Binding energies and spatial structures of small carrier complexes in monolayer transition-metal dichalcogenides via diffusion Monte Carlo

Ground-state diffusion Monte Carlo is used to investigate the binding energies and intercarrier radial probability distributions of excitons, trions, and biexcitons in a variety of two-dimensional transition-metal dichalcogenide materials. We compare these results to approximate variational calculations, as well as to analogous Monte Carlo calculations performed with simplified carrier interaction potentials. Our results highlight the successes and failures of approximate approaches as well as the physical features that determine the stability of small carrier complexes in monolayer transition-metal dichalcogenide materials. Lastly, we discuss points of agreement and disagreement with recent experiments.

Figure 1

(a) Radial probability distributions for the distance $r_{eh}$ of an exciton in ${\mathrm{MoS}}_2$. (b) Radial probability distributions for the distances $r_{eh}$ and $r_{ee}$ of a negative trion in ${\mathrm{MoS}}_2$. (c) Radial probability distributions for the distances $r_{eh},r_{ee}$, and $r_{hh}$ of a biexciton in ${\mathrm{WSe}}_2$. For the DMC calculation, the curves for $r_{ee}$ and $r_{hh}$ coincide because the electron and hole effective masses are taken to be equal.

Figure 2

(a) Radial probability distributions for the distances $r_{eh}$ and $r_{ee}$ in the trion $\left({\mathrm{X}}^{-}\right)$ and biexciton (XX) using a Keldysh form for the intercarrier potential. (c) The same $r_{ee}$ distributions as in panel (a), but the relocated repulsive weight is shaded. (b), (d) The same as in panels (a), (c) but using a Coulombic form for the intercarrier potential.