Electron density and compressibility in the Kitaev model with a spatially modulated Phase in the superconducting pairing

Abstract

A current flowing through a one-dimensional Kitaev chain induces a spatial modulation in its superconducting pairing, characterized by a wave vector $Q$, 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 $\rho$ and the compressibility $\kappa$ across the two types of transitions, as a function of the model parameters. We find that the behavior of $\rho$ as a function of $Q$ and chemical potential $\mu$ enables one to infer the ground state phase diagram. Moreover, the analysis of the compressibility $\kappa$ as a function of $\mu$ enables one to distinguish the two transitions: While $\kappa$ exhibits a symmetric divergence across the band topology transition, it displays an asymmetric jump across the Lifshitz transition.