Lifshitz transition in d-wave superconductors

The BCS-to-BEC evolution has been recently the focus of studies in superconductors and cold atomic gases. For a d-wave system, we show that a Lifshitz transition occurs at a critical particle density which separates two topologically distinct phases according to their quasiparticle excitation energies: a BCS-like gapless superconductor in the higher-density limit and a BEC-like fully gapped superconductor in the lower-density limit. This transition is second-order according to Ehrenfest's classification, but it occurs without a change in the symmetry of the order parameter and thus cannot be classified under Landau's scheme. To illustrate the nature of the transition, we compute the compressibility and the superfluid density as functions of particle density