Exciton complexes in low dimensional transition metal dichalcogenides

We examine the excitonic properties of layered configurations of low dimensional transition metal dichalcogenides (LTMDCs) using the fractional dimensional space approach. The binding energies of the exciton, trion and biexciton in LTMDCs of varying layers are analyzed, and linked to the dimensionality parameter $\alpha$, which provides insight into critical electro-optical properties (relative oscillator strength, absorption spectrum, exciton-exciton interaction) of the material systems. The usefulness of $\alpha$ is highlighted by its independence of the physical mechanisms underlying the confinement effects of geometrical structures. Our estimates of the binding energies of exciton complexes for the monolayer configuration of transition metal dichalcogenides suggest a non-collinear structure for the trion and a positronium-molecule-like square structure for the biexciton.