Möbius topological superconductivity in UPt${}_3$

Abstract

Intensive studies for more than three decades have elucidated multiple superconducting phases and odd-parity Cooper pairs in a heavy fermion superconductor UPt${}_3$. We identify a time-reversal invariant superconducting phase of UPt${}_3$ as a recently proposed topological nonsymmorphic superconductivity. Combining the band structure of UPt${}_3$, order parameter of $E_{2u}$ representation allowed by $P{6}_3/mmc$ space group symmetry, and topological classification by $K$-theory, we demonstrate the nontrivial $Z_2$-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.

21 pages, 13 figures, 6 tables

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