Superconductivity in Ultra-Low Density Dirac Materials Driven by a Ferroelectric Quantum Critical Point*

According to standard lore, low-density materials such as semimetals should not become superconducting. They are characterized by a small Fermi energy, which is comparable to the Debye frequency and moreover, their density of states is extremely small. Nonetheless, superconductivity is ubiquitous in topological materials, including YPtBi, Bi₂Se₃, Bi, Cd₃As₂, PbTe and SnTe, which raise the question regarding the microscopic picture of pairing in these systems. In this talk, I will discuss the option of pairing mediated by ferroelectric fluctuations close to a quantum critical point in a Dirac semimetal. I will show that such fluctuations lead to pairing, even when the Fermi energy is smaller than any bosonic frequency in the problem and possibly, even at charge neutrality.