Low-dimensional materials differ from their bulk counterpart in many respects. In particular, the screening of the Coulomb interaction is strongly reduced, which can have important consequences such as the significant increase of exciton binding energies. In bulk materials the binding energy is used as an indicator in optical spectra to distinguish different kinds of excitons, but this is not possible in low-dimensional materials, where the binding energy is large and comparable in size for excitons of very different localization. Here we demonstrate that the exciton band structure, which can be accessed experimentally, instead provides a powerful way to identify the exciton character. By comparing the ab initio solution of the many-body Bethe-Salpeter equation for graphane and single-layer hexagonal BN, we draw a general picture of the exciton dispersion in two-dimensional materials, highlighting the different role played by the exchange electron-hole interaction and by the electronic band structure. Our interpretation is substantiated by a prediction for phosphorene.
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