Superconductor vortex spectrum from Fermi arc states in Weyl semimetals

Vortices in type-II superconductors host discrete energy levels that carry critical information about the normal state and pairing symmetry. For example, ordinary metals produce equally spaced levels with finite zero-point energy, whereas massless Dirac metals yield exotic Majorana fermions at precisely zero energy. Weyl semimetals are gapless topological materials de ned by accidental band intersections or Weyl nodes in the bulk and a bizarre surface metal composed of open Fermi arcs instead of closed Fermi surfaces. We ask, "what is the vortex spectrum of a superconductor that descends from a Weyl semimetal?" Restricting to non-magnetic Weyl semimetals and superconductivity that is fully gapped when uniform, we show that the vortex spectrum is - contrary to previous results - generically gapped. At low energies, it is determined by the total Berry phase accrued by a wavepacket traversing closed orbits consisting of Fermi arcs on opposite surfaces connected by one-way bulk conduits. It is expected to produce periodic oscillations in physical properties such as the specific heat and tunneling conductance - the latter featuring 4e2/h quantization - as the vortex is tilted. Miraculously, tilting also transmutes the vortices between bosonic, fermionic, and supersymmetric, with the last category hosting a pair of nonlocal Majorana fermions. The spectrum becomes immune to the slab thickness at tilts that we dub "magic angles". In many

models and materials, nonlocal Majorana fermions and supersymmetry exist precisely at these tilts. We propose the well-known Weyl semimetals, NbP and TaP, as candidates for realizing our predictions.