Superconductivity at ultra low-densities*

Superconductivity at an anomalously low density of charge carriers has been measured in doped SrTiO3 a long time ago. Only recently though, a number of new materials exhibiting superconductivity at similar densities were discovered, making the anomaly into a phenomenon. In the extremely dilute limit, the screening of Coulomb repulsion is poor, and moreover, the conventional phonon mechanism for superconductivity is completely irrelevant. This raises the question: how can these materials be superconducting? I will propose two different mechanisms for superconductivity in low-density metals, based on dynamically screened Coulomb interactions and fluctuations near a structural quantum critical point. I will then specifically focus on the former mechanism to explain superconductivity in the two lowest density examples: SrTiO3 and elemental bismuth.