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

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.

5+15 pages, 4+3 figures

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• Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate
• A theory of criticality for quantum ferroelectric metals
• BCS-like disorder-driven instabilities and ultraviolet effects in nodal-line semimetals
• Phonon-Induced Collective Modes in Spin-Orbit Coupled Polar Metals
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Unconventional superconductivity from electronic dipole fluctuations