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The electronic and structural properties of excitons and trions in monolayertransition metal dichalcogenides are investigated using both a multiband and asingle-band model. In the multiband model we construct the excitonicHamiltonian in the product base of the single-particle states at the conductionand valence band edges. We decouple the corresponding energy eigenvalueequation and solve the resulting differential equation self-consistently, usingthe finite element method (FEM), to determine the energy eigenvalues and thewave functions. As a comparison, we also consider the simple single-band modelwhich is often used in numerical studies. We solve the energy eigenvalueequation using the FEM as well as with the stochastic variational method (SVM)in which a variational wave function is expanded in a basis of a large numberof correlated Gaussians. We find good agreement between the results of bothmethods, as well as with other theoretical works for excitons, and we alsocompare with available experimental data. For trions the agreement between bothmethods is not as good due to our neglect of angular correlations when usingthe FEM. Finally, when comparing the two models, we see that the presence ofthe valence bands in the mutiband model leads to differences with thesingle-band model when (interband) interactions are strong.

physical review. b./physical review. b

Excitons and trions in monolayer transition metal dichalcogenides: A  comparative study between the multiband model and the quadratic single-band  model