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.

arXiv comment5+15 pages, 4+3 figures

References in corpus (49)

• Topological Crystalline Insulators in the SnTe Material Class
• Experimental realization of a topological crystalline insulator in SnTe
• Quantum criticality in ferroelectrics
• Enhancement of superconductivity near a nematic quantum critical point
• Are non-Fermi-liquids stable to Cooper pairing?
• Superconductivity with topological surface state in SrxBi2Se3
• Superconductivity in the topological semimetal YPtBi
• A ferroelectric quantum phase transition inside the superconducting dome of Sr${}_{1-x}$Ca${}_x$TiO${}_{3-\delta }$
• Competing order and nature of the pairing state in the iron pnictides
• Quantum critical origin of the superconducting dome in SrTiO${}_3$
• Nonanalytic behavior of the spin susceptibility in clean Fermi systems
• Experimental evidence for bulk superconductivity in pure Bismuth single crystal at ambient pressure
• Critical doping for the onset of a two-band superconducting ground state in SrTiO${}_{3-\delta }$
• Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar orders
• Superconductivity and spin-density-waves in multi-band metals
• Superconductivity in dilute SrTiO${}_3$: a review
• Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin-orbit-coupled systems
• Ab Initio Phonon Dispersions for PbTe
• Critical enhancement of thermopower in a chemically tuned polar semimetal MoTe${}_2$
• Odd-parity superconductivity from phonon-mediated pairing: Application to Cu${}_x$Bi${}_2$Se${}_3$
• Superconductivity vs bound state formation in a two-band superconductor with small Fermi energy -- applications to Fe-pnictides/chalcogenides and doped SrTiO3
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• A pressure-induced topological phase with large Berry curvature in Pb${}_{1-x}$Sn${}_x$Te
• A possible mechanism for superconductivity in doped SrTiO3
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Superconductivity at low density near a ferroelectric quantum critical point: doped SrTiO
• Spin-orbit-coupled ferroelectric superconductivity
• Quantum Order-by-Disorder in Strongly Correlated Metals
• Quasiparticle and Nonquasiparticle Transport in Doped Quantum Paraelectrics
• Anisotropic superconductivity mediated by ferroelectric fluctuations in cubic systems with spin-orbit coupling
• Nonmonotonic $d_{x^2-y^2}$ superconducting gap in electron-doped Pr${}_{0.89}$LaCe${}_{0.11}$CuO${}_4$: Evidence of coexisting antiferromagnetism and superconductivity?
• Phonon mediated superconductivity in low carrier-density systems
• Nematic and chiral superconductivity induced by odd-parity fluctuations
• Superconductivity from energy fluctuations in dilute quantum critical polar metals
• Superconductivity near a ferroelectric quantum critical point in ultralow-density Dirac materials
• Competition between superconductivity and nematic order : anisotropy of superconducting coherence length
• Novel pairing mechanism for superconductivity at a vanishing level of doping driven by critical ferroelectric modes
• Quantum ferroelectric instabilities in superconducting SrTiO${}_3$
• Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics
• Odd-parity superconductivity near inversion breaking quantum critical point in one dimension
• Comment on "Superconductivity at low density near a ferroelectric quantum critical point: Doped SrTiO3"
• Ferroelectric order versus metallicity in Sr${}_{1-x}$Ca${}_x$TiO${}_{3-\delta }$ ($x=0.009$)
• Multiband Quantum Criticality of Polar Metals
• Unusual phonon density of states and response to the superconducting transition in the In-doped topological crystalline insulator Pb${}_{0.5}$Sn${}_{0.5}$Te
• Non-monotonic thickness dependence of Curie temperature and ferroelectricity in Two-dimensional SnTe film
• Revisiting (higher order and crystalline) topology in old models of lead telluride
• Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb${}_{0.5}$Sn${}_{0.5}$)${}_{1-x}$In${}_x$Te
• Triplet pairing due to spin-orbit-assisted electron-phonon coupling
• Conductivity of electronic liquid-crystalline mesophases

Cited by in corpus (7)

• 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