  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.
