Topological nodal surface semimetal states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> compounds <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">As</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Sb</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Bi</mml:mi><mml:mo>)</mml:mo></mml:math>

Topological nodal surface semimetals are a class of materials characterized by degenerate conduction and valence bands on closed nodal surfaces in the Brillouin zone that are protected by crystalline symmetries. These materials attract considerable attention for exhibiting intriguing, topologically driven quantum phenomena that are fundamentally interesting and practically useful. Here we identify by systematic ab initio calculations and topological quantum chemistry analysis prominent topological nodal surface semimetal states in ${\mathrm{Sr}}_{5}{X}_{3}(X$ = As, Sb, Bi) compounds in hexagonal $P{6}_{3}/mcm$ (${D}_{6h}^{3}$) symmetry. These nodal surface states comprise degenerate the highest occupied band and the lowest unoccupied band that overlap in a single band at the ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ plane and are protected by time-reversal and nonsymmorphic twofold screw rotation symmetry. Topological quantum chemistry theory analysis reveals a twofold band degeneracy without spin-orbit coupling at the high-symmetry and generic $\mathbit{k}$ points located at the ${k}_{z}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ plane, which is formed by the bands of (${\mathrm{A}}_{1}\ensuremath{\bigoplus}{\mathrm{B}}_{2})@6g$ band representations. Since the compounds studied here have been already experimentally synthesized, the present results have an immediate impact on the experimental detection and characterization of the theoretically predicted topological physics.