Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability.

Figure 1

Binding energies of trions at different mass ratios against rescaled in-plane polarizability $r_{*}$. The inset shows the binding energies of excitons against rescaled $r_{*}$. The lines show the fitting formulas of Eqs. (5) and (3).

Figure 2

Contact electron-hole pair densities of trions and excitons against rescaled in-plane polarizability $r_{*}$ at different mass ratios. The black curve is the fitting formula for an exciton, Eq. (4), while the yellow curve is the fitting formula for a trion, Eq. (6). The inset shows the (much smaller) contact pair density between the electrons in a negative trion and the fitting curve (in blue) of Eq. (7).

Figure 3

Binding energies of biexcitons against rescaled in-plane polarizability $r_{*}$ at different mass ratios. The lines show the fitting formula of Eq. (8). The left inset shows the electron-hole contact pair densities for a biexciton and the approximation formula [black curve, Eq. (9)]. Electron-electron contact pair densities for a biexciton are shown in the right inset, together with the approximation formula of Eq. (10).

Figure 4

Ratio of negative-trion binding energy to biexciton binding energy $({\mathcal{E}}_{\mathrm{T}}/{\mathcal{E}}_{\mathrm{XX}})$ as a function of rescaled in-plane polarizability $r_{*}$ and rescaled mass ratio. The thick black line shows the curve ${\mathcal{E}}_{\mathrm{T}}={\mathcal{E}}_{\mathrm{XX}}$. Experimentally relevant points for TMDCs are shown using symbols from Table 1.

Figure 5

Expected photoemission spectrum of a 2D semiconductor showing peaks for exciton (X), trion (${\mathrm{X}}^{-}$), and biexciton (XX) complexes. $\mathrm{\Delta }$ is the quasiparticle band gap.