Near-Field Coupling with a Nanoimprinted Probe for Dark Exciton Nanoimaging in Monolayer WSe2

Tip-enhanced photoluminescence (TRPL) is a powerful technique for spatially and spectrally probing local optical properties of 2-dimensional (2D) materials that are modulated by the local heterogeneities, revealing inaccessible dark states due to bright state overlap in conventional far-field microscopy at room temperature. While scattering-type near-field probes have shown the potential to selectively enhance and reveal dark exciton emission, their technical complexity and sensitivity can pose challenges under certain experimental conditions. Here, we present a highly reproducible and easy-to-fabricate near-field probe based on nanoimprint lithography and fiber-optic excitation and collection. The novel near-field measurement configuration provides an ∼3 orders of magnitude out-of-plane Purcell enhancement, diffraction-limited excitation spot, and subdiffraction hyperspectral imaging resolution (below 50 nm) of dark exciton emission. The effectiveness of this high spatial XD mapping technique was then demonstrated through reproducible hyperspectral mapping of oxidized sites and bubble areas.


Section S2: Numerical Simulation
The simulation of the detection and excitation profiles in Figure 1 (b) and (c) were conducted using the commercial Finite-Difference Time-Domain (FDTD) method based software, Ansys Lumerical FDTD. The relative permittivity of gold used for simulation was taken from Johnson and Christy's report, and the refractive index of the ( ) = -Ormocomp and SiO 2 were set as . The simulations were performed in 2 dimensions since the light propagations = 1.5 in both cases are symmetric in the in-plane direction (perpendicular to the plane of incidence). To simulate the probe, a cone structure with a curvature size of 20 nm, a taper angle of ~70°, an Au coating of 20 nm, and a height of 5.6 μm, was used. The probe is placed 15 nm above the gold substrate. The objects were placed in the center of a volume with a refractive index , surrounded by 16 layers of stretched coordinate Perfect Matched Layers (PML) on 4 sides to = 1 avoid unphysical reflections from the sides. All PMLs were placed far away from the objects to avoid spurious effects from a potential interaction between the evanescent waves and the PML. A mesh with a 1 nm step size in both horizontal and vertical directions was used at the apex of the probe to guarantee accuracy and mesh-independent results.
For the detection profile simulations, dipole emitters with an out-of-plane and in-plane polarization are placed 2 nm away from the gold substrate. The monitor was placed inside the pyramid to record the transmitted light intensity during the sweeping of the dipole position. The distance range was -250 nm to 250 nm for the out-of-plane oriented dipole and -900 nm -900 nm for the in-plane oriented dipole.
In the simulation of the light profiles at the probe, a plane wave with an electric field component , in the = 1 / direction parallel to the axis of the fiber. This was chosen due to the dominant nature of the linearly polarized transverse mode in the single-mode fiber. The light intensity profile was recorded by a monitor placed 12 nm away from the probe.

Section S3: Purcell enhancement of Dark exciton
This section provides additional information on our near-field configuration and the visualization of the dark state via the Purcell effect. Figure S3 (a) shows that the power dependence of the deconvoluted X B and X D emission can be fitted with linear curves, excluding the possible contribution of the bi-excitonic emission. Figure S3 (b) shows probe-sample distance dependence of emission peak intensity using the bare (uncoated) pyramid tip. A smooth increase was observed when the probe-sample distance was less than around 270 nm before landing, and no sharp increase and quench were observed. In Figure S3 (c), we confirm the gap-size dependent enhancement of the X D emission by showing its dependence on the thickness of the spacer layer. We found that only when the deposition cycle of Al 2 O 3 is less than 30 cycles (~3 nm), the X D is visible in the spectra, and the X D /X B intensity ratio increase as the thickness decreases. Together with the retraction curve in the main text, these gap distance dependent X D emission results provide further support that the Purcell enhancement of X D in our near-field configuration. In Figure S3 (d), we explain how we define the probesample distance, which we estimated to be around 12 nm. This estimate was obtained by comparing the position of the probe at the set point (around 95% of the free magnitude) to the position when the PL emission of the bright exciton starts to quench. This change in position signifies that the probe had entered the quantum tunneling regime, which has been reported to have a distance range of less than 2 nm. 2 Therefore, our estimated value of 12 nm for probe-sample distance was obtained from this comparison. While the precise determination of probe-sample distance using shear-force microscopy can be challenging, this estimate is a relatively accurate representation of our experimental conditions.

Section S4: Hyperspectral Image Reconstruction
The spectral fitting was conducted pixel-by-pixel within an acquired dataset using the Python lmfit package 3 . The fitting employed two Lorentzian peaks, with the X B peak fixed at 750 nm and a width of 20 nm, as determined from the normalized spectrum obtained by the uncoated pyramid tip (Figure 1d). The intensity of both X D and X B were left to be fitted, with the only further numerical constraints being the wavelength and width range of X D , which were set to 770 -778 nm and 20 -50 nm, respectively. This fitting method allowed for consistent modeling of all hyperspectral datasets, which typically consisted of several thousand individual spectra. The deconvolved peaks were then summed over a given intensity range and input into a dimensionally matching matrix for visualization and further analysis.   Figure S7.1 displays the data obtained from a rapid scan conducted prior to Figure 4 in the manuscript, which revealed similar emission intensity values in both nanobubbles. It is worth noting that the intensity difference presented in Figure  4 may have been caused by system drift during the long raster scan, which started from the bottom left. Figure S7.2 shows the repeated near-field measurements in Area 4 using a different gold-coated probe, where the dark states enhanced by the strain are reproducible.

Section S9: Estimation of strain
The strain that induced enhanced dark excitonic emission ~0.08%, as estimated using the following equation: 4 = , where is the area, height (of ~20 nm), is the layer thickness (of ~1 nm), is the bubble width (of ~ 500 ℎ nm), and is 0.19, the Poisson's ratio of WSe 2 , 5 respectively. Section S10: Dark exciton mapping in nanobubble (~0.16% strain) We utilized the near-field technique to investigate a new sample configuration, consisting of a WSe 2 monolayer separated from a gold substrate by a spacer layer of ~5 nm thick hBN flake. With this sample, we imaged a smaller nanobubble compared to those in Figure 4. By analyzing the shear-force image in Figure S10 (a), we estimated the strain present in bubble 1 to be ~0.16%, using measured parameters such as the height of the bubble (~10 nm) and its width (~250 nm). Comparing the spectra obtained from bubble 1 and the adjacent flat region 2, we observed a shift in the emission of the bright states by approximately 15 meV. This shift aligns well with the estimated strain, as it has been reported that the bandgap of the 2D materials decreases at approximately 100 meV/% for uniform biaxial strain. 6 Furthermore, we observed a relatively large dark-bright band splitting of approximately 72 meV within bubble 1. This splitting can potentially be attributed to changes in the momentum dark excitonic emission, as suggested by a recent theoretical paper. 7 Alternatively, it may be influenced by the presence of charged dark states. 8 These possibilities warrant further investigation and provide avenues for future research.