Superconductivity near a ferroelectric quantum critical point in ultralow-density Dirac materials

Abstract

The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the conventional theory. In this paper, we propose a mechanism for superconductivity in ultralow-density three-dimensional Dirac materials based on the proximity to a ferroelectric quantum critical point. We derive a low-energy theory that takes into account both the strong Coulomb interaction and the direct coupling between the electrons and the soft phonon modes. We show that the Coulomb repulsion is strongly screened by the lattice polarization near the critical point even in the case of vanishing carrier density. Using a renormalization group analysis, we demonstrate that the effective electron-electron interaction is dominantly mediated by the transverse phonon mode. We find that the system generically flows towards strong electron-phonon coupling. Hence, we propose a new mechanism to simultaneously produce an attractive interaction and suppress strong Coulomb repulsion, which does not require retardation. For comparison, we perform same analysis for covalent crystals, where lattice polarization is negligible. We obtain qualitatively similar results, though the screening of the Coulomb repulsion is much weaker. We then apply our results to study superconductivity in the low-density limit. We find strong enhancement of the transition temperature upon approaching the quantum critical point. Finally, we also discuss scenarios to realize a topological $p$-wave superconducting state in covalent crystals close to the critical point.

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• Metallic and Deconfined Quantum Criticality in Dirac Systems
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• Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate
• Multiband Quantum Criticality of Polar Metals
• A theory of criticality for quantum ferroelectric metals
• Synergetic ferroelectricity and superconductivity in zero-density Dirac semimetals near quantum criticality
• The effect of interorbital scattering on superconductivity in doped Dirac materials
• The field theory of a superconductor with repulsion
• Spin-Phonon Resonances in Nearly Polar Metals with Spin-Orbit Coupling
• Electron Interactions in Rashba Materials
• Phonon-Induced Collective Modes in Spin-Orbit Coupled Polar Metals
• Modeling polar order in compressively strained SrTiO${}_3$
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Spin-dependent anisotropic electron-phonon coupling in KTaO${}_3$
• Unconventional superconductivity from electronic dipole fluctuations
• Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities
• Effects of doping on polar order in SrTiO${}_3$ from first-principles modeling
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals