Brightening of dark excitons in ${\mathrm{WS}}_{2}$ via tensile strain-induced excitonic valley convergence (2024)

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  Figure 1

  (a)Schematic showing various excitonic species near the electronic dispersions in the $K$ and $\mathrm{\Lambda }$ valleys. Arrows indicate the spin orientations. (b)Field emission scanning electron microscope (FESEM) image of the C-99 nanotextured sample (side view). (c)FESEM image of the C-99 substrate as viewed from the top (scale bar is 20nm). The yellow line shows the interpillar separation $l$. (d)Schematic of the substrate with ML ${\mathrm{WS}}_2$ placed on top.

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  Figure 2

  Temperature-dependent PL spectra of ML ${\mathrm{WS}}_2$ placed on top of (a)C-99 (b)C-48, and (c)C-132 substrates. All the spectra are recorded at an excitation power of $\sim 100\mu \mathrm{W}$. The spectra are shifted along the $y$ axis for clarity. (d)The integrated intensity $I$ of ${\mathrm{X}}^D$ as a function of excitation power $P$ fitted with the relation $I\propto P^{\alpha }$, where $\alpha$ is the exponent. (e) Temperature dependence of the peak position of ${\mathrm{X}}^0$ (black solid circles) and ${\mathrm{X}}^D$(blue solid squares); the temperature dependence of ${\mathrm{X}}^0$ is fitted with Eq.(1) (red line). (f) FWHM of ${\mathrm{X}}^0$ as a function of temperature fitted with Eq.(2) (red line).

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  Figure 3

  (a)Raman spectra of ML ${\mathrm{WS}}_2$ placed on top of a C-99 substrate at 77K. Various peaks are labeled according to Ref.[35]. The main vibrational modes $E^{\prime }$ and $A_1{}^{\prime }$ are shown in the schematic. The blue and yellow balls represent tungsten and sulfur atoms, respectively. Anomalous behavior of the $E^{\prime }$ peak (b)position and (c)width as a function of temperature. Simulated ${\omega }_{\mathrm{ph}}$ and ${\gamma }_{\mathrm{ph}}$ are shown in the insets of (b)(blue curve) and (c)(green curve), respectively. $\gamma \left(T\right)={\gamma }_{\mathrm{ph}}+{\gamma }_{e\text{-ph}}$ (red curve) is simulated in the inset of (c).

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  Figure 4

  (a)DFT computed electronic band structure of ML ${\mathrm{WS}}_2$ with different strain values. (b)Schematic showing the $E^{\prime }$ phonon mediated scattering of the bright $K-K$ excitons to dark $K-\mathrm{\Lambda }$ excitons due to tensile strain. The $K-\mathrm{\Lambda }$ excitons then decay to a virtual state (dotted violet line marked as VS) inside the light cone (shaded area) by emitting phonons and finally recombine radiatively from the VS by emitting photons. (c)$\mathrm{\Delta }E$ as a function of strain on ML ${\mathrm{WS}}_2$. (d)Calculated phonon dispersion (left panel) and phonon density of states (DOS; right panel). $\nu$ represents the phonon band index. (e) Mean peak position of ${\mathrm{X}}^{-}$ in ML ${\mathrm{WS}}_2$ on top of ${\mathrm{SiO}}_2$/Si (flat) and C-99 extracted from the PL map. (f) Mean peak position of ${\mathrm{X}}^0$ in ML ${\mathrm{WS}}_2$ on top of C-48, C-99, and C-132 extracted from the PL map. The normal distribution and the raw data points are also shown.

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  Figure 5

  (a)and (b)Calculated $g_{mn}^{\nu }$ values for two degenerate $E^{\prime }$ phonon modes with $\nu =6$ and 7, respectively, which are responsible for the scattering of electrons from $\mathrm{CBM}+1$ at $K$ to CBM at the $\mathrm{\Lambda }$ valley. (c)Line cut along $k=K$ from (a)and (b)to show $g_{mn}^{\nu }$ along the phonon momentum $q$, in the $\mathrm{\Gamma }\to M\to K\to \mathrm{\Gamma }$ direction. The blue dashed line shows the $g_{mn}^{\nu }$ of $q=K-\mathrm{\Lambda }$ at $k=K$. (d)TRPL measurement on ML ${\mathrm{WS}}_2$ at 60K to determine the lifetime of ${\mathrm{X}}^D$.

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