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External fields are a powerful tool to probe optical excitations in amaterial. The linear energy shift of an excitation in a magnetic field isquantified by its effective g-factor. Here we show how exciton g-factors andtheir sign can be determined by converged first principles calculations. Weapply the method to monolayer excitons in semiconducting transition metaldichalcogenides and to interlayer excitons in MoSe$_2$/WSe$_2$ heterobilayersand obtain good agreement with recent experimental data. The precision of ourmethod allows to assign measured g-factors of optical peaks to specifictransitions in the band structure and also to specific regions of the samples.This revealed the nature of various, previously measured interlayer excitonpeaks. We further show that, due to specific optical selection rules, g-factorsin van der Waals heterostructures are strongly spin- and stacking-dependent.The calculation of orbital angular momenta requires the summation over hundredsof bands, indicating that for the considered two-dimensional materials thebasis set size is a critical numerical issue. The presented approach canpotentially be applied to a wide variety of semiconductors.

Exciton g-factors of van der Waals heterostructures from first principles calculations