UPt${}_3$ as a Topological Crystalline Superconductor

Abstract

We investigate the topological aspect of the spin-triplet $f$-wave superconductor UPt${}_3$ through microscopic calculations of edge- and vortex-bound states based on the quasiclassical Eilenberger and Bogoliubov-de Gennes theories. It is shown that a gapless and linear dispersion exists at the edge of the $ab$-plane. This forms a Majorana valley, protected by the mirror chiral symmetry. We also demonstrate that, with increasing magnetic field, vortex-bound quasiparticles undergo a topological phase transition from topologically trivial states in the double-core vortex to zero-energy states in the normal-core vortex. As long as the $d$-vector is locked into the $ab$-plane, the mirror symmetry holds the Majorana property of the zero-energy states, and thus UPt${}_3$ preserves topological crystalline superconductivity that is robust against the crystal field and spin-orbit interaction.

5 pages, 2 figures

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Topological Phase Transition without Gap Closing
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• The Fermi surface and f-valence electron count of UPt3
• Topological Fermi arcs in superfluid ${}^3$He

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