# Tip-induced excitonic luminescence nanoscopy of an atomically-resolved van
der Waals heterostructure

Luis E. Parra López  Université de Strasbourg, CNRS, Institut de Physique et
Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France  Anna
Rosławska  Université de Strasbourg, CNRS, Institut de Physique et Chimie des
Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France  Fabrice
Scheurer  Université de Strasbourg, CNRS, Institut de Physique et Chimie des
Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France  Stéphane
Berciaud<EMAIL_ADDRESS>Université de Strasbourg, CNRS,
Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000
Strasbourg, France  Guillaume Schull<EMAIL_ADDRESS>Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux
de Strasbourg, UMR 7504, F-67000 Strasbourg, France

###### Abstract

Low-temperature scanning tunneling microscopy is used to probe, with atomic-
scale spatial resolution, the intrinsic luminescence of a van der Waals
heterostructure, made of a transition metal dichalcogenide monolayer stacked
onto a few-layer graphene flake supported by an Au(111) substrate. Sharp
emission lines arising from neutral, charged and localised excitons are
reported. Their intensities and emission energies vary as a function of the
nanoscale environment of the van der Waals heterostructure, explaining the
variability of the emission properties observed with diffraction-limited
approaches. Our work paves the way towards understanding and control of
optoelectronic phenomena in moiré superlattices with atomic-scale resolution.

## Introduction

Van der Waals (vdW) heterostructures made from stacks of two-dimensional (2D)
materials, in particular semiconducting transition metal dichalcogenides
(TMDs), are ideal systems for studying fundamental phenomena related to the
confinement of tightly bound excitons Wang  _et al._ (2018) and their
exploitation in atomically thin optoelectronic devices Mak and Shan (2016);
Wilson  _et al._ (2021). The rich physics of excitons, trions (i.e., charged
excitons) and more complex many-body states in TMDs and related vdW
heterostructures has been addressed through optical spectroscopy Wang  _et
al._ (2018); Shree  _et al._ (2021), in particular by recording their micro-
photoluminescence ($\mu$PL) characteristics, with a diffraction-limited
spatial resolution of typically $\lesssim 1~{}\rm{\mu m}$. These far-field
optical studies have highlighted significant spatial variations in the optical
response of a given sample, due to inhomogeneities of the nanoscale
environment, including strain gradients Harats  _et al._ (2020), dielectric
disorder Raja  _et al._ (2019), as well as to localised defects Tongay  _et
al._ (2013a); Chow  _et al._ (2015) and dopants Tongay  _et al._ (2013b).
Taking advantage of these subtle structure/property relationships, periodic
nanoscale moiré super-potentials resulting from the controlled rotational
mismatch between stacked 2D layers have recently been used to tailor exciton
physics, with potential outcomes for quantum simulation and quantum
technologies Tang  _et al._ (2020); Li  _et al._ (2021); Wilson  _et al._
(2021); Kennes  _et al._ (2021). Understanding of such emergent phenomena
requires addressing excitons and their local-environment with a spatial
resolution below the moiré wavelength ($\lesssim 10~{}\rm{nm}$) and the
exciton Bohr radius ($\sim 1~{}\rm{nm}$)Yu  _et al._ (2017); Huang  _et al._
(2022), i.e., two to three orders of magnitude below the optical diffraction
limit.
Recently, attempts have been made to address excitons in TMDs with nanoscale
resolution Park  _et al._ (2018); Darlington  _et al._ (2020); Bonnet  _et
al._ (2021); Pommier  _et al._ (2019); Péchou  _et al._ (2020); Peña Román
_et al._ (2020); Zhang  _et al._ (2022). In particular, tip-enhanced PL
studies have provided original ways to control the emission characteristics of
TMD monolayers Park  _et al._ (2018) as well as to image nanoscale strain
gradients Darlington  _et al._ (2020) in ambient conditions with a resolution
of $\approx$ 15 nm. In parallel, atomically-resolved luminescence has been
reported on single molecules using scanning tunneling microscopy-induced
luminescence (STML)Qiu  _et al._ (2003); Wu  _et al._ (2008); Zhang  _et al._
(2016); Doppagne  _et al._ (2017); Zhang  _et al._ (2017a); Doppagne  _et al._
(2018); Kimura  _et al._ (2019), a method that was recently applied to
investigate excitonic emission from TMDs in ambient air Pommier  _et al._
(2019); Péchou  _et al._ (2020); Peña Román  _et al._ (2020). Under these
conditions, atomic-scale resolution could not be attained, probably because of
atmospheric contamination and lack of mechanical and thermal stability.
Attempts to address the excitonic properties of TMDs with STM in ultra-high
vacuum (UHV) at cryogenic temperatures have been reported Krane  _et al._
(2016); Schuler  _et al._ (2020), but the luminescence signals were dominated
by inelastic transitions between electrodes and TMD states, whereas radiative
recombination of excitons and trions was likely quenched by the strong
interaction with the supporting metallic substrate Velický  _et al._ (2018).
Approaches allowing investigating excitonic emission from vdW heterostructures
at the atomic scale are highly desirable, but still lacking.
In this article, we take up this challenge and demonstrate intrinsic excitonic
luminescence from a two-dimensional semiconductor with the nanoscale-
resolution provided by low-temperature STML. We show that a vdW
heterostructrure based on a TMD monolayer, decoupled from an Au(111) crystal
by a few-layer graphene flake (FLG) allows preserving its luminescence while
ensuring optimal STM imaging of surface atoms and moiré superlattices. Our
results provide insights into the mechanisms leading to STM-induced
luminescence in vdW heterostructures and further establish STM-based methods
as a unique tool to correlate the optical response of low-dimensional systems
to their nano- and atomic-scale environment.

## Results and discussion

Our measurements were performed on a vdW heterostructure made of a molybdenum
diselenide (MoSe2 ) monolayer stacked on top of a few layer ($\sim 3-5$)
graphene flake (FLG) deposited onto an Au(111) substrate (see Methods and
Supplementary Section S1 for more details). Figure 1a, b and c show a
schematic representation of the STM-induced luminescence (STML) experiment, as
well as an optical image of the MoSe2/FLG/Au(111) heterostructure and an
atomically-resolved constant current STM image, respectively. As further
discussed below, a STM silver (Ag) tip is used to locally generate excitonic
electroluminescence from the MoSe2 monolayer. Here, akin to hexagonal boron
nitride (hBN) Dean  _et al._ (2010); Cadiz  _et al._ (2017), the FLG provides
a smooth substrate for the TMD, while ensuring efficient electrical
conduction. This configuration also makes use of the plasmonic properties of
the Ag-tip Au-substrate junction (Fig. 1a), which is known to enhance
radiative recombination in STML experiments Rosławska  _et al._ (2022),
leading to an optimal configuration to detect excitonic luminescence.

We first report on low temperature $\mu$PL measurements recorded ex situ using
a laser beam of $\approx 1~{}\mu\rm m$ in diameter at various close-lying
spots on the sample, indicated in Fig. 1b. The strikingly different $\mu$PL
spectra shown in Fig. 1d suggest sizeable inhomogeneities at the sub-
micrometre scale. These inhomogeneities are likely due to the necessary
thermal annealing step performed before introducing the sample into the STM
chamber (see Methods) and are further resolved using STML, as discussed in
Fig. 2 and 3.

Figure 1: STM-induced luminescence of a MoSe2/FLG/Au(111) heterostructure. a.
Artistic view of the STML experiment. The red curved arrow represents a photon
emitted following the radiative recombination of excitons. b. Optical
microscopy image of the sample. The monolayer of MoSe2 is highlighted in red
and the FLG in black, while the underlying Au(111) covers the rest of the
image. c. Atomically-resolved constant-current STM image ($V=-1.3~{}$V and
$I=10~{}$pA) of the heterostructure surface. d. Series of normalised $\mu$PL
spectra acquired on the different points of the heterostructure shown in b.
The spectra were acquired on a home-built $\mu$PL setup at 14 K under
continuous wave laser-excitation centered at 532 nm and under an incident
laser intensity of $\sim 30~{}\mu$W/$\mu\rm{m}^{2}$. e. STML spectrum recorded
on MoSe2/FLG/Au(111) in the cross-marked area on c, with $V=-2.8~{}$V,
$I=90~{}\rm{pA}$. The labels $\rm X^{0}$, $\rm X^{-}$ and $\rm X^{\rm L}$ in d
and e denote the neutral, negatively charged and localised excitons,
respectively. The FWHM of the $\rm X^{0}$ line (denoted $\gamma_{\rm{X}^{0}}$)
is shown in the upper left corner of e.

Three types of low temperature $\mu$PL spectra are identified on the
MoSe2/FLG/Au(111) region shown in Fig. 1b (see Supplementary Section 2 for a
detailed analysis). First, we observe spectra dominated by a high-energy
emission line near 1.65 eV, followed by a lower intensity feature, situated
about 30 meV below the main line (top trace in Fig. 1d). Based on well-
established literature Ross  _et al._ (2013); Wang  _et al._ (2015), the main
and lower energy lines are safely assigned to the bright neutral exciton ($\rm
X^{0}$) and to the negative trion ($\rm X^{-}$), respectively. The negatively
charged nature of the trion will be discussed in details below. Next, we also
observe spectra that only display emission from the $\rm X^{0}$ line (middle
trace in Fig. 1d), as well as considerably more complex spectra, showing a
variety of sharper, spatially dependent and spectrally diffusing features
assigned to localised excitons Branny  _et al._ (2016) (bottom trace in Fig.
1d). These distinct behaviours are directly related to the quality of the
MoSe2/FLG and FLG/Au interfaces. In the event of a tight coupling between flat
MoS2 and FLG, we expect an efficient “filtering effect” to take place Lorchat
_et al._ (2020), which yields single line spectra akin to the middle trace in
Fig. 1d. This effect stems from complete neutralisation of the MoSe2 layer by
FLG, together with efficient PL quenching of long-lived localised excitons
through non-radiative energy transfer to the FLG, a decay pathway that affects
the short-lived $\rm X^{0}$ emission to a much lesser extent Lorchat  _et al._
(2020). Hence, the observation of $\rm X^{0}$ and $\rm X^{-}$ emission (top
trace in Fig. 1d) suggests partial decoupling between the top MoSe2 layer and
the FLG/Au(111) underneath. Dominant emission from localised states (bottom
trace in Fig. 1d) may stem from the local conformation of the MoSe2 layer to
the underlying substrate made rougher by thermal annealing. These observations
are consistent with complementary $\mu$PL measurements on MoSe2 monolayers
directly deposited onto a thermally evaporated polycristalline Au film Lorchat
_et al._ (2020).

Figure 2:  Spatially-resolved STML in an inhomogeneous nanoscale landscape. a.
Constant-current STM image ($V=-2.2~{}$V, $I=4~{}$pA) of the MoSe2/FLG
surface. During the fabrication process the heterostructure conforms to the
substrate underneath, resulting in nanoscale folds, ripples and bubbles (white
arrows).b. Constant-current STM image ($V=-2.1~{}$V, $I=4~{}$pA) of a nano-
bubble on the heterostructure surface. c. Normalised STML spectra acquired at
$V=-3.2~{}$V on the marked areas of image b with 4 pA (blue spectrum) and 10
pA (orange spectrum). d Constant-current STM image ($V=-1.85~{}$V, $I=5~{}$pA)
of an area displaying a rupture on the top layer of the heterostructure. Two
areas corresponding to the rupture (blue cross) and the flat area (orange
cross) are shown. e. Normalised STML spectra acquired under $V=-1.85~{}$V,
$I=5~{}$ pA on the marked areas of image b corresponding to rupture (blue
spectrum) or flat areas (orange spectrum). The spectra in c and e are
vertically offset for clarity.

In such an heterogeneous landscape, STM allows one to probe the topography of
a localised area with a resolution down to the atomic scale, making it
possible to select regions that are uniform over hundreds of nm2, or
individual defects, and eventually address their STML properties. In Fig. 1e,
we show a typical STML spectrum recorded with the STM tip localised on top of
an atomically-resolved area of the MoSe2/FLG/Au(111) heterostructure shown in
Fig. 1c. This spectrum is characterised by a prominent emission line located
at 1.659 $\pm$ 0.001 eV with a lower-intensity feature at 1.630 $\pm$ 0.001
eV. These two emission lines have full-width at half maximum (FWHM) of 11 meV
and 14 meV, respectively. Comparison with the $\mu$PL spectra discussed above
allows us to assign the high and low-energy emission lines to $\rm X^{0}$ and
$\rm X^{-}$, respectively. These spectra provide by far the sharpest excitonic
emission lines achieved in STML measurements on TMDs and are the first example
where intrinsic luminescence is obtained with the stability and cleanness
required for atomically-resolved imaging of the TMD atomic registry. We
conclude that the presence of the FLG interlayer preserves the low-temperature
luminescence yield of the supported MoSe2 that would otherwise be massively
quenched by non-radiative decay channels to the underlying Au(111) substrate
Krane  _et al._ (2016); Peña Román  _et al._ (2020); Velický  _et al._ (2018).

The $\rm X^{0}$ FWHM fitted from our STML spectra, even for the sharpest
example (2.9 meV, see Fig. 2e), still exceeds the homogeneous limit expected
in monolayer MoSe2-based vdW heterostructures ($\approx 330~{}\rm\mu$eV FWHM
for a typical $\rm X^{0}$ lifetime of 2 ps) Fang  _et al._ (2019). This extra
broadening may find its origin in the electronic coupling between TMD and FLG
as well as in the excitonic lifetime reduction due to the Purcell effect
taking place at the plasmonic tip-sample cavity Rosławska  _et al._ (2022).

We estimate an overall quantum yield of $\sim 10^{-7}$ photons/e- (assuming an
overall detection efficiency of $\sim$10$\%$) a value that is orders of
magnitude lower than the one reported for single molecules in STML experiments
Wu  _et al._ (2008). This rather small emission yield suggests that non-
radiative exciton decay plays a significant role here. This behaviour may be
assigned to the metallic character of graphene that has been shown to
efficiently quench hot excitons prior to their relaxation down to the light
cone Lorchat  _et al._ (2020); Robert  _et al._ (2016). Alternatively, the low
electroluminescence yield may reflect an intrinsically weak exciton formation
probability, a mechanism that is further discussed below.

Figure 3:  STML on atomically-resolved areas. a,b and c are atomically-
resolved constant-current STM images of three different areas of the MoSe2/FLG
surface ($V=-1.3~{}$ V, $I=10~{}$ pA for a; $V=-1.4~{}$V, $I=4.1~{}$pA for b;
$V=-1.4~{}$V, $I=6~{}$pA for c). Each region corresponds to different
interface qualities of the heterostructure. d. STML spectra recorded on the
different regions at locations marked by symbols ($V=-2.8~{}$V, $I=90~{}$pA;
for a; $V=-2.8~{}$V, $I=100~{}$pA for b; $V=-2.9~{}$V, $I=90~{}$pA for c).

STML can be used to identify and characterize inhomogeneities occurring at the
scale of atoms up to a few hundreds of nanometres, and how they affect
luminescence properties. To this end, we first recorded a STM image (Fig. 2a)
on a typical area of the heterostructure that approximately corresponds to the
area covered by a diffraction-limited laser spot. This image displays flat and
well-organised areas separated by ripples, folds and protrusions (arrows in
Fig. 2(a)) that stem from the conformation of the heterostructure to the
underlying Au(111) substrate. These protrusions, typically 1 nm-high – 10 nm-
wide, often referred to as nano-bubblesDarlington  _et al._ (2020), correspond
to areas where the TMD and the FLG are slightly decoupled, most likely because
of remaining organic adsorbates at the interfaces between MoSe2, FLG and
Au(111). These adsorbates segregate locally thanks to the so-called self-
cleaning mechanism inherent to 2D materials Castellanos-Gomez  _et al._
(2014). This mechanism that separates clean and flat regions from nano- or
microscale pockets of residues is favoured by the annealing step. A pseudo-3D
image of one of these protrusions located next to a flat area is provided in
Fig. 2b.

STML spectra acquired on top of the protrusion, and $\sim$ 5 nm away on the
nearby flat region are displayed in Fig. 2c. On the flat area, the spectrum
(in orange) is characterised by an $\rm X^{0}$ line at 1.590 $\pm$ 0.001 eV
and by the absence of trion emission, as we shall discuss below. On top of the
nano-bubble,the $\rm X^{0}$ emission (in blue) is much brighter (by a factor
of $\sim 6$) indicating a reduced quenching by the underlying FLG. Eventually,
this spectrum displays an additional peak below the $\rm X^{0}$ line. The
observed redshift (40 meV) is significantly larger than the $\rm X^{-}$
binding energy (Fig. 1e). This peak is therefore tentatively assigned to
excitons localised near defects ($\rm{X^{L}}$) Branny  _et al._ (2016).
Similarly, the STML spectrum is strongly altered in the vicinity of larger
heterogeneities such as ruptures and folds. An example is provided in the STM
image of Fig. 2d, where one observes a rupture in the heterostructure (blue
cross) next to a flat area (orange cross). Corresponding STML spectra are
shown in Fig. 2e. In the flat region, the STML spectrum is again characterised
by a single, narrow emission line (2.9 meV FWHM) assigned to $\rm X^{0}$. In
contrast, the rupture region displays a complex spectrum, where several narrow
resonances below the X0 emission appear, probably arising from localised
excitons Branny  _et al._ (2016). Interestingly, these lines show widths as
narrow as $\sim$ 700 $\mu$eV. Such sharp and red-shifted lines have been
reported in PL measurements of defective and highly strained TMDs, where they
were attributed to optically active quantum-dots that behave as single photon
sources He  _et al._ (2015); Chakraborty  _et al._ (2015); Koperski  _et al._
(2015); Srivastava  _et al._ (2015); Tonndorf  _et al._ (2015); Branny  _et
al._ (2016); Aharonovich  _et al._ (2016); Branny  _et al._ (2017); Palacios-
Berraquero  _et al._ (2017). Time-correlated photon counting measurements
Merino  _et al._ (2015); Zhang  _et al._ (2017b), which are beyond the scope
of the present study, would be necessary to ascertain the single-photon
emission from these centres. Overall, the data in Fig. 2 indicate that $\mu$PL
spectra spatially average emission features from nanoscale regions having
distinct spectral responses and emission yields, a complexity that we are able
to resolve using our STML approach.

As a next step, we evaluate how the atomic-scale landscape affects excitonic
emission from the MoSe2 monolayer. In Fig. 3a-c, we show atomically-resolved
STM images of three distinct flat regions of the heterostructure, separated by
several micrometres from one another. STML spectra (Fig. 3d) have been
acquired in each region for tip positions marked by colored symbols in Fig.
3a-c. In Fig. 3a the STM image reveals the atomic structure of the TMD as well
as bright and dark regions indicating smooth height modulation over several
nanometres. Here, the STML spectra do not appear to be affected by these
modulations, and are characterised by the typical $\rm X^{0}$ and $\rm X^{-}$
emission lines. In Fig. 3b and c, we distinguish a moiré pattern superimposed
on the atomic structure, suggesting a better quality of the MoSe2/FLG
interface than in Fig. 3a. This hypothesis is supported by the reduction of
the excitonic linewidth from 11 meV (Fig. 3a) to 9 meV (Fig. 3b) and 4 meV
(Fig. 3c), respectively. This linewidth narrowing can be assigned to reduced
dephasing due to a more homogeneous environment. This higher quality interface
may also lead to a more efficient static charge redistribution from the TMD to
the FLG flake Lorchat  _et al._ (2020); Hill  _et al._ (2017), explaining the
absence of trions in the STML spectrum acquired in Fig. 3b. Noteworthy, within
a given nanoscale area, the STML spectra do not depend on the position of the
tip with respect to the moiré pattern, as revealed in Fig. 3c.

Figure 4: Proposed microscopic mechanism for STML. a. Differential conductance
spectrum recorded on the MoSe2/FLG surface. The dI/dV spectrum is overlaid
with the integrated intensity associated to the STML-induced X0-emission at
different bias voltages (color code identical to the one in b). The close
agreement between the two suggests that the luminescence is driven by a charge
injection mechanism. b. Bias-dependent STML spectra of the sample recorded
under a constant current $I=30~{}$pA. The spectra are vertically offset for
clarity and the corresponding bias is shown next to each spectra. c. Energy
diagram displaying the luminescence mechanism. The system is originally in its
ground state (GS) and is driven by a tunneling event into one of two charged
resonances: a positively charged resonance denoted HR and a negative one
denoted ER. The orange (black) arrows represent an electron (hole) tunneling
event. Afterwards, following a second tunneling event, the system relaxes back
into GS. This relaxation process can happen either by direct neutralization of
HR (ER) or by forming an exciton (denoted ES) which can subsequently recombine
radiatively. Note that relaxation through exciton formation is only possible
for the HR resonance due to energy conservation.

However, in region (c) two emission lines, separated by only 20 meV appear.
The most prominent line is strongly redshifted by 70 meV with respect to the
$\rm X^{0}$ line in region (a). Here, an interpretation in terms of defect-
induced emission can be ruled out as no atomic defects are imaged in region
(c) and we tentatively assign this line to a screened $\rm X^{0}$. Note that a
small $\rm X^{0}$ redshift of typically 10 meV has already been reported in
TMD/monolayer graphene (1LG) and arises from the imperfect cancellation of two
effects: screening-induced reduction of the electronic bandgap and of the
exciton binding energy Lorchat  _et al._ (2020); Raja  _et al._ (2017). The
unusually large shift of 70 meV observed here could arise from the excellent
coupling between the MoSe2/FLG heterostructure and the Au(111) substrate,
illustrated by the clear observation of a moiré pattern. This tightly coupled
stack may favor charge transfer from Au(111) to the MoSe2 layer as well as
charge localization assisted by the moiré superpotential, hence enabling trion
formation. In keeping with this scenario, the faint line located only 20 meV
below $\rm X^{0}$ could arise from a strongly screened trion ($\rm X^{-}$)
with a binding energy reduced by about 10 meV and 5 meV, compared to a bare
MoSe2 monolayer Ross  _et al._ (2013) and to a MoSe2/1LG heterostructure
Lorchat  _et al._ (2020), respectively. In contrast, the absence of emission
from trions in region (b) is likely a consequence of the partial decoupling
between the coupled MoSe2/FLG heterostructure and the underlying Au(111)
substrate, a situation that prevents substrate mediated charge transfer to
MoSe2 and trion formation. The distinct signals reported for regions (a), (b)
and (c) that enable atomically-resolved STM imaging, therefore hint towards a
key role of the MoSe2/FLG and FLG/Au(111) interfaces.

Finally, we jointly address the dependence of the tunnel current and STML
spectra with the tip-sample bias $V$ at the same sample spot. The exciton
binding energy, $E_{\rm b}$ can in principle be estimated from the difference
between the local electronic gap inferred from scanning tunnelling
spectroscopy (STS) measurements and the optical gap determined from the $\rm
X^{0}$ energy. Figure 4a and b display a differential conductance (${\rm
d}I/{\rm d}V$) spectrum and set of STML spectra recorded with increasing bias
voltage, respectively. An electronic gap of $2.17\pm 0.04$ eV is deduced from
the ${\rm d}I/{\rm d}V$ spectrum (see Supplementary Section 3 for details),
with onsets of the valence and conductance bands at $-1.68\pm 0.03$ V and
$0.49\pm 0.01$ V respectively, indicating a weak $n$ doping. This doping
allows us to identify the trion introduced in Fig. 1c and discussed in Fig. 2
and 3 as negatively charged. The STML spectra in Fig. 4b reveal an $\rm X^{0}$
emission energy of 1.637 eV, leading to an energy difference of $533\pm 40$
meV that is close to the value estimated by Ugeda et al. on a similar system
using a combination of STS and $\mu$PL Ugeda  _et al._ (2014). This value is,
however, much larger than state-of-the-art optical measurements of $E_{\rm b}$
that converge towards values of 220 meV in hBN-capped monolayer MoSe2 Goryca
_et al._ (2019) and $\approx$ 150 meV in monolayer MoSe2/1LG heterostructures
Lorchat  _et al._ (2020). Our data therefore demonstrate that the
inconsistency between determinations of $E_{\rm b}$ based on the difference
between the STS gap and the optical gap versus all-optical measurements does
not stem from spatial inhomogenities, as both electronic and optical
measurements are local in our approach. We believe that this discrepancy
rather originates from the fact that STS measurements poorly resolve
electronic states with large in-plane momentum. This phenomenon ultimately
leads to an overestimation of the electronic bandgap in STS studies since
states near the $\boldsymbol{\Gamma}$ point contribute more to the STS
spectrum than those at the edges of the Brillouin zone ($\mathbf{K}$ and
$\mathbf{K^{\prime}}$ points), which define the direct electronic gap in TMD
monolayers and from which $\rm X^{0}$ wavefunctions are formed Zhang  _et al._
(2015).

The comparison between STS and STML spectra provides key information regarding
the STM-induced exciton formation mechanism. First, no STML signal could be
observed under positive $V$. Second, from Fig. 4b, one can deduce an $\rm
X^{0}$ emission onset at $V_{0}\approx-1.75~{}\rm V$. Reporting the integrated
intensity of the $\rm X^{0}$ line as a function of $V$ in the ${\rm d}I/{\rm
d}V$ spectrum (color-coded dots in Fig. 4a), one can see that the light
emission onset matches well with the onset of the TMD electronic resonance,
suggesting that hole injection from the tip is a preliminary step towards
excitonic luminescence from the TMD. In Fig. 4c, we propose a simple scheme to
explain the luminescence excitation mechanism. This scheme is inspired by a
many-body approach developed to interpret STML data of molecules Miwa  _et
al._ (2019). Originally in its ground state (GS), the system can be
approximated as a two-level system, where the low-energy level is occupied by
an electron and the high energy one is empty. GS is here used as the origin of
the energy scale on the left of the diagram. At a positive voltage
$V_{\rm{ER}}\approx$ 0.49 V, an electron can tunnel from the tip to the TMD
(orange arrow) which is driven into a negatively charged (electron) resonance,
denoted ER. This state is only transiently populated as the TMD can be
efficiently driven back to GS by tunneling of the extra electron to the
FLG/Au(111) substrate (black arrow). We can therefore associate the $V=0.49$ V
feature in the ${\rm d}I/{\rm d}V$ spectrum of Fig. 4a to the GS $\rightarrow$
ER transition. The same reasoning applies for a negative voltage of
$V_{\rm{HR}}\approx\,-1.68~{}\rm V$ that corresponds to a transient positively
charged (hole) resonance, denoted HR. Here, since $\mid E_{\rm{HR}}\mid>E_{\rm
X^{0}}$, neutralization by electron transfer from the substrate can lead to
the formation of an excited state (ES) in the MoSe2 monolayer that may rapidly
relax as an optically active exciton ($X^{0}$), whose radiative recombination
(ES $\rightarrow$ GS, red dotted line) is detected at 1.637 eV. Noteworthy,
the $\rm X^{0}$ STML line is accompanied by lower energy sideband, redshifted
by about 40-50 meV and that we assign to STML from $\rm{X^{L}}$. In contrast
to $\rm X^{0}$, the onset for $\rm{X^{L}}$ emission occurs at $V=-1.65~{}\rm
V$ (see Fig. 4b). As $\rm X^{0}$ cannot be generated at this voltage, we
deduce that $\rm{X^{L}}$ are not generated from neutral excitons $\rm X^{0}$
diffusing to defective areas of the sample, but instead formed directly at the
tunneling junction. Their direct excitation may therefore involve in-gap
localised electronic states of defects (not identified in the ${\rm d}I/{\rm
d}V$ spectrum) or direct energy transfer from inelastic electrons. Further
studies are needed to conclude on this point.

In conclusion, we have demonstrated STM-induced excitonic luminescence
nanoscopy of an atomically-resolved van der Waals heterostructure. Our work
directly reveals how the nanoscale environment influences the emission
characteristics, leading to sizeable excitonic energy shifts and the emergence
of emission features from charged and localised excitons on areas separated
only by a few nanometres. Hyperspectral mapping of the STML response of
atomically-resolved van der Waals heterostructures is still necessary to
establish whether STM-induced luminescence imaging reaches sub-nanometre
resolution in an extended 2D system, as it does in molecules Chen  _et al._
(2010); Zhang  _et al._ (2016); Doppagne  _et al._ (2017); Doležal  _et al._
(2021); Rosławska  _et al._ (2022), or whether exciton diffusion Kulig  _et
al._ (2018) in TMD monolayers needs to be taken into account.
Further STML investigations could enable important advances in quantum
materials science. First, STML offers exciting opportunities to unveil near-
field charge and energy transfer Froehlicher  _et al._ (2018); Bradac  _et
al._ (2021) and proximity effects Huang  _et al._ (2020); Zutic  _et al._
(2019) in vdW heterostructures with unprecedented accuracy, offering natural
outcomes in photonics, opto-electronics and nano-electronics. Second, STML is
an ideal tool to investigate correlated electronic phases Tang  _et al._
(2020); Li  _et al._ (2021); Wilson  _et al._ (2021) and excitons in twist-
engineered vdW heterostructures, starting with moiré-trapped interlayer
excitons Seyler  _et al._ (2019); Baek  _et al._ (2020) and trions Liu  _et
al._ (2021) in TMD heterobilayers. Last but not least, STML can be combined
with tip-enhanced photoluminescence spectroscopy Imada  _et al._ (2021) to
reach a holistic picture of exciton physics in van der Waals materials at the
atomic scale.

## Methods

Sample fabrication. The measurements were performed on a vdW heterostructure
made using a dry transfer method described in Ref. Castellanos-Gomez  _et al._
, 2014. In brief, large-area monolayer MoSe2 and FLG were mechanically
exfoliated from their bulk crystals on top of a thin film of
polydimethylsiloxane (PDMS). This polymer is used as a temporary substrate in
order to fabricate the vdW heterostructure. Its transparency allows for a
precise alignment of the layers during the fabrication process. The FLG was
then transferred onto a commercial Au(111) thin film grown on mica and the
MoSe2 monolayer was afterwards stacked on top of it. The sample was then
integrated onto a STM-compatible sample holder, allowing contacting the
substrate from two sides (see Supplementary Section 1). The sample was
annealed at $200^{\circ}$C for 24 h under ultra-high vacuum to reduce surface
contamination prior STM measurements.

$\boldsymbol{\mu}$PL characterization. The $\mu$PL response of our sample was
studied in vacuum ($\sim 10^{-5}$ mbar) at a temperature of 14 K in an optical
cryostat coupled to a home-built confocal microscopy setup as in Ref. Lorchat
_et al._ , 2020. A linearly polarised continuous-wave laser beam at a
wavelength of 532 nm (2.33 eV) with an intensity of 30
$\mu\rm{W}/\mu\rm{m}^{2}$ at the sample was used for all measurements. The
$\mu$PL signal was collected in a backscattering geometry and dispersed onto a
liquid-nitrogen cooled CCD array using a 500 mm monochromator equipped with a
150 grooves/mm grating.

STM and STML measurements. STM-based measurements were performed in a low
temperature (6 K) Unisoku STM operating in ultrahigh vacuum and adapted to
optical measurements. A first lens (numerical aperture of 0.55), mounted on a
three axis piezo controller, is used to collect and collimate the light
emitted at the tip-sample junction. This light is then redirected outside of
the vacuum chamber through successive windows and viewports. Afterwards, it is
refocused on an optical fiber, itself connected to a spectrometer, and
eventually detected using a nitrogen-cooled CCD camera. Three different
gratings were used, yielding spectral resolutions ranging from 0.6 nm down to
0.06 nm. Silver (Ag) STM tips were used to optimise the plasmonic response of
the junction and tested on a separate Ag(111) sample to maximise the radiative
recombination rate at the tip-sample junction. The STS spectrum shown in Fig.
4a was acquired at constant height with a current setpoint $I=30~{}$pA and a
modulation voltage $V_{mod}=20~{}$mV.

Data analysis All $\mu$PL and STML spectra presented in this work present both
raw (light gray) and the smoothed data (solid colored line). Unless specified
in the text, all spectra were fitted using Voigt profiles.

## Acknowledgments

We thank Michael Chong, Benjamin Doppagne, Guillaume Froehlicher, Arnaud
Gloppe, Eric Le Moal, Etienne Lorchat and Tomáš Neuman for fruitful
discussions. We are grateful to the IPCMS mechanical workshop, in particular
Halit Sumar, and Virginie Speisser, Michelangelo Romeo and the STnano clean
room staff for technical support. This project has received funding from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation program (grant agreement No 771850) and the European
Union’s Horizon 2020 research and innovation program under the Marie
Skłodowska-Curie grant agreement No 894434. We acknowledge financial support
from the Agence Nationale de la Recherche under grant ATOEMS ANR-20-CE24-0010.
This work of the Interdisciplinary Thematic Institute QMat, as part of the ITI
2021 2028 program of the University of Strasbourg, CNRS and Inserm, was
supported by IdEx Unistra (ANR 10 IDEX 0002), and by SFRI STRAT’US project
(ANR 20 SFRI 0012) and EUR QMAT ANR-17-EURE-0024 under the framework of the
French Investments for the Future Program. S.B. acknowledges support from the
Indo-French Centre for the Promotion of Advanced Research (CEFIPRA) and from
the Institut Universitaire de France (IUF).

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Supplementary Information for:
Tip-induced excitonic luminescence nanoscopy of an atomically-resolved van der
Waals heterostructure

##  S1 Sample architecture

The sample consists of a monolayer of MoSe2 stacked on top of a few ($\sim
3-5$) layer graphene flake (FLG). The layers were isolated by mechanical
exfoliation from bulk crystals and subsequent deposition onto
polydimethylsiloxane (PDMS) films. After optical identification of individual
layers, the stacking was performed in a homemade stamping station following
the dry transfer method described in Ref. Castellanos-Gomez  _et al._
(2014).To ensure compatibility with our STM setup, we used, as a substrate, a
commercial thin Au(111) film grown on mica. An optical image of the sample is
shown in Fig. S1a. Finally, the sample was integrated into a STM-compatible
sample holder, which allows us to contact the substrate from two sides. The
final configuration of the sample is shown in Fig. S1b.

Figure S1: Sample design. a. Optical microscopy image of a MoSe2/few-layer
graphene (FLG) heterostructure deposited onto an Au(111) film on mica. b.
Picture of the sample holder.

##  S2 Micro-photoluminescence ($\mu$PL) characterization at 14 K

Following the fabrication, the sample is rapidly introduced in a preparation
chamber and annealed for 24 h at 200 ${}^{\circ}\text{C}$ under ultra high
vacuum (UHV) conditions. Although this step is crucial to perform STM
measurements, it can significantly modify the optical properties of the
monolayer Lorchat  _et al._ (2020); Peña Román  _et al._ (2020). The rise in
temperature enhances contaminant diffusion at the different interfaces,
resulting in a spatially-dependent coupling between the component layers and
between the heterostructure and the substrate itself. These variations would
then modify nanoscale landscape and ultimately determine the optical
properties of the heterostructure. At room temperature, it has been observed
that the annealing of mechanically exfoliated TMD on Au(111) can lead to a
drastic quenching of the PL and STML signals Peña Román  _et al._ (2020). At
cryogenic temperatures, a wide variety of spectra have been reported in TMD/Au
heterostructures. From ”typical” spectra akin to the ones observed on
monolayer TMD deposited onto non-metallic substrates, to spectra composed of
multiple resonances and dominated by dielectric screening and quenching
Grzeszczyk  _et al._ (2020); Lorchat  _et al._ (2020). In the case of
extremely clean TMD/metal interfaces, such as the ones obtained using
epitaxial growth, a complete quenching of the luminescence has been reported
Krane  _et al._ (2016); Schuler  _et al._ (2020). This points towards the
interface quality as the main driver of the optical properties of the
heterostructure.

Figure S2: Low temperature $\boldsymbol{\mu}$PL mapping. Hyperspectral $\mu$PL
maps of the MoSe2/FLG/Au(111) sample studied in the main manuscript showing a
the total integrated intensity (denoted $\rm{I}_{\rm{tot}}$) and b the ratio
between the integrated intensity from the exciton emission
($\rm{I}_{\rm{X}^{0}}$) and the total integrated $\mu$PL intensity.
Correlations between $\rm{I}_{\rm{X}^{0}}/\rm{I}_{\rm{tot}}$ and
$\rm{I}_{tot}$ for c MoSe2/FLG/Au(111) and d MoSe2/Au(111) e. Series of
$\mu$PL spectra acquired at the positions marked in a. The spectra are
representative of coupled MoSe2/FLG/Au(111) area e, decoupled
MoSe2/FLG/Au(111) f and MoSe2/Au(111) g. All spectra were acquired at 14 K
under continuous wave laser-excitation centered at 532 nm and under an
incident laser intensity of about $\sim 30~{}\mu$W/$\mu\rm{m}^{2}$.

In our case, the self-cleaning mechanism clusters contaminants together at the
MoSe2/FLG interface. This ensures the presence of locally contaminant-free
areas as can be seen in Fig. 2a in the main text. As a result, the nanoscopic
landscape of the sample is composed of different “patches” of homogeneous
areas displaying varying degrees of coupling, strain and screening. This
heterogeneity has a direct impact on the $\mu$PL spectra, which spatially
average excitonic recombination over a diffraction-limited area. Figure S2a
shows a hyperspectral map of the total integrated PL intensity
($\rm{I}_{\rm{tot}}$) of the MoSe2/FLG/Au(111) heterostructure. We observe
$\mu$PL signal variations of one order of magnitude between coupled (dim
areas) and decoupled areas (bright areas) in both MoSe2/FLG/Au(111) and
MoSe2/Au(111) surfaces. This is a direct signature of the local interface
quality between the components. In the case of MoSe2/FLG, there are two
interfaces that may play a role: the MoSe2/FLG interface regulating exciton
transfer from MoSe2 to graphene and the FLG/Au(111) interface, which can
further contribute to luminescence quenching and dielectric screening. We can
illustrate this by plotting, in Fig. S2b, the ratio between the integrated
intensity of the neutral exciton ($\rm{X}^{0}$) emission
($\rm{I}_{\rm{X}^{0}}$) and $\rm{I}_{\rm{tot}}$. Qualitatively, We observe
that the dimmest areas (low $I_{\rm{tot}}$) tend to display near unity $I_{\rm
X^{0}}/I_{\rm{tot}}$ ratios. To substantiate this observation, we have plotted
the correlation between the observed ratio and $\rm{I}_{\rm{tot}}$ for spectra
taken from coupled and decoupled areas of the heterostructure (Fig. S2c-d). In
both regions, MoSe2/FLG/Au(111) and MoSe2/Au(111), a correlation between large
$I_{\rm X^{0}}/I_{\rm{tot}}$ ratios and correspondingly low
$\rm{I}_{\rm{tot}}$ is revealed. This is consistent with a scenario where the
layers that compose the heterostructure are well coupled and the emission
arises solely from $\rm X^{0}$, as observed in samples encapsulated in
hexagonal Boron Nitride (hBN) Lorchat  _et al._ (2020). In inhomogeneous
areas, the presence of contaminants and bubbles contributes to exciton
localization, resulting in extrinsic, low energy features in the $\mu$PL
spectra, which reduce the overall ratio.

Typical $\mu$PL spectra recorded on the positions marked in Fig. S2a are shown
in Fig. S2e-g. The spectra are characteristic of the main areas of the sample
(also summarised in Fig. 1d: coupled MoSe2/FLG/Au(111) (light blue), decoupled
MoSe2/FLG/Au(111) (blue), coupled MoSe2/Au(111) (orange), decoupled
MoSe2/Au(111) (red) and MoSe2/Au(111) in the vicinity of bubbles (dark red).
In coupled areas (Fig. S2e and g), single-line $\mu$PL spectra are observed,
as previously reported in hBN-capped TMD/graphene heterostructures Lorchat
_et al._ (2020). On the other hand, decoupled areas display multiple low-
energy peaks arising from neutral, charged and localised excitons
($\mathrm{X}^{0}$, $\mathrm{X}^{-}$ and $\mathrm{X^{L}}$ respectively) as
shown in Fig. S2f,g. The number of peaks and their positions are spatially
dependent and are a direct signature of the homogeneity of the probed area.
Nevertheless, one can recover ”typical” spectra composed of two peaks
($\mathrm{X}^{0}$ and $\mathrm{X}^{-}$). Interestingly, we observe redshifts
of the excitonic emission as large as 40 meV within decoupled regions (bottom
spectra in Fig. S2f and red spectra in Fig S2g). We speculate that these
redshifts are due to a combination of strain and screening from the Au(111)
substrate.

##  S3 Determination of the electronic gap

To determine the onset of the bands in the differential conductance spectra
(see Fig. 4a in the main text), we used a similar procedure as in Ref. Ugeda
_et al._ , 2014. This procedure is illustrated in Fig. S3 and can be
summarised as follows:

Figure S3: Determination of the band onsets and electronic gap. a.
Differential conductance spectrum shown in Fig. 4a of the main manuscript. The
spectrum is shown in semi-logarithmic scale and it has been vertically offset
to avoid negative values. The gray dashed line corresponds to the average
noise level. The blue (red) horizontal dashed line marks a threshold for which
the signal is $2\sigma$ ($3\sigma$) above the noise level. b. Differential
conductance spectrum shown in a around the negative resonance onset. The value
of the onset is determined by fitting the band at a given threshold value. The
linear fits are represented by solid lines and correspond to a $2\sigma$
(blue) and $3\sigma$ (red) threshold.

  * •

First, we plot the spectrum on a semi-logarithmic scale (Fig. S3a). A rigid
vertical offset was applied to avoid running into negative values.

  * •

To estimate the noise level of the measured conductance, we compute the
average value (gray dashed line in Fig. S3a) and the standard deviation of the
noise inside the gap.

  * •

We defined two thresholds from which we consider that the signal is
sufficiently different from the noise floor. These correspond to $2\sigma$ and
$3\sigma$ ($\sigma$ being the standard deviation) above the average noise.
These thresholds are represented by the blue and red dashed lines in Fig. S3a,
respectively.

  * •

Finally, we used linear fits of the bands within a range of
$\mathrm{E}_{\mathrm{VB},n\sigma}-\Delta\mathrm{E}<\mathrm{E}<\mathrm{E}_{\mathrm{VB},n\sigma}$
and
$\mathrm{E}_{\mathrm{CB},n\sigma}<\mathrm{E}<\mathrm{E}_{\mathrm{CB},n\sigma}+\Delta\mathrm{E}$
with $n=2,~{}3$. $\Delta\mathrm{E}$ was chosen so that the Pearson coefficient
$R^{2}$ of the fits is not smaller than 0.95.

  * •

The onset of the bands is then defined as the intersection between the linear
fit and the floor level for each threshold. We then calculate the average of
both values.

  * •

These values are marked with the dashed vertical lines in Fig. S3b.

Using this procedure, we could determine an electronic gap of $2.17\pm 0.04$
eV all over the sampled region.