  The large tunability of band gaps and optical absorptions of armchair MoS$_2$
nanoribbons of different widths under bending is studied using density
functional theory and many-body perturbation GW and Bethe-Salpeter equation
approaches. We find that there are two critical bending curvatures, and the
non-edge and edge band gaps generally show a non-monotonic trend with bending.
The non-degenerate edge gap splits show an oscillating feature with ribbon
width n, with a period delta_n=3, due to quantum confinement effects. The
complex strain patterns on the bent nanoribbons control the varying features of
band structures and band gaps that result in varying exciton formations and
optical properties. The binding energy and the spin singlet-triplet split of
the exciton forming the lowest absorption peak generally decrease with bending
curvatures. The large tunability of optical properties of bent MoS$_2$
nanoribbons is promising and will find applications in tunable optoelectronic
nanodevices.
