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The effect of anisotropy in the energy spectrum on the binding energy andstructural properties of excitons, trions, and biexcitons is investigated. Tothis end we employ the stochastic variational method with a correlated Gaussianbasis. We present results for the binding energy of different excitoniccomplexes in black phosphorus (bP) and TiS$_3$ and compare them with recentresults in the literature when available, for which we find good agreement. Thebinding energies of excitonic complexes in bP are larger than those in TiS$_3$.We calculate the different average interparticle distances in bP and TiS$_3$and show that excitonic complexes in bP are strongly anisotropic whereas inTiS$_3$ they are almost isotropic, even though the constituent particles havean anisotropic energy spectrum. This is also confirmed by the correlationfunctions.

Excitonic complexes in anisotropic atomically thin two-dimensional materials: black phosphorus and TiS$_3$