  In this work, we present a model of the surface states of nonsymmorphic
semimetals. These are derived from surface mass terms that lift the high
degeneracy imposed in the band structure by the nonsymmorphic bulk symmetries.
Reflecting the reduced symmetry at the surface, the bulk bands are strongly
modified. This leads to the creation of two-dimensional floating bands, which
are distinct from Shockley states, quantum well states or topologically
protected surface states. We focus on the layered semimetal ZrSiS to clarify
the origin of its surface states. We demonstrate an excellent agreement between
DFT calculations and ARPES measurements and present an effective four-band
model in which similar surface bands appear. Finally, we emphasize the role of
the surface chemical potential by comparing the surface density of states in
samples with and without potassium coating. Our findings can be extended to
related compounds and generalized to other crystals with nonsymmorphic
symmetries.
