Three-Dimensional Majorana Fermions in Chiral Superconductors

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.

12 pages, 3 figures + appendices; published version

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• Complete classification of band nodal structures
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• Topology and symmetry of surface Majorana arcs in cyclic superconductors
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• Broken time-reversal symmetry in superconducting Pr${}_{1-x}$La${}_x$Pt${}_4$Ge${}_{12}$
• Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2
• Topological Anomalous Skin Effect in Weyl Superconductors
• Spontaneous vortex-antivortex lattice and Majorana fermions in rhombohedral graphene
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• Majorana fermion arcs and the local density of states of UTe${}_2$
• Spontaneous magnetization in unitary superconductors with time reversal symmetry breaking
• Topological gapless points in superconductors: From the viewpoint of symmetry
• The Future of the Correlated Electron Problem
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Visualizing the Odd-parity Superconducting Order Parameter and its Quasiparticle Surface Band in UTe2
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Pairing-induced Momentum-space Magnetism and Its Implication In Optical Anomalous Hall Effect In Chiral Superconductors