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., ${\mathrm{Pb}}_x{\mathrm{Sn}}_{1-x}\mathrm{Te}$, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

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近量子临界零密度狄拉克半金属的协同铁电性和超导性

我们研究了接近铁电量子临界点的三维零密度狄拉克半金属的超导性。我们发现临界性、反转对称性破缺和狄拉克色散的相互作用在电荷中性点产生了稳健的超导态，那里不存在费米面。使用 Eliashberg 理论，我们表明铁电量子临界点对于铁电密度波 (FDW) 的形成是不稳定的，其波动反过来导致一阶超导跃迁。令人惊讶的是，发现远程超导和 FDW 订单相互合作，这与更常见的相位竞争情况形成鲜明对比。因此，我们建议驱动电荷中性的 Dirac 材料，例如，${铅}_X{锡}_{\mathrm{1个}-X}特$，通过铁电量子临界点可能导致与 FDW 阶交织的超导性。