Doping a semiconductor will eventually lead to the emergence of a metallic ground state.  In contrast to silicon and germanium, infinitesimal doping transforms strontium titanate (SrTiO ₃ ) to a metal. Thanks to its long Bohr radius, the dilute metallic state hosts extremely mobile carriers in a shallow Fermi sea over a seafloor carved by distant dopants.  Two mysteries will be highlighted in this talk. The first is the occurrence of superconductivity in spite of the tiny Fermi energy, thirty times lower than the Debye energy [1]. Our recent results point to s-wave symmetry of the superconducting order parameter. The second is the persistence of T ² resistivity in the dilute limit. Electron-electron scattering generates a distinct contribution to electrical resistivity following quadratic temperature dependence.  The T ² behavior in SrTiO ₃ can be tuned over four orders of magnitude. It persists in the single-band dilute limit despite the absence of two known mechanisms for T ² behavior, distinct electron reservoirs and Umklapp processes [2].

1)     X. Lin, Z. Zhu, B. Fauqué  and K. Behnia, Phys. Rev. X 3 , 021002 (2013)

2)     X. Lin, B. Fauqué and K. Behnia, Science 349 , 945 (2015)