We investigate the properties of trions in transition-metal dichalcogenides (TMDCs) monolayers using the Gaussian expansion method (GEM) adapted to two-dimensional systems. Excitons and trions in monolayer TMDCs with the chemical composition ${MX}_2$ in the 2H phase are studied systematically. We computed the associated exciton and trion binding energies. We find, in addition to the known $J=0$ trion, the existence of a bound state with orbital angular momentum $J=1$. The results for $J=0$ are benchmarked against existing calculations from the stochastic variational method (SVM) and quantum Monte Carlo (QMC). Furthermore, we give further insight on the trion internal structure and geometry through their probability-density distributions, accounting for the effects of different materials. We also show that GEM—widely used in studies of strongly interacting few-body systems—is well adapted to allow comprehensive and computationally efficient investigations of trions in layered materials. In addition, we systematically explore the effect of strain and the dielectric environment on the $J=1$ trion predictions, illustrated for the ${\mathrm{MoS}}_2$ monolayer.

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• Excitons
• Few-body systems
• Trions
• Layered semiconductors
• Two-dimensional electron system
• Variational wave functional methods