Three-Dimensional Majorana Fermions in Chiral Superconductors

TL;DR

This paper classifies and analyzes three-dimensional Majorana fermions in chiral superconductors with strong spin-orbit coupling, highlighting their topological properties, experimental signatures, and potential material realizations.

Contribution

It provides a comprehensive symmetry and topology-based classification of 3D Majorana quasiparticles in chiral superconductors, linking their existence to non-unitary pairing and surface states.

Findings

Majorana quasiparticles are spin-non-degenerate and occur near spin-selective point nodes.

NMR spin relaxation rate is suppressed for nuclear spins aligned with nodal directions.

Majorana nodes have nontrivial topology and produce surface arcs.

Abstract

Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs$_4$Sb$_{12}$ and related materials as promising candidates for non-unitary chiral superconductors hosting three-dimensional Majorana fermions.