Superconductor vortex spectrum of the Fermi arc metal in Weyl semimetals

The surface of a Weyl semimetal hosts open Fermi arcs that form closed contours with Fermi arcs on the opposite surface. The resulting 2D Fermi surface, when subjected to a magnetic field, exhibits characteristic quantum oscillations stemming from semiclassical cyclotron orbits that involve both bulk and surface travel and obey a subtle form of Bohr-Sommerfeld quantization conditions. In this work, we use similar semiclassical ideas to derive the superconductor vortex spectrum of this 2D metal. We first recall that each Weyl node produces a chiral Majorana fermion in the bulk inside the vortex. We then show that the vortex spectrum is governed by the total Berry phase acquired by a wavepacket traversing a closed orbit consisting of Fermi arcs on opposite surfaces and the bulk chiral modes. In particular, the vortex gap closes and reopens when the total Berry phase sweeps through $(2n+1)\pi$ . The Berry phase contributed by the chiral modes depends on the vortex orientation relative to the separation between the Weyl nodes. We, therefore, predict characteristic features in the vortex tilt-dependence of the local density of states that can be probed by standard scanning tunneling measurements.