Imaging strain-localized excitons in 
nanoscale bubbles of monolayer WSe2 at 
room temperature 
Authors: Thomas P. Darlington, Christian Carmesin, 
Matthias Florian, Emanuil Yanev, Obafunso Ajayi, Jenny 
Ardelean, Daniel A. Rhodes, Augusto Ghiotto, Andrey 
Krayev, Kenji Watanabe, Takashi Taniguchi, Jeffrey W. 
Kysar, Abhay N. Pasupathy, James C. Hone, Frank Jahnke, 
Nicholas J. Borys, P. James Schuck 
This is a post-peer-review, pre-copyedit version of an article published in Nature Nanotechnology. 
The final authenticated version is available online at: https://doi.org/10.1038/s41565-020-0730-5. 
The following terms of use apply: https://www.springer.com/gp/open-access/publication-policies/
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Darlington, Thomas P., Christian Carmesin, Matthias Florian, Emanuil Yanev, Obafunso Ajayi, 
Jenny Ardelean, Daniel A. Rhodes, et al. “Imaging Strain-Localized Excitons in Nanoscale Bubbles 
of Monolayer WSe2 at Room Temperature.” Nature Nanotechnology 15, no. 10 (July 13, 2020): 
854–860. doi:10.1038/s41565-020-0730-5.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
Imaging strain-localized exciton states in nanoscale bubbles in 
monolayer WSe2 at room temperature 
Thomas P. Darlington1, Christian Carmesin2, Matthias Florian2, Emanuil Yanev3, Obafunso 
Ajayi3, Jenny Ardelean3, Daniel A. Rhodes3, Augusto Ghiotto4, Andrey Krayev5, K. Watanabe6, 
T. Taniguchi6, Jeffrey W. Kysar3, Abhay N. Pasupathy4, James C. Hone3, Frank Jahnke2, 
Nicholas J. Borys7,∗, and P. James Schuck3,†  
1Department of Physics, UC Berkeley, Berkeley, CA, United States. 
2Institute for Theoretical Physics, University of Bremen, Bremen, Germany. 
3Department of Mechanical Engineering, Columbia University, New York, NY, United States. 
4Department of Physics, Columbia University, New York, NY, United States. 
5Horiba Scientific, Novato, CA, United States. 
6 National Institute for Materials Science, Tsukuba, 305-0047, Japan. 
7Department of Physics, Montana State University, Bozeman, MT, United States. 
Abstract:   
In monolayer transition metal dichalcogenides, quantum emitters are associated with localized 
strain that can be deterministically applied to create designer nano-arrays of single photon sources. 
Despite an overwhelming empirical correlation with local strain, the nanoscale interplay between 
strain, excitons, defects and local crystalline structure that gives rise to these quantum emitters is 
poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopy 
of excitons in nanobubbles of localized strain in monolayer WSe2 with atomistic structural models 
to elucidate how strain induces nanoscale confinement potentials that give rise to highly localized 
exciton states in 2D semiconductors. Nano-optical imaging of nanobubbles in low-defect 
monolayers reveal localized excitons on length scales of ~10 nm at multiple sites along the 
periphery of individual nanobubbles, which is in stark contrast to predictions of continuum models 
of strain. These results agree with theoretical confinement potentials that are atomistically derived 
from measured topographies of existing nanobubbles. Our results provide one-of-a-kind 
experimental and theoretical insight of how strain-induced confinement—without crystalline 
defects—can efficiently localize excitons on length scales commensurate with exciton size, 
providing key nanoscale structure-property information for quantum emitter phenomena in 
monolayer WSe2.  
 
The intense light-matter interactions of two-dimensional (2D) monolayer transition metal 
dichalcogenides (1L-TMDs) are mediated by a diverse suite of excitonic phenomena that present 
a wealth of opportunities for novel optoelectronic functionalities in areas spanning from high-
 
∗ nicholoas.borys@montana.edu 
† p.j.schuck@columbia.edu 
performance sensing and non-traditional photovoltaics to the quantum information sciences. Many 
of these opportunities emerge from—and heavily rely on—the unique ways in which the 2D TMD 
semiconductors enable the manipulation of excitonic phenomena on the nanoscale. Within this 
quiver of capabilities1-8, strain engineering is preeminent, offering unprecedented flexibility and 
precision, and opening new routes for highly tailored optoelectronic materials. Extrinsic strains of 
up to several percent can be endured without fracture9-11 and have been shown to continuously 
reduce the optical bandgap9,12  as well as modify the exciton-phonon coupling, thus narrowing the 
photoluminescence (PL) linewidth13. Further, such strain can be localized, embedding nanoscale 
potential energy wells for the funneling and localization of excitons14-16. Notably, in 1L-WSe2, it 
has become evident that local strain is a key ingredient for the formation of low-temperature 
quantum emitters11,17,18, and that strain-engineering can potentially extend their operating range to 
room-temperature19,20. The resulting highly integrable solid-state non-classical light sources21 
underscore the remarkable technological potential of harnessing nanoscale strain engineering of 
exciton localization in 2D TMD semiconductors. 
Despite the observations of exciton funneling and single-photon emission in localized 
strained regions of 2D TMDs, an understanding of the induced exciton localization is notably 
lacking, especially on the nanoscale. This absence of a fundamental picture has led to critical 
ambiguities, particularly for the formation of quantum emitters in 1L-WSe2 where the roles and 
interplay between strain, excitons, and crystallographic defects remain largely a mystery. For 
instance, it has been shown that the quantum emission can be co-localized with a nanobubble11 
where strain models derived from continuum elastic plate theory predict that a single region of 
maximum strain (and thus exciton localization) occurs at the apex of the nanobubble9,10. However, 
multiple emitters per nanobubble are typically observed, which is at odds with a single localization 
site and suggests a possible role of crystallographic defect states or some other sub-nanobubble 
inhomogeneity11,18,22-25. Recently, improved microscopic theoretical models predict that quantum-
dot-like electronic states in TMDs can form within nanobubbles in the absence of defects26,27. In 
particular, a first-principles approach that carefully considers the strain-induced atomic structure27 
(and which we employ here) predicts that strain maxima and multiple low-energy states form in a 
doughnut-like distribution near the nanobubble periphery. This surprising strain distribution is an 
apparent result of atomic scale wrinkling around the edges of highly-strained nanobubbles, leading 
to more localized lower energy states relative to the case of a nanobubble with a smooth 
topography. Such predicted states provide a critical missing puzzle piece for understanding and 
controlling strain-localization of excitons in 2D TMD semiconductors. However, due to their 
nanoscale size and distribution within a nanobubble, these localized energy states cannot be 
directly resolved with far-field optical characterization, necessitating interrogation by more 
sophisticated higher-resolution techniques. 
 In this work, we employ apertureless scanning near-field optical microscopy to image the 
localized exciton (LX) states within nanobubbles in 1L-WSe2. Using hyperspectral nano-
photoluminescence (nano-PL) mapping, we achieve a sub-20 nm spatial resolution and resolve 
individual localized low-energy states that are separated by distances less than 50 nm within single 
nanobubbles at room temperature. Furthermore, we observe that these localized states form in 
doughnut-like patterns that are consistent with the first-principles predictions27 that refine those of 
continuum plate and membrane models9,10. These LXs are also identified in nanobubbles of “flux-
grown” 1L-WSe2, which has a much lower defect density as compared to monolayers exfoliated 
from commercially available crystals (ca. 100× lower defect density)28. Our results are consistent 
and reproducible across multiple samples and numerous bubbles (N>50; see, for example, 
Supplementary Fig. 3).  The combination of nano-optical characterization with atomistic modeling 
and materials engineering indicates that (i) exciton localization by inhomogeneous strain occurs 
via the formation of wrinkles near the edges and bending near the base of nanobubbles; (ii) that 
these excitons remain localized at elevated (room) temperature; and (iii) the optical emission of 
LXs at room temperature can be enhanced by nano-optical/plasmonic techniques by at least 100×. 
Together, these findings provide key experimental evidence of highly-confined localized states in 
nanobubbles, which constitute a new paradigm of nanoscale strain engineering in 2D TMD 
semiconductors that is particularly relevant for developing non-classical light sources for practical 
quantum optical devices. 
Numerous processes that are critical for developing advanced functionality and novel 
devices with 1L-TMD semiconductors have been studied with nano-optical methods, revealing a 
rich suite of highly localized optoelectronic phenomena29-34. Figure 1a illustrates the experimental 
configuration of our nano-PL investigations of individual nanobubbles of 1L-WSe2 where a sharp 
silver tip (Horiba Scientific) has been positioned within 2 nm of the 1L-WSe2 (Fig. 1a). The tip-
sample junction was illuminated from the side with p-polarized, continuous wave laser excitation 
(637.27 nm; 75-100 µW) at an oblique angle of incidence such that the induced polarization of the 
tip can couple to the in-plane and out-of-plane transition dipoles35. As the sample is raster scanned, 
nano-PL from the tip-sample junction and local topography of the 1L-WSe2 are simultaneously 
recorded.  
As indicated in the atomic force microscopy (AFM) micrograph (Fig. 1b), the entirety of 
the 1L-WSe2 in Figs 1-3 is supported by an underlying crystal of hexagonal boron nitride (hBN; 
~200 nm thick) forming a 2D 1L-WSe2/hBN heterostructure. We note that a portion of this 1L-
WSe2 flake is fully encapsulated and covered by a second, thin hBN crystal (~3 nm). However, all 
of the results presented here were acquired from the exposed 1L-WSe2 that is directly accessible 
to the nano-optical antenna (as illustrated in Fig. 1a). The details of the “dry-stamping” sample 
fabrication are provided in earlier work11 and Supplementary Information. This process is known 
to produce structural “imperfections” such as nanobubbles, tears, folds and wrinkles. In our case, 
a portion of the 1L-WSe2 is folded on top of itself to form a bilayer and several pronounced creases 
(Fig. 1b). In addition, small topographical nanobubbles, with characteristic heights of ~2-10 nm, 
are observed in the 1L-WSe2 and are attributed to trapped substances between the layers10. Such 
nanobubbles have been repeatedly observed in heterostructures of layered materials11,15,36, and as 
noted above are known to be correlated with quantum emitters in 1L-WSe2 at cryogenic 
temperatures11. 
Figure 1c contrasts nano-PL spectra collected from a flat region and a nanobubble of the 
1L-WSe2 acquired at room temperature. On the flat region, the spectrum is composed of the 
standard excitonic PL of 1L-WSe2 at ~1.65 eV,29,37 which we will refer to as the primary exciton 
(PX). When the nano-optical antenna is positioned over a nanobubble, the emission spectrum 
shows a dramatic change, exhibiting red-shifted excitonic emission and an additional intense low-
energy emission band that is centered at ~1.56 eV, as determined by Gaussian peak fitting 
(Supplementary Fig. 2 and Supplementary Methods). In the 1L-WSe2, every region that was found 
to exhibit strong low-energy emission was correlated with a nanobubble. A selection of such 
emission spectra from four individual nanobubbles and their associated topographies is shown in 
Supplementary Figure 1. The lateral extents of the nanobubbles range from ~30–140 nm with 
heights from 1.5-20 nm, and depending on size, exhibit a diverse set of broad emission spectra, 
some of which show signatures of multiple low-energy states. In general, low-energy emission 
occurs at emission energies that span a range of about 70 meV, from ~80 meV to ~150 meV below 
the PX, and exhibits linewidths of ~150 meV that are attributed to thermal broadening20 and 
plasmonic coupling to the tip38.   
Close inspection of the nano-PL spectra in Fig. 1c reveals several characteristics of the 
low-energy PL that are different from the well-studied PX state. First, we concurrently observe 
both the low-energy emission and strong emission at ~1.65 eV, corresponding to the PX spectra 
measured in the far-field (inset Fig. 1c), within our nano-optical mode volume. Second, the low-
energy band here is well below the energies of other native excitonic complexes in this material 
(e.g. trions, the dark exciton39,40, and biexcitons41) and in an energetic region often associated with 
defect states41. Third, the linewidth is substantially larger than that of the PX, which contrasts with 
what has been observed for strain-tuned PX states13. And finally, the energy separation of this band 
with respect to the PX state (see also Supplementary Fig. 2) and its localization to nanobubble 
regions are in-line with corresponding observations for single emitter states at cryogenic 
temperatures in 1L-WSe211,18,23-25,42,43. Based on these considerations, we deduce that this low-
energy band, which is amplified significantly by the nano-optical antenna (consistent with the 
observation in ref. [20] of plasmon-enhanced localized emission at elevated temperatures), 
originates from LX states in the nanobubbles.  
The nano-PL directly probes the LX emission on length scales that are commensurate with 
– and even smaller than – the nanobubbles themselves, allowing us to explore the origins of the 
diverse emission spectra and nanoscale structure-property relationships in more detail. Here, we 
estimate that our spatial resolution is ~15 nm. In Figure 2, the spatial distribution of LX emission 
is shown for a larger nanobubble (approximate radius of 75 nm; peak height of 12 nm; aspect ratio 
of 0.16). With nano-PL, we resolve nanoscale variations of the LX emission within the nanobubble 
itself, finding that the integrated emission intensity is not uniform (integrated over the LX spectral 
region of 1.5-1.6 eV; Fig. 2a): it is concentrated to specific locations of the nanobubble that do not 
clearly correspond to its apex (cf. inset of Fig. 2a). Furthermore, different points of the nanobubble 
separated by distances as small as 30 nm exhibit clearly distinct spectra (Fig. 2b). The dashed 
curve is drawn as guide to the eye between the maxima of LX spectral peaks, clearly showing that 
the redder LX states are positioned to the edges of the nanobubble, where the maximum 
confinement potential and possible wrinkle formation are expected to occur. Clearly, larger 
nanobubbles host multiple emissive localization centers for LXs, an effect that to date has only 
been inferred spectroscopically11,42. 
Our hyperspectral mapping of the nanobubble in Fig 2 shows that the lowest-energy states 
(and thus deepest confinement potentials) are concentrated around the edge. To gain more insight 
into the physical mechanism, we applied the theory of ref. [27], which considers the influence of 
local strain within the nanobubbles on electronic and optical properties. Our method is based on 
atomistic calculations, in which the relevant part of the nanostructure is modeled using a lattice of 
atomic sites. For the present calculations, we use the nanobubble geometry obtained from AFM 
measurements and determine the corresponding relaxed positions of the individual atoms in a 
valence force field simulation. The result provides the strain field in the structure and confirms the 
existence of atomic-scale wrinkling. In a second step, the information about the displaced atomic 
positions is used within a tight-binding calculation in order to quantify how the strain field of the 
individual atoms within the nanobubble translates into a confinement potential and local electronic 
states.  
For the nanobubble topography given by the AFM data of Fig. 2a (inset), the calculated 
confinement potential (Fig. 3a) exhibits a doughnut pattern, with deeper potentials located on the 
nanobubble periphery that traces the wrinkling effect (Fig. 3b) and corresponds remarkably well 
to the nanoscale spatial distribution of measured LX energies (Fig. 3c; see Supplementary 
Information for fitting details). This correspondence is further in direct accordance with the 
experimental spectra in Figure 2b, which shows that the low-energy emission is isolated to the 
nanobubble periphery. To demonstrate the correlation between the theoretical predictions and 
experimental data, Fig. 3d shows the measured LX energy plotted against the predicted 
confinement potential at the corresponding region of the nanobubble (see Supplementary 
Information for analysis details). Around the periphery of the nanobubble, a strong correlation 
between the LX energy and the depth of the confinement potential is observed: regions of stronger 
confinement correspond to lower LX energies. In contrast, in the center region, very little 
correlation of energy with confinement potential is observed, which suggests a lack of strongly 
confined excitons in that area (masks for each of these regions is shown in Supplementary Fig. 
4). This different behavior may indicate a more-general exciton funneling effect in the central 
region14, whereas the periphery is dominated by highly confined states. 
The correspondence between the theoretical analysis of the strain and resulting electronic 
states within the nanobubble and our nano-optical dataset presented in Fig. 3 strongly suggests that 
the experimentally localized states observed are the predicted quantum-dot-like states27. In 
principle, point defects in the 1L-WSe2 lattice can also localize excitons in a similarly 
inhomogeneous way. To better elucidate the potential role of defects, we repeated our nanobubble 
PL mapping and theoretical calculations in high-quality flux-grown 1L-WSe2, which has been 
shown to have defect densities approximately two orders of magnitude lower than commercially 
grown crystals–providing for the first time an average spacing between defects on the order of 
nano-optical resolution28. As shown in detail in the Supplementary Information, every nanobubble 
identified in this higher-quality material exhibits similar LX emission to that of the commercial 
material (see Supplementary Fig. 3 and corresponding discussion). More specifically, the 
occurrence of the LX emission band in the nanobubbles does not depend on the defect density in 
the ranges probed here. 
In Figure 4, we provide a collage of four nanobubbles in the monolayer area of the high-
quality (i.e., flux-grown) 1L-WSe2. Row I of Figure 4 contains the measured AFM topography for 
the four nanobubbles with their corresponding spatial distributions of LX emission energies using 
785 nm excitation shown in Row II. Exciting with 785 nm light, which is below the energy of the 
PX, enhances the contrast between the LX and PX states, allowing the LX states to be observed 
with a greater signal-to-noise ratio (see Supplementary Information). Rows III, IV, and V 
summarize the theoretical results of the confinement potentials, overlap of the electron-hole 
wavefunctions, and the predicted shifts in PL emission energies, respectively. As with the 
nanobubble shown in Fig. 3b, each nanobubble in the flux-grown 1L-WSe2 exhibits lower energy 
emission concentrated at the nanobubble periphery. This peripheral spatial distribution of low-
energy states is replicated in the predicted confinement potentials and electron-hole wavefunction 
overlap shown Rows III and IV of Fig. 4, respectively. Finally, the predicted PL energy shifts and 
corresponding spatial distributions shown in Row V agree well with the measured LX emission 
energy (Row II). Considering the challenges of room-temperature hyperspectral imaging at the 10-
20 nm length scale, limitations of the topographical maps in Row I to a resolution of ~15 nm, as 
well as the complexities to directly incorporate these measurements into a feasible atomistic model 
(for details, see Supplementary Information), the agreement between experiment and theory is 
particularly remarkable.  
The similarities between Figures 3 and 4—despite dramatically different defect densities— 
suggest that LX emission distribution in nanobubbles is not significantly determined by atomic 
defects in the lattice. As noted above, since there is approximately one defect every 15 nm × 15 nm 
on average in flux-grown material – near the spatial resolution of the nano-optical probe – then 
major defect-associated optical changes would be resolvable. While defects may still play a role 
in the emission, the implication here is that the primary effect in terms of the nanoscale spatial 
distribution and creation of quantum-dot-like states is the local strain profile, with localized 
maximum strain occurring at locations around the edge of nanobubbles leading to LX emission 
observable at room temperature with a nano-optical probe. Still, it is certainly possible that defects 
play a role in e.g. further localization or the exact distribution of wrinkles at the atomic scale. Such 
angstrom-level effects are beyond the resolution of our current nano-optical probes, which utilize 
AFM tips with radii of curvature ranging from ~15 to ~40 nm. Future correlations with e.g. atomic-
resolution AFM44 should be able to map these effects. 
In conclusion, using nano-optical techniques, strain localized exciton states within single 
nanobubbles of 1L-WSe2 are observed at room temperature with localization lengths scales of less 
than 50 nm and significantly smaller than the nanobubble itself. In general, the spatial distribution 
of these low-energy states forms a doughnut-like pattern around the periphery of the nanobubble 
that surrounds a region of higher-energy states at its center, which is consistent with previous 
theoretical predictions of atomic-scale strain effects. By integrating the experimentally determined 
topography with this atomistic model, the experimental results are qualitatively replicated by the 
theoretical model, establishing the first robust experiment-theory connection of the formation of 
strain-induced quantum-dot states in monolayer TMD semiconductors. Furthermore, we reproduce 
these findings in 1L-WSe2 with orders-of-magnitude lower defect densities, implying the 
nanoscale localization is primarily influenced by strain and not crystalline defects. Our results 
show that LX states accessed with nano-optical techniques remain localized at room temperature, 
leading to compelling potential applications in practical strain-engineered optoelectronic and 
quantum-optical architectures. 
 
Acknowledgements: NJB and PJS gratefully acknowledge support from the National Science 
Foundation under award NSF-1838403. PJS thanks Prof. S. Strauf for stimulating and enlightening 
discussions. JWK gratefully acknowledges support from the National Science Foundation under 
awards NSF-1437450 and NSF-1363093.  Preparation and characterization of nanobubbles in the 
flux-grown low-defect-density WSe2 is partially supported as part of Programmable Quantum 
Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), 
Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. CC, MF, and FJ 
gratefully acknowledge computational resources from HLRN Berlin and funding from the German 
Science Foundation (DFG) via the graduate school "Quantum-Mechanical Material Modeling". 
KW and TT acknowledge support from the Elemental Strategy Initiative 
conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.  
 
Figure 1 – nano-optical detection of room-temperature photoluminescence from localized\ exciton 
(LX) states localized to nanobubbles in 1L-WSe2. (a) Schematic of the room-temperature nano-
PL imaging and spectroscopy of 1L-WSe2 on top of a hBN. Inset: simple level diagram illustrating 
the energetic ordering between the primary exciton (PX), LX and ground (G) states of 1L-WSe2. 
(b) AFM topography of the 1L-WSe2 flake exfoliated on top of the hBN substrate. The white 
arrows mark several nanobubbles in the 1L-WSe2. (c) Comparison of nano-PL emission spectra 
collected from the 1L-WSe2 on and off a nanobubble with a resolution of 20 nm. Inset: typical far 
field spectrum of the 1L-WSe2. (d) Spatial map of the LX emission (integrated from 1.5-1.6 eV) 
showing that the LX emission in the 1L-WSe2 is localized to spatially discrete regions that 
correspond to nanobubbles in the topography. Inset: similar map of the PX state showing 
diminished intensity in the bilayer region. All scale bars are 500 nm. 
  
Figure 2 - high-resolution nano-PL imaging and spectroscopy of distinct LX localization centers 
within a single nanobubble. (a) Nano-PL image of the spatial distribution of LX emission 
(integrated intensity from 1.5-1.6 eV) of a single nanobubble. The three grey pixels are a scan 
artifact where nano-optical signal was not acquired. Scale bar: 100 nm. Inset is the topography of 
the nanobubble (scale bar: 100 nm). Its overall height is 12 nm and its average radius is 74 nm. (b) 
Sample emission spectra from the corresponding points labeled in panel (a). The distance between 
the red and blue marks is 45 nm. 
  
 
Figure 3 – (a) Calculated carrier confinement potential for the nanobubble topography shown in 
Fig. 2a inset. The solid lines represent topographic contours based on the AFM measurement. (b) 
Corresponding values of the surface normal deviation, defined as the average angle α between 
normal vectors at neighboring unit cells, obtained from relaxed atomic positions, showing 
wrinkling of the unit cell. (c) Map of experimentally measured LX emission energy from the 
hyperspectral nano-PL shown in Fig 2. (d) Correlation between the local confinement potentials 
in (a) and LX emission energy shown in (c).  The datapoints are separated into points from the 
center of the nanobubble (red triangles) and points from the periphery of the nanobubble (blue 
diamonds). The scale bar of the experiment in (c) is 50 nm, while theory calculations with atomic 
resolution are scaled up by 5x (see Supplementary Information). 
 
 
 
 
 
 
 
Figure 4 – Comparison of experiment and theory for 4 nanobubbles in low-defect monolayer 
WSe2. Rows I and II show the measured AFM topography and nano-PL emission energy, 
respectively. The inset of row II shows the integrated PL intensity after a low pass energy filter to 
isolate the LX emission. Row III provides theoretical results of the confinement potential obtained 
from displaced atomic positions using nanobubble strain calculations and the Harrison rule47. 
Rows IV and V contain electron and hole wavefunction overlap, and predicted PL energy shift, 
respectively.  The solid lines in rows III-V represent topographic contours using the nanobubble 
topographies shown in Row 1. Scale bars are 50 nm in Row I and II. Theory calculations with 
atomic resolution are scaled up by 5x (see Supplementary Information).  
 
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