Superconductivity near a Ferroelectric Quantum Critical Point in a Dirac Semimetal

According to standard lore, doped materials such as semimetals and semiconductors, 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 very small. Nonetheless, superconductivity is observed in a wide range of materials, including YPtBi, Bi2Se3, Bi, PbTe and SnTe, which raise the question regarding the microscopic pairing mechanism. In this talk I will discuss the option of pairing mediated by ferroelectric fluctuations close to a quantum critical point in a Dirac semimetal and show why such fluctuations are particularly effective in the low density limit.