Luttinger Liquid Physics in the Superconductor Vortex Core

We study several aspects of the structure of vortices in conventional s-wave Type $II$ superconductors. It is well-known that there are low energy quasiparticles bound to the core of a vortex. We show that under certain conditions, these quasiparticles form a degenerate Fermi gas with a finite density of states at the Fermi energy. In three dimensional superconductors, the result is a one dimensional Fermi gas of quasiparticles bound to the core of a vortex line. As is usual in one dimensional systems, interactions between the quasiparticles lead to Luttinger liquid behaviour. This may be probed through STM tunneling into the vortex core. We further suggest that a novel Peierls-type instability in the shape of the vortex line may develop due to interactions between the quasiparticle gas and fluctuations in the vortex line shape.