In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial—tens of teslas or more—due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer $${{\rm{MoS}}}_{2},{{\rm{MoSe}}}_{2},{{\rm{MoTe}}}_{2}$$ MoS 2 , MoSe 2 , MoTe 2 , and $${{\rm{WS}}}_{2}$$ WS 2 in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton’s $$1s$$ 1 s ground state but also its excited $$2s,3s,\ldots ,ns$$ 2 s , 3 s , … , n s Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

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