The Lifshitz Transition in d-wave Superconductors

TL;DR

This paper investigates a Lifshitz transition in d-wave superconductors, revealing a topological change at a critical density that separates gapless and gapped phases without symmetry change.

Contribution

It demonstrates the occurrence of a Lifshitz transition in d-wave superconductors, characterized by a topological change without symmetry breaking, and analyzes its properties.

Findings

A Lifshitz transition occurs at a critical density in d-wave superconductors.

The transition separates a gapless BCS-like phase from a gapped BEC-like phase.

The transition is second order and involves changes in compressibility and superfluid density.

Abstract

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: a BCS-like gapless superconductor/superfluid in the higher density limit and a BEC-like fully gapped superconductor/superfluid 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 can not 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.