Representation-protected topology of spin-singlet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math>-wave superconductors

We show that spin-singlet $s$-wave multiband superconductors have a topological phase protected by rotation symmetry and time-reversal symmetry without spin-orbit coupling in two and three dimensions. This topological phase, an example of a representation-protected topological phase, has a ${\mathbb{Z}}_{2}$ topological index and is stable as long as the bands at the Fermi energy are formed by a doublet of orbital states with finite angular momenta. In the limit of weak superconducting pair potential, the ${\mathbb{Z}}_{2}$ index gives a Fermi-surface formula and is related to the winding number of three-dimensional strong topological superconductors of class CI. We present a model of a topological ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave superconductor that has gapless surface states with a quadratic dispersion and suggest a connection with iron-based superconductors.