Transition metal dichalcogenide dimer nano-antennas with ultra-small gaps
Panaiot G. Zoteva∗, Yue Wangb∗∗, Luca Sortinoa,c Toby Severs Millarda, Nic
Mullina, Donato Conteducab, Mostafa Shagara, Armando Gencoa, Jamie K. Hobbsa,
Thomas F. Kraussb, Alexander I. Tartakovskiia∗∗∗ aDepartment of Physics and
Astronomy, University of Sheffield, Sheffield S3 7RH, UK
bDepartment of Physics, University of York, York, YO10 5DD, UK
cChair in Hybrid Nanosystems, Nanoinstitute Munich, Faculty of Physics,
Ludwig-Maximilians-Universität, München, 80539, Munich, Germany
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>

Transition metal dichalcogenides have emerged as promising materials for nano-
photonic resonators due to their large refractive index, low absorption within
the visible spectrum and compatibility with a wide variety of substrates. Here
we use these properties to fabricate WS2 monomer and dimer nano-antennas in a
variety of geometries enabled by the anisotropy in the crystal structure.
Using dark field spectroscopy, we reveal multiple Mie resonances, including
anapole modes, for which we show polarization-sensitive second harmonic
generation in the dimer nano-antennas. We introduce post-fabrication atomic
force microscopy repositioning and rotation of dimer nano-antennas, achieving
gaps as small as 10$\pm$5 nm and opening a host of potential applications. We
further studied these structures with numerical simulations yielding electric
field intensity enhancements of >103 corresponding to Purcell factors as high
as 157 for emitters positioned within the nano-antenna hotspots. Optical
trapping simulations of small dimer gaps yield attractive forces of >350 fN
for colloidal quantum dots and > 70 fN for protein-like, polystyrene beads.
Our findings highlight the advantages of using transition metal
dichalcogenides for nano-photonics by exploring new applications enabled by
their unique properties.

Transition metal dichalcogenides (TMDs) have drawn large scientific and
technological interest in the past decade since the discovery of a direct band
gap in monolayers due to quantum confinement effects [1], which in conjunction
with reduced dielectric screening led to strongly bound excitons [2]. These
layered materials found their way to research involving integration with nano-
photonic structures such as plasmonic and dielectric cavities to realize both
weak and strong coupling [3, 4, 5, 6, 7], low-threshold lasing [8], Purcell
[9, 10] and quantum efficiency enhancement [11] of single photon emitters
(SPEs) in WSe2 as well as coupling to collective resonances such as in
periodic structures [12, 13]. In these studies, the use of TMDs was limited to
single and few-layer samples focusing on coupling emitted light from the
material to resonances and cavity modes in different material systems[14].

Alternatively, the fabrication of a photonic resonator from a layered material
similar to TMDs was first achieved in hexagonal boron nitride (hBN). Recent
reports utilized electron beam induced as well as reactive ion etching of hBN
to fabricate suspended one- and two-dimensional photonic crystal cavities as
well as ring resonators, circular bragg gratings and waveguides [15, 16].
Moreover, hBN microcavity-like structures have been shown to control the
spontaneous emission rate of excitons in MoS2 monolayers [17]. Micro-rotator
structures, twisted with atomic force microscopy (AFM), have also been shown
to facilitate the control of second harmonic generation (SHG) enhancement in
hBN. Photonic resonators fabricated in TMDs, however, have only recently been
reported even though these materials offer a number of advantages. The
refractive index of WS2 in the visible range (n>4) [18] is higher than that of
hBN [19] or other high-index dielectrics traditionally used to fabricate nano-
photonic resonators such as gallium phosphide [20] or silicon [21, 22, 23].
TMDs also often maintain a sizable transparency window in the visible [24] and
offer advantages due to their layered nature such as large optical anisotropy
[25] and adhesion to a large variety of substrates owing to their van-der-
Waals attractive forces [26]. These properties offer the possibility of
producing a highly contrasting refractive index boundary by deposition of TMD
crystals onto low refractive index materials such as SiO2 [27] thereby
providing a straightforward route to highly confined optical resonances.

Reports on TMD photonic structures have demonstrated strong coupling using WS2
photonic crystals [28], gratings [29], nano-antenna resonators [18] as well as
TMD bulk flakes [30]. Waveguiding or quasi-waveguiding has also been achieved
in monolayer WS2 photonic crystals [31] and bulk TMD flakes [25]. TMD nano-
disk Mie resonators have also been fabricated to show second and third
harmonic generation enhancement [32] and Raman scattering enhancement [33].
Both of the latter reports employed a non-radiative anapole mode which arises
due to destructive interference between a dipole electric and a toroidal
magnetic mode leading to suppressed far-field scattering and confinement of
incident radiation [34]. Numerical studies have also explored the possibility
of entire optical circuits in TMDs including rib waveguides, photonic crystal
cavities and electro-optic modulators [35]. Further theoretical reports open
the possibility for realization of MoS2 nano-resonator modes [36] as well as
WS2 nano-antenna metasurface resonances [37] characterized as bound states in
continuum.

Photonic elements with ultra small gaps are highly desirable due to the
possibility of strong confinement of electric and magnetic fields, similar to
ultra-narrow nano-structures fabricated using the etching anisotropy of WS2
crystallographic axes [38]. As evidenced from tip cavity structures in
photonic crystal nano-beam cavities [39] as well as from the use of plasmonic
bowtie antennas [40], resonators containing a closely spaced double-vertex
structure can confine electric fields to far below the wavelength of light due
to the boundary conditions on the normal and parallel components of the
electric field at a sharp refractive index contrasting boundary[39]. The
confined field intensity increases as the separation between high refractive
index vertices is reduced [39]. Therefore, very small, low-index gaps yield
very large field intensities which can be advantageous for Purcell enhancement
of SPEs. The highly confined electric fields in high-index resonators with
ultra-small gaps are a prerequisite for large local densities of optical
states, which from Fermi’s Golden rule, lead to high radiative emission rates
of quantum emitters [41].

An application which would also greatly benefit from the large electric field
intensities in such small separations and could aid in the precise positioning
of SPEs is optical trapping of nano-particles. These experience an attractive
force in the direction of an electromagnetic hotspot under optical excitation.
The force is dependent on the particle size, refractive index, the input pump
power and the energy confinement provided by the photonic environment[42].
Previous reports of nano-antenna optical trapping utilize plasmonic resonators
which have been shown to apply large forces to nano-particles [43], however,
they suffer from large changes in temperature leading to loss in stability as
well as quenching of emission due to increased optical absorption processes
[23, 44]. Alternatively, dielectric nano-resonators, such as silicon dimer
nano-antennas [23, 45], can be advantageous for optical trapping in different
applications including biological nano-particles at risk of degrading due to
heating effects as well as quantum dot positioning without emission quenching.

The smallest achievable lateral, low refractive index gap between two vertex-
shaped plasmonic structures has, to the best of our knowledge, only been
reported for gold nanotriangles (5 nm) manipulated with an AFM tip [46]. For
high-index dielectric structures, the limit is set by focused ion beam (FIB)
milling which results in gaps on the order of 10 nm [47] yet it is an
irreversible process and damages the crystal, therefore disadvantageous for
some applications.

In this work, we pattern nano-antenna structures into thin WS2 crystals. We
exfoliate 25 nm - 500 nm thick flakes of WS2 onto a SiO2 substrate and utilize
established nano-fabrication techniques such as electron beam lithography
(EBL) and reactive ion etching (RIE) to define nanometer-scale antennas. We
observe that WS2 can be selectively fabricated in circular, square or novel
hexagonal geometries with potentially atomically sharp edges and vertices
depending on the etching recipe used. Dark field spectroscopy of single
(monomer) and double (dimer) nano-pillar resonators reveals geometric Mie
resonances which we compare with finite-difference time-domain (FDTD)
simulations. We perform SHG experiments on fabricated structures and reveal
polarization dependent enhancement of the signal through coupling to a dimer
anapole mode. Subsequently, we utilize contact mode atomic force microscopy
(AFM) as a post-fabrication step to reposition the constituent nano-pillars of
dimer nano-antennas achieving gaps of 10$\pm$5 nm. This also introduces a
route to modulate the photonic environment in the dimer gap through separation
distance as well as relative rotation of the nano-pillar vertices. We further
numerically study the viability of utilizing dimer nano-antennas for photonic
enhancement of single photon emitters. We simulate the electric field
confinement as well as the Purcell factor for an SPE positioned at the
hotspots of the dimer nano-antenna mode. These simulations yield electric
field intensity enhancement of >103 compared to vacuum and Purcell factors of
>150 for the hexagonal and square geometries. We further explore different
pathways to modulate the enhancement of SPEs in the dimer hotspots using
separation of nano-pillars as well as relative rotation, which is intrinsic to
the novel hexagonal and square structures. We subsequently numerically explore
the prospect of using WS2 dimer nano-antennas with ultra-small gaps in optical
trapping. For the smallest experimentally achieved dimer gap, we calculate
attractive forces towards the electric field hotspots of >350 fN for colloidal
quantum dots (QDs) and >70 fN for polystyrene beads (PBs) which closely
emulate large proteins. Our experimental and numerical studies of TMD material
photonic resonators opens possibilities for novel research and applications.

Results

Fabrication of nano-antennas WS2 consists of covalently bonded monolayers
(Fig. 1(a)) with a hexagonal crystal structure and a thickness of 0.7 nm.
These layers are held together by van-der-Waals forces in bulk crystals. We
mechanically exfoliated WS2 flakes onto a 290 nm SiO2 on silicon substrate
with thicknesses ranging from 25 to 500 nm. Fig. 1(b) shows a schematic
representation of the fabrication process. We spun a positive resist onto the
sample and patterned circular disks and squares with varying radii using EBL.
After development, we transferred the pattern into the WS2 crystals with RIE
using two different recipes completed once the etch depth matched the
thickness of the exfoliated crystal, defining the nano-antenna height. An
anisotropic etch using a mixture of CHF3 and SF6 gases along with a high DC
bias and low chamber pressure yielded circular nano-pillars with vertical
sidewalls which resulted from the physical etching of the resist pattern into
the WS2. Examples of the structure are shown in the AFM and scanning electron
microscopy (SEM) images in the upper row of Fig. 1(c).

Upon substitution of the CHF3 with additional SF6 gas, a reduction of the DC
bias and an increase in the chamber pressure, the resulting nano-antennas
exhibited a hexagonal geometry with a radius defined from the center of the
structure to one of the vertices at the edge, as shown in the middle right
panel of Fig. 1(b). This radial definition corresponds to the radius of the
previously circular resist pattern. The physical etching mechanism was
suppressed and the increased proportion of reactive fluorine radicals ensured
a dominant chemical etch which preferentially removed the WS2 crystal in the
armchair crystal axis leading to zigzag terminated sidewalls at 120∘ angles to
each other following the crystal symmetry. This agrees with DFT results which
also predict that zigzag edges are more stable [48, 49]. The AFM and SEM
images in the middle row of Fig. 1(c) display an example of hexagonal nano-
antennas.

The final geometry we achieved was that of a square which resulted from a
combination of resist patterning and chemical etching of the WS2. We defined a
square resist pattern with sides oriented parallel to the zigzag axis of the
crystal. The subsequent chemical etching similarly removed the WS2 in the
armchair crystal axes ultimately leading to 90∘ angles describing a square
shaped nano-antenna, examples of which are displayed in the lower panels of
Fig. 1(c). The hexagonal geometry and, in part, the square nano-antenna
geometry are formed due to the relative stability of the zigzag axis and can
therefore lead to atomically sharp vertices.

Photonic resonances of WS2 nano-antennas We studied the fabricated structures
using dark field spectroscopy and compared the experimental results to FDTD
simulations which yielded close agreement (see methods and Supplementary Note
1). We identified an electric dipole resonance with small contributions from
higher order modes as well as anapole and higher order anapole modes (HOAM).
As expected from Mie theory, the resonances forming in the studied nano-
antennas red-shifted with increasing radius and blue-shifted with decreasing
height. The ability to change the geometry of nano-antennas through a choice
of etching recipe provides an additional, more precise tuning mechanism for
the observed resonances (see Supplementary Note 2).

Next we considered more complex architectures by placing a pair of the novel
hexagonal nano-pillars in close proximity to form a dimer nano-antenna shown
schematically in the left panel of Fig. 2(a). An SEM image of a fabricated
structure is also displayed in the right panel of Fig 2(a). When two single
nano-pillars are placed in close proximity, their photonic resonances
hybridize forming two cross-polarized modes with an energy splitting (see
Supplementary Note 3). One of these modes is excited with polarization
parallel to the axis connecting the midpoints of the single nano-pillars
(dimer axis), which we name the X-pol mode, while the other is excited
perpendicularly, here named the Y-pol mode.

We recorded dark field spectra for dimer nano-antenna structures with a height
of h = 60 nm and compared these to simulations. Fig. 2(b) shows this
comparison for unpolarized excitation at three different radii (165 nm, 185 nm
and 200 nm) and a dimer gap of g = 130 nm yielding close agreement. Dark field
scattering spectra for the X-pol and the Y-pol modes can be found in
Supplementary Note 4 showing the hybridization of the anapole resonance.
Moreover, we measured a larger set of nano-antennas with a similar height (60
nm) spanning a range of radii from 165 nm to 220 nm which can be found in
Supplementary Note 5. This study also revealed a red-shift of all resonances
with increasing radius confirming their geometric origins and asserting the
tuning mechanism for the dimer nano-antenna modes to be the same as for the
monomer.

The dashed, red lines in Fig. 2(b) represent the normalized, confined electric
energy inside the structure, simulated for a surface at the midpoint of the
nano-antenna height. Similar to the behavior seen in the monomer nano-
antennas, we recorded a minimum in the scattering spectra of the dimer nano-
antennas at long wavelengths (800 nm for r = 200 nm) coinciding with a maximum
in the simulated, confined electric energy. This correlation, together with
the electric and magnetic field intensity pattern at this wavelength, shown in
Fig. 2(c), are all characteristic of a dimer anapole mode [34]. When compared
to the same resonance in monomers, the dimer anapole mode yields a more
tightly confined electric energy (see Supplementary Note 6).

Second harmonic generation enhancement We recorded second harmonic generation
spectra from a dimer (r = 205 nm, h = 60 nm, g = 130 nm) and monomer nano-
antenna (r = 215 nm, h = 50 nm), which both host anapole modes near 800 nm, as
well as from a bulk crystal (h = 60 nm) using a 804 nm pulsed Ti-sapphire
laser excitation linearly polarized perpendicular to the dimer axis (Y-pol).
Fig. 2(d) displays the SHG spectra normalized to the excited area. For the
bulk measurement, the intensity was normalized to the area of the laser spot
size ($A=\pi r^{2}$ for r = 700 nm). The hexagonal nano-antenna measurements
were normalized to their respective areas ($A_{mono}=3r^{2}\sqrt{3}/2$ for the
monomer with r = 215 nm and $A_{di}=3r^{2}\sqrt{3}$ for the dimer with r = 205
nm). We extracted an SHG enhancement factor by integrating the normalized
second harmonic signal at the dimer nano-antenna position (yellow in Fig.
2(d)) and dividing by a the similarly integrated signal from the bulk flake
(purple dots), yielding a factor of 7.2. The recorded signal from the monomer
was comparable to the dimer nano-antenna which is expected from simulations of
the electric energy stored in the anapole mode (see Supplementary Note 6).

We further studied the polarization dependence of the nano-antennas by
shifting the excitation laser to 850 nm, rotating its linear polarization and
collecting integrated second harmonic signal through the use of an avalanche
photo-diode (APD). The laser wavelength used for these experiments was chosen
due to the larger difference of confined electric energy expected for the
X-pol and Y-pol modes of the dimer. The normalized polarization dependent SHG
intensity was recorded for a dimer (r = 200 nm, h = 60 nm, g = 130 nm),
monomer (r = 240, h = 50 nm) and bulk as shown in Fig. 2(e). Upon comparison
of the measured signals, we observed a clear polarization of the second
harmonic signal for the dimer nano-antenna while the same is not evident for
the bulk or monomer nano-antenna measurements. As the excitation polarization
is rotated, the X-pol and subsequently the Y-pol modes confine incident light
differently leading to the observed polarization dependence. The electric
field is mainly confined to the outside edges of the nano-antenna for the
X-pol anapole mode, thereby not contributing to the SHG enhancement. For the
Y-pol mode, however, the confinement is mostly inside the nano-antenna
structure. The position of the confined electric field in the monomer and bulk
does not change, therefore, leading to no polarization dependence of the SHG
enhancement. We compare the experimental data to simulations of the relative
SHG signal (possible due to its dependence on the electric energy squared
[20]) and observed good agreement between simulation and experiment for both
structures shown in Fig. 2(e).

AFM repositioning The fabrication procedure outlined in Fig. 1 yields minimum
dimer separation gaps of 50 nm, therefore, we attempted to improve upon this
by using the properties of layered materials to our advantage. The relatively
weak van-der-Waals forces which facilitate mechanical exfoliation of thin WS2
crystals also allow for a weak adhesion of the fabricated structures to the
SiO2/Si substrate. As a post-fabrication procedure, we employed an AFM
cantilever in order to translate one nano-pillar with respect to the other and
achieve gaps as small as 10 nm without damaging the nano-antenna. Smaller
separation distances may be achievable, however, the accurate measurement of
the gap width is a considerable challenge due to the finite size of the AFM
tip which is <5 nm.

The method of repositioning used a contact mode AFM cantilever which scanned
parallel to the dimer axis on the outside edge of a dimer nano-antenna.
Choosing a low set-point in order to position the cantilever close to the
sample surface forced it to collide with the nano-antenna during each sweep
and displace it. A schematic representation of the translation can be seen in
Fig. 3(a). Very fine positioning can be achieved using this method as shown in
Fig. 3(b) where we translated one nano-pillar with respect to other reducing
the dimer gap separation from 105 nm to 15$\pm$5 nm.

An additional advantage of using this repositioning method is the ability to
rotate the nano-pillars with great precision (<1∘). As shown in the bottom
panel of Fig 3(b), by scanning the AFM cantilever along a tangent of one of
the nano-pillars colliding with only the edge, it was rotated by over 8∘ as
well as translated closer to the other nano-pillar allowing fine positioning
of the inside vertices of the dimer. Further atomic force microscopy scans of
repositioned nano-antennas are displayed in Supplementary Note 7 confirming
the reproducibility of the procedure and showing the minimum gap separation we
have achieved (10$\pm$5 nm).

To confirm that the photonic response was modified by the AFM repositioning,
we performed dark field spectroscopy before and after the translation
procedure. As shown in Fig. 3(c), the dipolar resonance seen in scattering
increased for an excitation parallel to the dimer axis, which is the most
sensitive configuration to changes in gap separation. The dashed lines in the
same figure represent simulations of the geometry before and after
repositioning with close agreement to experiment confirming the achieved 15 nm
gap.

Electric field and Purcell enhancement of emission Ultra-small gaps, such as
those achieved with the AFM repositioning technique are expected to provide
very high electric field confinements [39]. We therefore simulated the
electric field intensity and Purcell enhancement induced by three dimer
designs, corresponding to the different geometries shown in Fig. 1, with a gap
of 10 nm. Each design was optimized for electric field confinement at the top
surface of the dimer.

We have simulated the electric field intensity spatial distribution 0.5 nm
above the top surface of the dimers, shown in the left column of Fig. 4(a), as
well as a cross sectional cut along the z-axis through the middle of the
individual nano-pillars, shown in the right column of Fig. 4(a). Each
distribution was calculated at the wavelength of the maximum electric field
intensity (751.5 nm, 749.5 nm, 697.5 nm for the circular, hexagonal and square
geometries respectively). The radii of the optimized geometries are r = 225
nm, r = 240 nm and r = 260 nm for the circular, hexagonal and square
geometries respectively, while their heights are h = 200 nm, h = 200 nm and h
= 150 nm. In order to closely approximate realistic structures which can be
fabricated, we measured the radius of curvature of the vertices of fabricated
hexagonal and square dimer nano-antennas using atomic force microscopy. This
yielded vertex radii of curvature as low as 22 nm for the hexagonal and 10 nm
for the square geometry (see Supplementary Note 8). These values were then
subsequently taken into account in the simulation of the hexagonal and square
geometries. The electric field hotspots forming at the vertices between the
two nano-pillars for an incident plane wave polarized parallel to the dimer
axis exhibit intensities of more than 103 compared to vacuum as shown in Fig.
4(a). We compare the hotspots simulated for the three geometries achievable
through the fabrication process. The hexagonal and square shaped nano-antennas
induce a higher electric field intensity confinement than the circular design,
with the hexagonal geometry inducing the largest enhancement.

Furthermore, we evaluated the Purcell factor for a single photon source
positioned onto these structures by simulating a dipole emitter at positions
along the dimer axis with a polarization parallel to the same axis. It is
displaced by 0.5 nm from the top surface of the structure and its emission
wavelength was set to the one used for Fig. 4(a). The calculated Purcell
factors at each position are shown in Fig. 4(b). Solid white lines in the left
panels of Fig. 4(a) indicate the simulated positions of the emitter. The
maxima seen at positions corresponding to the inner edges of the nano-antenna
yield the largest results (>100) as expected from the electric field hotspots
seen in Fig.4(a). Weakly confined hotspots at the outside edges of the
structure also exhibit local maxima in the Purcell factor with values as high
as 20. For the minimum achieved gap separation in the post-fabrication AFM
repositioning, the hexagonal geometry exhibits the highest Purcell factor
within its hotspot (157) with the square as a close second (153). The
circularly shaped dimer leads to a maximal Purcell factor of 105. We have also
simulated the Purcell factors for the minimum gap separation achievable
without the use of AFM repositioning (50 nm), which are shown in Fig. 4(b) as
dashed lines. This yields much smaller Purcell enhancements (as high as 46).

There are several degrees of freedom in the fabrication process as well as the
AFM repositioning which can be used to control the magnitude of the
enhancement of single photon emission within these hotspots. One approach
involves the separation of the two nano-pillars in the dimer. We numerically
studied the effect of moving the two nano-pillars apart from each other
(schematically depicted in Fig. 4(c)) on the electric field intensity and
Purcell factor at the hotspots in Fig. 4(d) and (e). We also compared these
effects for the three dimer designs. Both the electric field intensity and
Purcell factor decrease exponentially with separation distance. The hexagonal
structure yields the highest electric field confinement at small separations,
however the intensity induced by the square structure is highest for large gap
values (>75 nm). The Purcell factor of the square structure, however, exceeds
that of the hexagonal at separation values as low as 20 nm.

Another approach available only to the hexagonal and square nano-antennas
takes into account the control of the alignment of the two nano-pillars
relative to each other. One method to achieve such alignment was previously
shown in Fig. 3 through AFM positioning, while another method utilizes the
chemical etching mechanism which etches faster in the armchair axis of the
crystal. Therefore, two nano-pillars fabricated spatially close to each other
will always have the same orientation with respect to the symmetry of the
original crystal. However, if the dimer nano-antenna design is rotated at the
electron beam patterning stage of the fabrication procedure, as displayed in
Fig.4(f), the relative orientation of the antennas will have changed along the
new axis connecting their centers, thereby, positioning their vertices closer
or further apart from each other. As shown in Fig.4(g) and (h), this can lead
to a more subtle modulation of the the electric field intensity and the
Purcell enhancement for a quantum emitter located within the hotspots. The
range of angles available to the hexagonal geometry is limited to 30∘, while
the square structure can be rotated to 45∘ before the electric field intensity
and Purcell factor begin to increase once more.

Dimer nano-antenna optical trapping In order to study the potential of ultra-
small gap WS2 dimer nano-antennas for optical trapping, we perform numerical
simulations based on the Finite Element Method (FEM) to determine the Maxwell
Stress Tensor (MST) and calculate the force exerted on small dielectric
particles. The simulation geometry consists of the earlier optimized hexagonal
nano-antenna with the addition of a nano-sphere (r = 5 nm) with a refractive
index corresponding to either an approximated colloidal quantum dot (n = 2.4)
[45] or a polystyrene bead (n = 1.6), which closely mimics the refractive
index and size of a large protein [50]. Since optical trapping experiments
often require a suspension of the nano-particles in a solution, we set the
background refractive index to that of water. For all simulations, we use an
experimentally feasible pump power density of 10 $mW/\mu m^{2}$. A schematic
representation of the simulation is shown in Fig. 5(a).

We explore the optical force applied to the QD and the PB, as shown Fig. 5(b)
and (c) respectively, as they are translated along the the z-axis in the
middle of the dimer gap. We simulate the forces for two gap separations of the
dimer hexagonal nano-antenna (10 nm and 15 nm) and observe an attractive
(negative) force which is maximized at the top surface of the nano-antenna
where the electric field hotspots are formed. We observe a maximum optical
force of 353 fN on the QD and 73 fN on the PB for the dimer nano-antennas with
a 10 nm separation. For the larger dimer gap (15 nm), this reduces to 123 fN
on the QD and 31 fN on the PB. We also study the dependence of this maximum
optical force in the electric field hotspots on the dimer gap, which is varied
from 10 nm to 50 nm. As shown in Fig. 5(d), the maximum attractive force
imparted on the nano-particles decreases exponentially by one order of
magnitude as expected from the decay of the electric field intensity with an
increased separation, shown in Fig. 4(d). We subsequently explore the spatial
dependence of the optical force by simulating the QD and PB in a plane which
is 5 nm above the top surface of the dimer nano-antenna with a 10 nm gap, as
shown in Fig. 5(e) and (f). This is an emulation of the position of nano-
particles placed onto the top surface of the dimer. The optical force, as
expected, is maximized at the position of the electric field hotspots yet
still maintains values of more than 100 fN for the QD and 20 fN for the PB.

Discussion

We have fabricated and characterized both monomer and dimer WS2 nano-antennas
with the aim to highlight the advantages of their use in photonic applications
such as polarization dependent SHG enhancement, SPE enhancement and optical
trapping thereby broadening the versatility of TMD nano-antennas. Dark field
studies on monomer and dimer nano-antennas reveal a straightforward approach
for tuning resonances inside the nano-antennas in order to fit with different
applications by varying the radius, height or geometry. Through the use of a
dimer anapole mode, we not only show enhanced second harmonic generation from
a nanometer-scale structure but also polarization dependent SHG, not present
in bulk TMD flakes or monomer nano-antennas. Post-fabrication repositioning of
dimer nano-antennas utilizing AFM led us to attain ultra-small gaps of
10$\pm$5 nm, on the order of the feature resolution limit set by FIB milling
[47], which we achieve through a more precise, less damaging and reversible
technique. Although a previous report has demonstrated AFM positioning of
plasmonic bowtie nano-antennas [46], this technique has only become possible
for dielectric nano-antennas made from layered materials due to their
intrinsic van-der-Waals attractive forces. This allows us to achieve the
smallest separation recorded for a dielectric resonator defined through the
use of electron beam lithography followed by reactive ion etching[51, 23].
Another advantage of this method is the possibility to change the relative
orientation of individual nano-pillars, thereby, aligning their potentially
atomically sharp vertices in closer or further proximity.

The numerical simulation studies of dimer nano-antennas exhibiting an ultra-
small gap yield highly confined electric field intensity hotspots (103
enhancement compared to vacuum). We predict the practical utility of WS2 nano-
antennas for radiative rate enhancement of single photon emission with Purcell
factors of up to 157 for a hexagonal and 153 for a square geometry. The
expected quantum emission enhancement in the dimer nano-antennas is higher
than the largest currently achieved in photonic crystal cavities [52] due to
the previously inaccessibly small proximity attained with the AFM
repositioning method. We also discuss two different routes to modulate the
photonic enhancement through variation of the dimer gap as well as the
relative rotation of the individual nano-pillars which are both controllable
through either the fabrication process or, to a greater precision, the post-
fabrication repositioning. These methods of controlling the emission
properties of single photon sources may prove useful for WSe2 SPEs which form
at high strain gradients in monolayers transferred onto dimer nano-antennas
collocated with the electric field hotspots [53]. Previous reports have shown
quantum efficiency enhancement for WSe2 SPEs [11] as well as rotation of the
emitter dipole moment due to a change in the strain gradient [54] both of
which can be controlled through a decrease in separation and a rotation of
individual nano-pillars in the dimer nano-antenna through AFM repositioning.

We further explored a route to the precise positioning of SPEs by simulating
optical trapping forces due to the highly confined electric field in the gap
of the dimer nano-antennas. We calculated a maximum attractive force of 353 fN
for a colloidal quantum dot and 73 fN for a protein-like, polystyrene bead
both with a radius of 5 nm under a pump power density of 10 $mW/\mu m^{2}$.
When compared to previous examples of dielectric nano-antennas for optical
trapping, the WS2 dimers yield higher attractive forces by a factor of >83 for
QDs [45] and >40 for PBs [23] with the same size and under the same pump power
conditions. Therefore, WS2 dimer nano-antennas with ultra-small gaps show
great potential for applications of stable trapping of very small nano-
particles with a moderate optical power, once again highlighting the advantage
of the AFM repositioning technique to reduce the dimer gap below the limits
available to standard nano-fabrication. The large Purcell enhancements and
optical trapping forces predicted for WS2 dimer nano-antennas with ultra-small
gaps highlight the unique potential for TMD nano-resonator research and
applications. This is possible due to the refractive index and van-der-Waals
forces which allow the formation of highly confined resonances and hotspots
while simultaneously opening the possibility of AFM repositioning. The field
of nano-photonics includes a diverse library of materials and here we assert
and expand the possibilities provided by adding thin crystals of TMDs to the
list.

Methods

Sample fabrication

Exfoliation: WS2 flakes were mechanically exfoliated from bulk crystal (HQ-
graphene) onto a nominally 290 nm SiO2 on silicon substrate. Large flakes with
recognizable crystal axes via straight edged sides at 120∘ to each other were
identified and their positions within the sample were recorded for further
patterning.

Electron beam lithography: Samples were spin coated with ARP-9 resist
(AllResist GmbH) at 3500 rpm for 60 s and baked at 180∘ for 5 min yielding a
film of 200 nm thickness. Electron beam lithography was performed in a Raith
GmbH Voyager system operating at 50 kV using a beam current of 560 pA.

Reactive ion etching Anisotropic etching to imprint the resist pattern into
the WS2 flakes physically was carried out using a mixture of CHF3 (14.5 sccm)
and SF6 (12.5 sccm) at a DC bias of 180 V and a pressure of 0.039 mbar for 40
seconds. Isotropic etching was achieved by using a more chemical recipe with
solely SF6 (20 sccm) at a DC bias of 50 V and a pressure of 0.13 mbar for 40
seconds. Removal of the remaining resist after etching was accomplished by a
bath in warm 1165 resist remover (1 hour) followed by Acetone (5 min) and IPA
(5 min). If resist is still found on the sample, final cleaning is done in a
bath of Acetone (1 hour) and IPA (5 min) followed by 1 hour in a UV ozone
treatment.

Dark field spectroscopy Optical spectroscopy in a dark field configuration was
achieved using a Nikon LV150N microscope with a fiber-coupled output. Incident
illumination from a tungsten halogen lamp in the microscope was guided to a
circular beam block with a diameter smaller than the beam diameter. The light
was then reflected by a 50:50 beam-splitter towards a 50x Nikon (0.8 NA) dark-
field objective which only illuminates the sample at large angles to the
normal. Reflected light from the sample is guided back through the same
objective towards a fiber coupler. Due to the small diameter of the mult-mode
fiber core used, only light reflected back at small angles to the normal is
collected. The fiber from the microscope was subsequently coupled to a
Princeton Instruments spectrometer and charge coupled device (CCD).

Second Harmonic Generation In order to probe the second harmonic generated
signal from the nano-antennas, we used a home-built setup with a Spectra-
Physics Ti-sapphire mode-locked fs laser as the excitation source. The
collimated laser light passed through a linear film polarizer, dichroic mirror
and half wave plate was incident on a 100x (0.7 NA) Mitutoyo objective which
focused the excitation light onto the sample allowing us to probe single nano-
antennas. Second harmonic generated light was then collected using the same
objective subsequently passing the light through the half wave plate and
reflecting it from the dichroic mirror. The collected light is then filtered
by 3 long-pass filters (450, 550, 750 nm cutoff) and coupled to a multi-mode
fiber and sent to a Princeton Instruments spectrometer and CCD (data displayed
in Fig. 2(d)) or an ID Quantique avalanche photo-diode (id100) (data displayed
in Fig. 2(e)). The incident illumination used for Fig. 2(d) (Fig. 2(e)) was
set to 804 nm (850 nm) with 1 mW (3 mW) average power. In order to confirm
that we measured second harmonic signal using the APD with minimal background
noise, we first confirmed the spectral response of the signal from a bulk
flake on the CCD.

Atomic force microscope repositioning and imaging All repositioning was
carried out using a JPK Nanowizard 3 Ultra AFM using Bruker SNL probes
(cantilever C, nominal stiffness 0.24 N/m). First, nano-antennas were imaged
in QI mode with a setpoint of 1 nN, a Z length of 400 nm and a pixel time of
15 ms. To reposition the antennas, the AFM was switched to contact mode and
200 nm scans were performed with a setpoint of 1 nN and a scan rate of 2 Hz on
the substrate immediately adjacent to the antenna. The fast scan axis was
oriented along the desired direction of movement and the scan area was
progressively moved so that the scan overlapped with the antenna to translate
it in the desired direction in increments of 5-50 nm at a time. Periodically,
the antenna was re-imaged in QI mode to check the relative position and
orientation of the pillars. Final characterization after repositioning was
performed in QI mode.

FDTD simulations The finite-difference time-domain simulations were carried
out using Lumerical Inc. software.

Scattering simulations: Calculations of the scattering cross section shown in
Figs. 2 and 3 were carried out by defining the geometry of the WS2 nano-
antennas onto a SiO2 substrate utilizing the refractive index of WS2 from
reference [18]. Illumination with a plane wave was sent normal to the surface
using a TFSF source from the air side. For Fig. 2 the illumination was
unpolarized, however, for Fig. 3 the polarization was set parallel to the
dimer axis. The scattered intensity was subsequently collected from a monitor
set above the illumination plane (in the far-field) so that the dark field
spectroscopy experiments could be closely emulated.

Electric field intensity simulations: Calculations of the near-field electric
field intensity normalized to vacuum, shown in Fig. 4(a), (d) and (g) were
simulated using the same geometry and illumination scheme as for the
scattering simulations (polarization is shown as a white double arrow in top
left corner of each panel) with a monitor recording the electric field 0.5 nm
above the top surface of the nano-antennas or as a vertical cross-section of
the structure passing through the dimer axis as shown in the right-most panels
of Fig. 4(a). For Fig. 2(c), the monitor was designed as a cross-sectional
profile through the midpoint of the nano-antenna height. For Figs. 2(c) and
4(a) this monitor was defined to encompass the entire cross section of the
nano-antennas. For Figs. 4(d) and (g) only a single point 1 nm from the inside
edge of the dimer nano-antenna within the hotspot was recorded.

Electric energy simulations: Calculations of the confined electric energy
inside dimer nano-antennas shown in Fig. 2(b) was performed according to
equation 1 in Supplementary Note 6. The spatial distribution of the electric
field intensity was first simulated for a cross-sectional cut through the
midpoint of the nano-antenna height for a range of wavelengths. Subsequently,
the integration of the intensities was carried out over the cross-sectional
surface only for positions inside the nano-antenna structure. In order to
simulate the relative, integrated polarization dependent SHG signal in Fig.
2(e), we performed the same electric energy calculation as for Fig. 2(b) over
a range of polarization angles for the dimer and monomer structures and
squared the results obtained [20]. For each polarization angle, we integrated
the squared electric energy over the laser spectrum in order to be able to
compare the simulation to experiment.

Purcell factor simulations: Simulations of the Purcell factor were carried out
using the same geometry as for the electric field intensity simulations. The
illumination was achieved through a dipole source placed at positions along
the dimer axis 0.5 nm above the top surface of the nano-antenna with a
polarization parallel to the dimer axis for Fig. 4(b). For Figs. 4(e) and (h)
however, the position was set to 0.5 nm above the top surface of the nano-
antenna and 1 nm away from the inside edge within the electric field hotspot.
The polarization of the dipole in Fig. 4(e) and (h) was kept the same as in
Fig. 4(b).

Optical trapping force simulations: We have used the 3D finite element method
(COMSOL Multiphysics) to calculate the optical forces in the hexagonal dimer
nano-antenna. The structure is illuminated with a plane wave propogating in a
normal direction to the top surface of the structure with a polarization along
the dimer axis. The background refractive index was set to that of water to
enable access of the bead to the trapping site. We have calculated the optical
forces at the resonance of the nano-antenna, corresponding to the maximum
energy enhancement. The value of the optical force is obtained by integrating
the Maxwell Stress Tensor on the surface of the target nano-particle [42]. A
fine mesh (resolution of $\leq$ 3 nm) has been employed in the dimer gap to
calculate the electromagnetic distribution with a high accuracy, minimizing
the error on the evaluation of the optical force. The computational domain has
been set to a sufficiently large value (>2 $\mu m$) and surrounded by
perfectly matched layers in order to avoid undesired reflection and scattering
from the boundary.

Acknowledgments

P. G. Z., L. S., T.S.M., M.S., A. G. and A. I. T. thank the financial support
of the European Graphene Flagship Project under grant agreements 881603 and
EPSRC grants EP/S030751/1, EP/V006975/1 and EP/P026850/1. L. S. and A. I. T.
thank the European Union’s Horizon 2020 research and innovation programme
under ITN Spin-NANO Marie Sklodowska-Curie grant agreement no. 676108. P. G.
Z. and A. I. T. thank the European Union’s Horizon 2020 research and
innovation programme under ITN 4PHOTON Marie Sklodowska-Curie grant agreement
no. 721394. T.F.K. acknowledges the support of the Engineering and Physical
Sciences Research Council (grant number EP/P030017/1). Y.W. acknowledges a
Research Fellowship (TOAST) awarded by the Royal Academy of Engineering.

Author contributions

P.G.Z and L.S. exfoliated WS2 layers onto SiO2 substrates. Y.W. fabricated
nano-antenna structures using EBL and RIE. P.G.Z and Y.W. performed AFM and
SEM characterization of fabricated nano-antennas. P.G.Z. carried out dark
field spectroscopy measurements, scattering cross section simulations and
electric/magnetic field intensity profile simulations for identification of
WS2 nano-antenna resonances. P.G.Z., T.S.M. and A.G. performed second harmonic
generation experiments on WS2 nano-antennas. N.M. repositioned dimer nano-
antennas using AFM. P.G.Z. and M.S., simulated electric field intensity
profiles and Purcell factors for optimized dimer nano-antennas as well as for
studies on dimer gap separation and rotation. D.C. performed optical trapping
simulations and analyzed the results with Y.W., T.F.K. P.G.Z., L.S., T.S.M.
and A.I.T. analyzed various optical spectroscopy data. J.H., T.F.K., Y.W. and
A.I.T. managed various aspects of the project. P.G.Z. and A.I.T. wrote the
manuscript with contributions from all co-authors. P.G.Z., L.S., Y.W., N.M.,
D.C., J.H., A.I.T. and T.F.K. conceived the experiments and simulations.
A.I.T. oversaw the entire project.

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Figure 1: Fabrication procedure for WS2 nano-antennas. (a) Representation of a
top view of a single layer of WS2 found at the top of a hexagonal nano-antenna
at the position of the vertex. The zigzag axis defines the edges of the
structure due to its higher stability as shown by the two bonds on outlying
sulfur atoms when compared to the armchair axis with its single bond for
outlying sulfur atoms. (b) Fabrication steps and their order following the
black outline arrows. The first step includes spinning of resist onto a WS2
flake. The second step is patterning and development after electron beam
lithography into a circular or square geometry. The final step is reactive ion
etching using either a more physical or chemical etching recipe. The height
(h) is defined by the thickness of the original flake. The radius of the
structure is defined as the distance from the center of the structure to an
outside vertex for hexagonal and square geometries. (c) AFM and SEM images of
fabricated nano-antennas. The left column shows 3D representations of AFM
scans of circular, hexagonal and square nano-antennas in the top, middle and
bottom row respectively. Scale bars in AFM scans = 200 nm. The right column
shows SEM images of similar structures taken at a 60∘ tilt of the sample.
Scale bars in SEM images = 100 nm. Figure 2: Dark field spectroscopy and
second harmonic generation enhancement of hexagonal dimer nano-antennas. (a)
Left panel: Schematic illustration of a hexagonal dimer nano-antenna. Right
panel: SEM image of the top view of a fabricated hexagonal dimer nano-antenna.
(b) Dark field spectroscopy experiments (blue, purple, yellow lines) compared
to scattering cross section simulations (black dashed lines) of dimer nano-
antennas with different radii (r = 165 nm, r = 185 nm , r = 200 nm) and a
height of 60 nm. Dashed red lines correspond to simulated electric energy
confined in the nano-antenna at mid-height. The anapole mode is highlighted
with a vertical green dashed line. (c) Left (Right) panel: Top view of the
electric (magnetic) field intensity in the plane positioned at mid-height of
the dimer nano-antenna (r = 200 nm, h = 60 nm, g = 70 nm) height at the
anapole mode (800 nm) under illumination with a polarization parallel to the
double white arrow in the top left of the image. Grey field lines represent
the electric charge currents inside and surrounding the structure,
highlighting the characteristic anapole mode pattern. Dashed white outlines
represent the physical edges of the structure. Scale bars = 100 nm. (d)
Spectrum of second harmonic generation normalized to the excited area from a
dimer nano-antenna (yellow) (r = 205 nm, h = 60 nm, g = 130 nm), a monomer
nano-antenna (red) (r = 215 nm, h = 50 nm) and a bulk crystal (purple) (h = 60
nm). Excitation polarized perpendicular to the dimer axis as shown by the
double black arrow in the inset. Dashed curves represent a Gaussian fit to the
data. (e) Normalized, integrated polarization resolved second harmonic signal
emitted from the dimer (yellow) (r = 200 nm, h = 60 nm, g = 130 nm) and
monomer (red) (r = 240 nm, h = 50 nm) nano-antennas as well as the bulk
crystal (purple) (h = 60 nm). The linear polarization of the excitation was
set at an angle defined with respect to the dimer axis explained by the inset.
Dashed lines represent the scaled FDTD simulated $\|W_{S}^{E}\|^{2}$
polarization dependence for dimer (yellow) and monomer (red) nano-antennas
with a similar geometry. Figure 3: AFM repositioning of dimer nano-antennas.
(a) Schematic illustration of the scanning technique used in contact mode AFM
to translate and rotate single nano-pillars of the dimer nano-antenna. (b) AFM
scan of a dimer structure (r = 140 nm, h = 170 nm, gap = 105nm) before and
after manipulation. The dimer gap is reduced to 15 nm and one pillar is
rotated by 8∘ in order to position inside vertices closer to each other. (c)
Dark field scattering spectra of the dimer-nano-antenna for excitation
parallel to the dimer axis (as shown in inset) before and after repositioning
compared to a simulated scattering cross section with gaps of 105 nm and 15
nm. Figure 4: Simulations of the electric field hotspots and Purcell
enhancement for single photon emission. (a) Top-view and side-view spatial
distributions of the electric field intensity in and surrounding optimized
designs of each geometry of WS2 dimer nano-antennas at 10 nm separation gap.
Circular design: r = 225 nm, h = 200 nm, wavelength = 751.5. Hexagonal design:
r = 240 nm, h = 200 nm, radius of curvature of vertices = 22 nm, wavelength =
749.5. Square design: r = 260 nm, h = 150 nm, radius of curvature of vertices
= 10 nm, wavelength = 697.5. Hotspots of electric field confinement form at
inner and outer edges of the dimer. Incident plane wave polarization (X-pol)
is parallel to the double white arrow in the top left corner of the panels.
Axes indicate cross-section with (x,y) indicating a surface 0.5 nm above the
top of the dimer and (x,z) indicating a vertical cut through the dimer axis.
Dashed white outlines represent the physical edges of the structures. Scale
bars = 100 nm. (b) Purcell enhancement for a dipole placed at different
positions with polarization parallel to the dimer axis, 0.5 nm above the top
surface of the structures. Solid dots and lines indicate dimers with a gap of
10 nm and dashed lines indicate dimers with a gap of 50 nm. Placement
positions of the dipole above the dimer are shown as solid white lines in (a).
(c) Illustration of the change in dimer gap used for the simulations in (d)
and (e). (d),(e) Gap dependent maximum electric field intensity and Purcell
factor within the hotspot of the optimized dimer designs for each geometry at
the previously used wavelengths. (f) Top-view SEM images of hexagonal dimer
nano-antennas demonstrating the ability to utilize the crystal symmetry to
fabricate structures with a rotation ($\theta$) relative to the dimer axis.
Red circles indicate position of electric field hotspot or dipole source for
Purcell enhancement in (c) and (f) (g),(h) Rotation angle dependent maximum
electric field intensity and Purcell factor within the hotspot of the
optimized dimer designs for the square and hexagonal geometries at the
previously used wavelengths. Figure 5: Optical trapping simulations of nano-
particles using WS2 hexagonal nano-antennas. (a) Schematic illustration of
optical trapping of a nano-particle in water through the use of WS2 hexagonal
dimer nano-antenna hotspots. (b),(c) Comparison of the optical force for a
spherical nano-particle (r = 5 nm) placed in the middle of the dimer nano-
antenna (r = 240 nm, h = 200 nm) gap, along the z-axis for gaps of 10 nm and
15 nm. The trapping force is calculated at the wavelength of its maximum value
for a QD (b) (763 nm) and a PB (c) (755 nm). Insets illustrate the positioning
of the respective nano-particle with the zero position at the top surface of
the nano-antenna. (d) Maximum electric force applied to a QD (purple line) and
a PB (yellow line) at the top surface of a dimer nano-antenna (r = 240 nm, h =
200 nm) with a varying gap separation. (e),(f) Attractive force distribution
for a nano-particle in a plane 5 nm from the top surface of a dimer nano-
antenna (r = 240 nm, h = 200 nm, g = 10 nm) centered at the dimer nano-antenna
gap. The trapping force is calculated at the wavelength of its maximum value
for a QD (e) (763 nm) and a PB (f) (755 nm). Double white arrow in upper left
portion of figure identifies the pump polarization along the dimer axis
(X-pol). Dashed white lines identify the physical edges of the structure.
Inset schematics highlight the position of the plane over which the optical
force is simulated. Maximum force values coincide with the electric field
hotspots. Input pump power density used for all simulations is 10 $mW/\mu
m^{2}$.