Vortex-Bound States in Nodal Loop Semimetals

Nodal semimetals host one-dimensional band loops in momentum space, giving rise to unique topological and transport phenomena distinct from point-node Weyl or Dirac systems. In this work, we investigate the superconducting vortex spectrum in a nodal loop semimetal using a  framework that incorporates Berry phase effects. 

Unlike Weyl semimetals, where chiral modes dominate, the nodal loop geometry introduces extended drumhead surface states that participate in closed semiclassical orbits involving both surface and bulk propagation. We show that the vortex-bound state spectrum is governed by the total Berry phase accumulated along these hybrid orbits, which includes contributions from drumhead states and bulk modes.  We predict a strong dependence of the vortex spectrum on the orientation of the vortex relative to the nodal loop plane, providing a distinctive experimental signature accessible via scanning tunneling spectroscopy. Our results establish a direct link between nodal-loop topology and superconducting vortex physics, offering a new route to probe topological superconductivity in loop semimetals.