  We suggest the tried approach of impurity band engineering to produce flat
bands and additional nodes in Dirac materials. We show that surface impurities
give rise to nearly flat impurity bands close to the Dirac point. The
hybridization of the Dirac nodal state induces the splitting of the surface
Dirac nodes and the appearance of new nodes at high-symmetry points of the
Brillouin zone. The results are robust and not model dependent: the
tight-binding calculations are supported by a low-energy effective model of a
topological insulator surface state hybridized with an impurity band. Finally,
we address the effects of electron-electron interactions between localized
electrons on the impurity site. We confirm that the correlation effects, while
producing band hybridization and Kondo effect, keep the hybridized band flat.
Our findings open up prospects for impurity band engineering of nodal
structures and flat-band correlated phases in doped Dirac materials.
