrate by the custombuilt transfer system. The monolayer was annealed at 350 °C for 2 h to remove the polymer residue from the transfer process. Further, some of the monolayers were encapsulated within hBN layers and annealed again at 350 °C for another 2 h.
Experimental set up
Angleresolved reflectivity measurements were performed in a back focal plane configuration with a slit spectrometer coupled to a liquidnitrogencooled imaging CCD camera (Princeton Instruments SP2500+PyLoN), using white light from a halogen lamp for illumination. The sample was mounted in an ultralowvibration closedcycle helium cryostat (Advanced Research Systems) and maintained at a controllable temperature down to 7 K. To resolve the topological edge modes, we used a slittype spatial filter in the image plane of the detection channel that allowed to collect signal only from the vicinity of a single domain wall. For polarized reflectivity maps, the polarization selection was performed both in excitation and in collection channels. The maps for aligned polarizers were additionally postprocessed to suppress the FabryPérot background originating from the bottom silicon layer of the SOI substrate (see Supplementary Note 6). For PL CPD measurements with WSe_{2} sample, the linear polarizer was removed from the collection channel to exclude any polarization sensitivity that interferes with CPD extraction.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
The work was supported by the National Science Foundation with grants No. DMR1809915 and NSF QII TAQS OMA1936351, by the Defense Advanced Research Project Agency Nascent Program, by the Office of Naval Research with grants No. N000142112092 and N000141912011, and by the Simons Foundation. The work on transferring TMD monolayers and hBN crystals on top of metasurfaces was supported by the Ministry of Science and Higher Education of Russian Federation, goszadanie no. 20191246 and megagrant 14.Y26.31.0015. Optical measurements were funded by RFBR, project number 203270185. Optical measurements on WSe_{2}based photonic structures were funded by the Russian Science Foundation (project no. 197220120). DNK and MSS acknowledge the support from UK EPSRC grants EP/R04385X/1 and EP/N031776/1. IS acknowledges the support from The Russian Federation President Grant Council, project no. MK4652.2021.1.2.
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M.L., I.S., F.B., T.I., E.K., S.K., A.V., S.G., M.S., V.M., D.K., A.A., A.S., A.B.K. contributed extensively to the work presented in this paper, preformed theoretical and experimental studies, and prepared the manuscript. M.L. and I.S. contributed equally to this work.
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Li, M., Sinev, I., Benimetskiy, F. et al. Experimental observation of topological Z_{2} excitonpolaritons in transition metal dichalcogenide monolayers. Nat Commun 12, 4425 (2021). https://doi.org/10.1038/s4146702124728y
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DOI: https://doi.org/10.1038/s4146702124728y
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