  Two common difficulties in the design of topological quantum materials are
that the desired features lie too far from the Fermi level and are spread over
a too large energy range. Doping-induced states at the Fermi level provide a
solution, where non-trivial topological properties are enforced by the
doping-reduced symmetry. To show this, we consider a regular placement of
dopants in a lattice of space group (SG) 176 (P6$\text{}_3$/m), which reduces
the symmetry to SG 143 (P3). Our two- and four-band models feature
symmetry-enforced double Weyl points at $\Gamma$ and A with Chern bands for
$k_z\neq 0,\pi$, Van Hove singularities, nontrivial multiband quantum geometry
due to mixed orbital character, and a singular flat band. The excellent
agreement with density-functional theory (DFT) calculations on copper-doped
lead apatite ('LK-99') provides evidence that minimal topological bands at the
Fermi level can be realized in doped materials.
