We present a variational-empirical model describing the magnetic-field dependence of exciton energies in two-dimensional semiconductors. We focus on Rydberg excitons in monolayer transition metal dichalcogenides (${\mathrm{MoS}}_2, {\mathrm{MoSe}}_2, {\mathrm{MoTe}}_2, {\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$) encapsulated by hexagonal boron nitride. Using a variational parameter, the model yields exciton binding energies at zero magnetic field in reasonable agreement with experimental results from helicity-resolved magnetophotocurrent spectroscopy. Adding two empirical parameters, the model is able to predict the magnetic-field dependence of exciton energies. The model describes the diamagnetic shift and gives exciton radii as well as diamagnetic coefficients in reasonable agreement with experimental data from magneto-optical spectroscopy measurements.

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• Excitons
• 2-dimensional systems
• Transition metal trichalcogenides
• Variational wave functional methods