  Band inversions are key to stabilising a variety of novel electronic states
in solids, from topological surface states in inverted bulk band gaps of
topological insulators to the formation of symmetry-protected three-dimensional
Dirac and Weyl points and nodal-line semimetals. Here, we create a band
inversion not of bulk states, but rather between manifolds of surface states.
We realise this by aliovalent substitution of Nb for Zr and Sb for S in the
ZrSiS family of nonsymmorphic semimetals. Using angle-resolved photoemission
and density-functional theory, we show how two pairs of surface states, known
from ZrSiS, are driven to intersect each other in the vicinity of the Fermi
level in NbGeSb, as well as to develop pronounced spin-orbit mediated spin
splittings. We demonstrate how mirror symmetry leads to protected crossing
points in the resulting spin-orbital entangled surface band structure, thereby
stabilising surface state analogues of three-dimensional Weyl points. More
generally, our observations suggest new opportunities for engineering
topologically and symmetry-protected states via band inversions of surface
states.
