Synergetic ferroelectricity and superconductivity in zero-density Dirac semimetals near quantum criticality

TL;DR

This paper explores how ferroelectric quantum criticality can induce and enhance superconductivity in zero-density Dirac semimetals, revealing a cooperative interplay between ferroelectric density waves and superconducting order.

Contribution

It demonstrates that ferroelectric quantum critical fluctuations can stabilize a superconducting state at charge neutrality, with a novel cooperative interaction between ferroelectric density waves and superconductivity.

Findings

Superconductivity arises at the charge-neutrality point without a Fermi surface.

Ferroelectric quantum criticality leads to a first-order transition mediated by density wave fluctuations.

Superconducting and ferroelectric density wave orders cooperate, not compete, in this system.

Abstract

We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., Pb$_x$Sn$_{1-x}$Te, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.