Excited-State Trions in Monolayer ${\mathrm{WS}}_2$

We discover an excited bound three-particle state, the $2s$ trion, appearing energetically below the $2s$ exciton in monolayer ${\mathrm{WS}}_2$, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the $2s$ trion (22 meV) is smaller compared to the $1s$ intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the $1s$ and $2s$ trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Figure 1

(a) Optical absorption spectrum of a hBN-encapsulated ${\mathrm{WS}}_2$ monolayer on sapphire substrate measured at a temperature $T=5\mathrm{K}$ (orange) along with the fitted curve (black, see Supplemental Material [38] for details). The ground ($n=1$) state of the $A$ exciton, $X_A^{1s}$, the intravalley and intervalley trions $T_{A1}^{1s}$ and $T_{A2}^{1s}$, respectively, are clearly identified. Additionally, excited ($n=2$) states of $A$ excitations $X_A^{2s}$ and $T_A^{2s}$ are visible. (b) Experimental and fitted spectra for ($n=1$) states, where shaded green and blue regions represent the contributions from trions and excitons, respectively. (c) Zoomed-in view highlighting ($n=2$) excited state trions $T_A^{2s}$ and excitons $X_A^{2s}$ along with the fitted spectrum. (d),(e) Calculated optical absorption of neutral excitons (shaded blue) and positive (dashed-red line) and negative trions (shaded green). The bound excitations are labeled, while the unlabeled excitations (red or black bars) represent scattering states which are not fully converged (and thus excluded in the plotted curves). We use an artificial Lorentzian broadening with a width of 10 meV. Left panels of (f) and (g) display top views of the calculated probability distribution of the $1s$ [in (f)] and $2s$ [in (g)] exciton and trion states, as described in the text and Supplemental Material [38]. The right side represents cross-sectional views around the mid vertical of the spatial distribution displayed on the left.

Figure 2

(a) Absorption spectrum around the ($n=1$) A exciton measured as a function of temperature ($T=5–300\mathrm{K}$). The spectra are shifted along the $\mathit{y}$ axis for clarity. The spectral line shapes are fitted as described in the text. The transition energies, FWHM linewidths, and oscillator strength parameters of the $1s$ intravalley ($T_{A1}^{1s}$) and intervalley ($T_{A2}^{1s}$) trions, and $1s$ exciton ($X_A^{1s}$) are plotted in (b), (c), and (d), respectively. Notably, in (d), both $1s$ trions lose oscillator strength, while the $1s$ exciton gains strength, as the temperature is increased.

Figure 3

(a) Absorption spectrum around the ($n=2$) A exciton measured as a function of temperature ($T=5–300\mathrm{K}$). The spectra are shifted along the $\mathit{y}$ axis for clarity. The spectral line shapes are fitted as described in the text. The transition energies, FWHM linewidths, and oscillator strength parameters of the $2s$ trion $T_A^{2s}$, and the $2s$ exciton $X_A^{2s}$ are plotted in (b),(c), and (d), respectively. Notably in (d), $T_A^{2s}$ loses oscillator strength, while the $X_A^{2s}$ gains strength, as the temperature is increased. This is trend is accompanied by an initial reduction of the $X_A^{2s}$ linewidth shown in (c).