Majorana Fermions in Superconductor Vortices in Time-Reversal Symmetric Weyl Semimetals


Many clever routes to Majorana fermions (MF) have been discovered by exploiting the interplay between superconductivity and band topology in metals and insulators. However, realizations of Superconductor vortex modes from time-reversal symmetric Weyl semimetal (TWSM) have been largely less explored. A TWSM hosts quadruplets of Weyl nodes, where a pair of Weyl nodes of same chirality are related by time-reversal symmetry, and a pair of opposite chirality Weyl nodes are joined by surface projections of bulk Weyl nodes i.e. Fermi-arcs. The vortex core of a type-II superconductor hosts discrete energy levels that carry critical information about the normal state material. This dissertation is focused on emergent excitations of the Weyl nodes and surface Fermi-arcs of TWSM. We ask, ”under what conditions do superconductor vortices in TWSMs trap Majorana fermions on the surface?”. The vortex induces Fermi geodesics on the surface and it depends on the Fermiarc structure and proximity of Weyl nodes. A surface MF exist if kz-planes have a 0-chirality and there is an number of Fermi geodesic loop on the surface. If kz-planes have net-chirality, a chiral MFs will emerge per Weyl node and the surface will have Fermi geodesic arcs. On the surface, a Fermi-arc is a metallic system whose dimensionality is not well defined. Both edges of a Fermi-arc merge with the surface projections of the bulk Weyl nodes. This bizarre structure places Fermi-arcs beyond a conventional Hamiltonian description; ”If the Fermi-arcs develop gapped superconductivity, what is the energy spectrum of such a vortex?”. The vortex states form cyclotron-like closed orbits consisting of Fermi arcs on opposite surfaces connected by uni-direction bulk paths whose spectrum is governed by the total Berry phase acquired by a wavepacket along this orbit and has characteristic dependencies on the Berry phases and penetration depth of the Fermi arcs, bulk Weyl node locations, vortex orientation and sample thickness. The zero-point energy can be eliminated by tilting the vortex, yielding a pair of non-local Majorana fermions, while the thickness dependence disappears at a certain vortex orientation “magic angle”. Interestingly many lattice models and materials, non-local Majorana fermions exist precisely at the magic angle.



Majorana Fermion, Weyl Semimetal, Topological superconductor, Weyl Fermion