Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment

Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of ${\mathrm{MoS}}_2, {\mathrm{MoSe}}_2, {\mathrm{MoTe}}_2, {\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$ are studied by means of density functional theory and path-integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar to or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex “dissociates” to a biexciton rather than to an exciton and a trion.

Figure 1

(a) Schematic illustration of the system geometry. (b) Illustration of the exciton, trion, and biexciton systems constructed from the electrons on the conduction band and holes in the valence band. (c) Effective interaction potential in the case of ${\varepsilon }_{\mathrm{env}}=1, 3.9$ (silica), and 10 (sapphire), as compared to Coulomb interaction in homogeneous system scaled by $\kappa$.

Figure 2

Particle coordinate distributions in the case of (a) exciton, (b) trion, and (c) biexciton. In (a), the hole is fixed at the origin. In (b) and (c), the $x$ axis is chosen to pass along two particles as illustrated. Origin is at the center of mass of these two particles. In (c), the distributions for electron-electron distance larger (solid lines) and smaller (dashed lines) than 40 bohrs are distinguished.

Figure 3

(a) Calculated exciton binding energies as a function of $\kappa$ together with error bars ($2\sigma$). Dotted line is guide for the eye. Two fits are also shown: The coefficients for the first (solid line) are $a=-325$ meV and $b=853$ meV. The second fit (dashed line) was proposed in Ref. [22]. (b) Binding energies and error bars for trion, biexciton, and exciton-trion complex as a function of $\kappa$.

Figure 4

Selected average interparticle distances for exciton (a), trion (b), biexciton (c), and exciton-trion complex (d) in ${\mathrm{MoS}}_2$ as a function of $\kappa$.