Condensation of fermion zero modes in the vortex

Abstract

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems which contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli-de Gennes-Matricon branches with different angular momentum quantum number $n$ approach zero energy level at $p_z\rightarrow 0$. Such condensation of the energy levels is the consequence of the bulk-vortex correspondence in topological superfluids/superconductors. In a given case this is the connection between the Dirac line of zeroes in the bulk spectrum and the level condensation in the vortex core. The density of states of the bound fermions diverges at zero energy giving rise to the $\sqrt{\Omega}$ dependence of DoS in the polar phase of superfluid $^3$He rotating with the angular velocity $\Omega$ and to the $\sqrt{B}$ dependence of DoS for superconductors in the $(d_{xz} + i d_{yz})$-wave pairing state.