Non-Abelian Majorana modes protected by an emergent second Chern number

TL;DR

This paper proposes a method to realize non-Abelian Majorana modes in a Weyl semimetal with a PDW phase, protected by an emergent second Chern number, enabling potential applications in topological quantum computing.

Contribution

It introduces a novel topological phase hosting non-Abelian Majorana modes protected by an emergent second Chern number in a synthetic 4D space.

Findings

Vortex lines in the PDW phase host chiral Majorana modes.

These modes obey non-Abelian loop-braiding statistics.

The modes are protected by an emergent second Chern number.

Abstract

The search for topological superconductors and non-Abelian Majorana modes ranks among the most fascinating topics in condensed matter physics. There now exist several fundamental superconducting phases which host symmetry protected or chiral Majorana modes. The latter, namely the chiral Majorana modes are protected by Chern numbers in even dimensions. Here we propose to observe novel chiral Majorana modes by realizing Fulde-Ferrell-Larkin-Ovchinnikov state, i.e. the pairing density wave (PDW) phase in a Weyl semimetal which breaks time-reversal symmetry. Without symmetry protection, the 3D gapped PDW phase is topologically trivial. However, a vortex line generated in such phase can host chiral Majorana modes, which are shown to be protected by an emergent second Chern number of a synthetic 4D space generalized from the PDW phase. We further show that these chiral modes in the vortex rings obey 3D non-Abelian loop-braiding statistics, which can be applied to topological quantum computation.