UPt$_3$ as a Topological Crystalline Superconductor

TL;DR

This paper explores the topological properties of UPt$_3$, revealing Majorana states at edges and vortices, and demonstrating a magnetic field-induced topological phase transition, establishing UPt$_3$ as a topological crystalline superconductor.

Contribution

It provides a microscopic analysis showing UPt$_3$ hosts Majorana states protected by mirror symmetry, and identifies a topological phase transition in vortex-bound states.

Findings

Existence of a Majorana valley at the edge of UPt$_3$

Topological phase transition in vortex-bound quasiparticles under magnetic field

Robustness of topological states against crystal field and spin-orbit interaction

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.