Topologically protected emergent Fermi surface in an Abrikosov vortex lattice

We show that a three-dimensional (3D), fully gapped type-II superconductor can feature emergent in-gap Fermi surfaces of Caroli--de Gennes-Matricon (CdGM) quasiparticles in the presence of an Abrikosov vortex lattice. In particular, these CdGM Fermi surfaces manifest in the emergent 3D band structure enabled by the intervortex tunneling physics, and their stability is guaranteed by both ${\mathbb{Z}}_{2}$ and $2\mathbb{Z}$ topological charges. By developing an effective analytical theory, we find that each vortex line carrying a one-dimensional nodal dispersion is a sufficient condition for the vortex lattice to form CdGM Fermi surfaces. Following this prediction, in-gap CdGM Fermi surfaces are numerically confirmed in a microscopic vortex-lattice simulation of a superconducting Dirac semimetal with an $s$-wave spin-singlet pairing, which is directly applicable to a large class of type-II superconductors such as LiFeAs. Remarkably, the CdGM Fermi surfaces persist even when the normal state is deformed to a doped insulator of trivial band topology. Our work establishes the vortex lattice as an experimentally feasible control knob for emergent topological phenomena in superconductors.