  Recent studies on excitons in two-dimensional materials have been widely
conducted for their potential usages for novel electronic and optical devices.
Especially, sophisticated manipulation techniques of quantum degrees of freedom
of excitons are demanded. In this paper we propose a technique of forming an
optical dipole trap for excitons in graphane, a two-dimensional wide gap
semiconductor, based on first principles calculations. We develop a first
principles method to evaluate the exciton transition dipole matrix and combine
it with the density functional theory and GW+BSE calculations. We reveal that
in graphane the huge exciton binding energy and the large dipole moments of
Wannier-like excitons enable us to induce the dipole trap of the order of meV
depth and $\mu$m width. This work opens a new way to control light-exciton
interacting systems based on a newly developed numerically robust ab initio
calculations.
