Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide

The isolation of the two-dimensional semiconductor molybdenum disulphide introduced a new optically active material possessing a band gap that can be facilely tuned via elastic strain. As an atomically thin membrane with exceptional strength, monolayer molybdenum disulphide subjected to biaxial strain can embed wide band gap variations overlapping the visible light spectrum, with calculations showing the modified electronic potential emanating from point-induced tensile strain perturbations mimics the Coulomb potential in a mesoscopic atom. Here we realize and confirm this ‘artificial atom' concept via capillary-pressure-induced nanoindentation of monolayer molybdenum disulphide from a tailored nanopattern, and demonstrate that a synthetic superlattice of these building blocks forms an optoelectronic crystal capable of broadband light absorption and efficient funnelling of photogenerated excitons to points of maximum strain at the artificial-atom nuclei. Such two-dimensional semiconductors with spatially textured band gaps represent a new class of materials, which may find applications in next-generation optoelectronics or photovoltaics.

Raman images with (b) peak intensity of silicon at 521 cm -1 , c, E 2g ! peak frequency, and d A 1g peak frequency of MoS 2 in the square in (a). Scale bars are 1 µm.

Growth of MoS 2 using chemical vapor deposition (CVD) method
Molybdenum trioxide (MoO 3 ) and sulfur (S) powder were used as sources. 5 mg MoO 3 powder was loaded in a ceramic boat. A piece of Si wafer capped with 270 nm SiO 2 layer was suspended on the ceramic boat with the polished side facing down. Then the ceramic boat was located at the center of a quartz tube furnace. Another ceramic boat containing sulfur powder (1 g) was placed at an upstream position where the temperature would reach 200 ºC during the growth. After sealing, the tube was purged with 50 sccm argon (Ar) gas for 10 min at room temperature, then heated to 750 ºC within 15 min, and maintained at 750 ºC for 20 min. The system was then allowed to cool down to room temperature naturally 1 .

Transmission electron microscopy (TEM) characterization of CVD-grown monolayer MoS 2
The as-grown MoS 2 film was spin coated with 1 µm-thick PMMA film and immersed in 1M  Figures 2e-f). We noted that MoS 2 can be directly grown on top of the nanocones to achieve the conformal coating, but non-uniform multilayer MoS 2 flakes were usually grown on nanocones. The poor growth was likely due to that the etched SiO 2 nanocone surface has many nucleation sites. This is one of the motivations for developing the transferstrain process.

Contact angle measurement of ethylene glycol on MoS 2
As the CVD-grown monolayer MoS 2 was not a continuous film, natural MoS 2 flake (purchased from SPI supplies) were used to measure the contact angle between EG and MoS 2 .
100 µL of EG solution was dropped onto MoS 2 flake surface using a micropipette. The side-view image of the droplet was taken, as shown in Supplementary Figure 2e (inset). A contact angle of about 58° was obtained.

Estimation of capillary pressure
A noticeable feature of our straining method is the utilization of capillary force 2,3 to generate biaxial tensile strain in monolayer MoS 2 . The magnitude of the capillary pressure can be estimated from !"# = 2 cos / , where is the surface tension of the solvent, is the contact angle between the solvent and MoS 2 sheet, and is the distance between MoS 2 sheet and substrate 3 . We used EG as the solvent since it has a large surface tension about 48 mN/m at room temperature 4 , as well as a good wettability with the MoS 2 surface (the contact angle between MoS 2 flake and EG is 58° as shown in Supplementary Figure 2e, inset). Since the SiO 2 nanocone is about 90 nm in height, the estimated capillary pressure !"# is about 5×10 ! Pa. The amount of pressure required to pull the center of MoS 2 sheet between two nanocones to contact the substrate can be estimated from !"# = 64 ! ! / ! , where ≈ 270 GPa is the Young's modulus of monolayer MoS 2 , t = 0.67 nm is monolayer MoS 2 thickness, = 490 nm is the width of the membrane (nanocone tip-to-tip distance), and ! ≅ 90 nm is the amount of vertical deformation. The required pressure is estimated to be !"# = 1×10 ! Pa, which is much smaller than the capillary pressure !"# that can be generated by EG evaporation. In other words, the capillary force is sufficient to deform the MoS 2 to contact the nanocone surface.

Supplementary Note 3: Comparison between strained and unstrained MoS 2
The AFM image of the nanocone substrate is shown in Supplementary Figure 3a Figure  4b displays the silicon Raman peak (around 521 cm -1 ) intensity image. As the nanocones are taller than the flat area, more silicon atoms are in the depth of focus of the Raman objective, resulting in higher Raman peak intensity. As such, the periodic nanocone array can be clearly visualized in the lower part of silicon Raman peak intensity mapping. Supplementary Figures 4cd show the scanning Raman images of E 2g ! and A 1g peak frequencies of MoS 2 , respectively, where bright color indicates higher frequency and dark color represents lower frequency. It is noted that lower frequency appears centered on nanocones while higher frequency appears between nanocones. In contrast, even higher frequency appears on the flat SiO 2 surface. Since tensile strain decreases the Raman peak frequencies of MoS 2 , one can see that MoS 2 on nanocones is more strained while that between nanocones is less strained, and that on the flat surface is least strained (or unstrained).

Supplementary Note 4: Scanning tunneling microscopy characterization
Scanning tunneling microscopy and spectroscopy (STM/STS) measurements were The STS raw I(V) measurements were smoothed using a locally weighted polynomial regression (LOESS) and dI/dV was calculated numerically using a two point central difference.
To extract the band gap from dI/dV accurately the curve was first normalized by calculating

Theoretical optical absorption spectra of strained monolayer MoS 2
The theoretical biaxial-strain-dependent optical absorption spectra were calculated by solving the Bethe-Salpeter equation 6 within the Tamm-Dancoff approximation. The key parameters used in the Bethe-Salpeter equation, including quasiparticle energies and screened-Coulomb interactions, were obtained from many-body perturbation theory with the Hedin's GW approximation [7][8][9] . All the calculations were performed using the Vienna Ab initio Simulation Package (VASP) 10,11 with plane-wave basis and the projector-augmented wave (PAW) method 12 .
We used a plane-wave cutoff of 350 eV, a Monkhorst-Pack k-point sampling 13 of 18×18×1, and an exchange correlation functional of the Perdew-Berke-Ernzerhof form 14 within the generalized gradient approximation 15,16 . All biaxially-strained configuration were fully relaxed with the maximal residual force of no more than 0.0001 eV/Å using density-functional theory calculations 17,18 . The calculation was carried out in a periodic supercell with a vacuum spacing of 20 Å along the z (plane normal) direction in order to reduce the spurious interaction between the neighboring unit cells. Although spin-orbit coupling was not included in the present calculations, the peak position and the strain-dependent peak shift of the first low energy exciton were expected to be minimal. The calculated optical absorption spectra of MoS 2 under average biaxial tensile strain bi from 0 to 1% are presented in Supplementary Figure 7a.

Theoretical Raman spectra of strained monolayer MoS 2
The theoretical biaxial-strain-dependent Raman spectra were calculated using first-principles density-functional perturbation theory implemented in the QUATUM-ESPRESSO package 19,20 with a plane-wave cutoff of 120 Rydberg, a Monkhorst-Pack k-point sampling of 12×12×1, and an exchange correlation functional of the Perdew-Zunger 21 form within the local density approximation. The spin-orbit coupling was not included. In addition, norm-conserving Hartwigsen-Goedecker-Hutter pseudopotentials 22 were used in order to take into account the core electrons and reduce the computational efforts. All biaxially-strained configuration were fully relaxed with a convergence criteria of 0.0001 a.u. for the maximal residual force. The calculation was carried out in a periodic supercell with a vacuum spacing of 20 Å along the z (plane normal) direction in order to reduce the spurious interaction between the neighboring unit cells. At the long wavelength limit, the degeneracy between longitudinal and transverse optical phonons is lifted due to the macroscopic electric field induced by infrared-active phonon modes, which leads to a splitting in the E 2g ! mode into the transverse optical (TO) and longitudinal optical (LO) modes, respectively 23 . For simplicity, we plot the average frequency of TO-and LO-E 2g ! modes in the manuscript. The calculated Raman spectra of monolayer MoS 2 under average biaxial tensile strain bi from 0% to 1% are shown in Supplementary Figure 7b.