Electron Density and Compressibility in the Kitaev Model with a Spatially Modulated Phase in the Superconducting Pairing

A current flowing through a one-dimensional Kitaev chain induces a spatial modulation in its superconducting pairing, characterized by a wavevector Q, which is known to induce two types of topological phase transitions: one is the customary band topology transition between gapped phases, while the other is a Lifshitz transition related to the Fermi surface topology and leading to a gapless superconducting phase. We investigate the behavior of the electron density ρ and the compressibility κ across the two types of transitions, as a function of the model parameters. We find that the behavior of ρ as a function of Q and chemical potential μ enables one to infer the ground state phase diagram. Moreover, the analysis of the compressibility κ as a function of μ enables one to distinguish the two transitions: While κ exhibits a symmetric divergence across the band topology transition, it displays an asymmetric jump across the Lifshitz transition.