Intensive studies for more than three decades have elucidated multiple superconducting phases and odd-parity Cooper pairs in a heavy fermion superconductor ${\mathrm{UPt}}_3$. We identify a time-reversal invariant superconducting phase of ${\mathrm{UPt}}_3$ as a recently proposed topological nonsymmorphic superconductivity. Combining the band structure of ${\mathrm{UPt}}_3$, order parameter of $E_{2\mathrm{u}}$ representation allowed by $P{6}_3/mmc$ space group symmetry, and topological classification by $K$ theory, we demonstrate the nontrivial ${\mathbb{Z}}_2$-invariant of three-dimensional DIII class enriched by glide symmetry. Correspondingly, double Majorana cone surface states appear at the surface Brillouin zone boundary. Furthermore, we show a variety of surface states and clarify the topological protection by crystal symmetry. Majorana arcs corresponding to tunable Weyl points appear in the time-reversal symmetry broken B phase. Majorana cone protected by mirror Chern number and Majorana flat band by glide-winding number are also revealed.

• Received 10 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.224514