  We introduce and study the notion of atomic sheaves and complexes on
higher-dimensional hyper-K\"ahler manifolds and show that they share many of
the intriguing properties of simple sheaves on K3 surfaces. For example, we
prove formality of the dg algebra of derived endomorphisms for stable atomic
bundles. We further demonstrate the characteristics of atomic objects by
studying atomic Lagrangian submanifolds. In the appendix, we prove
non-existence results for spherical objects on hyper-K\"ahler manifolds.
