Lifshitz transition in the double-core vortex in 3He-B

We study the spectrum of fermion states localized within the vortex core of a weak-coupling p-wave superfluid. The low energy spectrum consists of two anomalous branches that cross the Fermi level as functions of the impact parameter, and generate large density of states at the locations of the half cores of the vortex. Fermi liquid interactions significantly change the vortex structure, which leads to Lifshitz transition in the effective Fermi surface of the vortex core fermions. We apply the results to revise the interpretation of an experiment on rotational dynamics of vortices in superfluid 3He-B.