Metallicity without quasi-particles in room-temperature strontium titanate

Cooling oxygen-deficient strontium titanate to liquid-helium temperature leads to a decrease in its electrical resistivity by several orders of magnitude. The temperature dependence of resistivity follows a rough T$^{3}$ behavior before becoming T$^{2}$ in the low-temperature limit, as expected in a Fermi liquid. Here, we show that the roughly cubic resistivity above 100K corresponds to a regime where the quasi-particle mean-free-path is shorter than the electron wave-length and the interatomic distance. These criteria define the Mott-Ioffe-Regel limit. Exceeding this limit is the hallmark of strange metallicity, which occurs in strontium titanate well below room temperature, in contrast to other perovskytes. We argue that the T$^{3}$-resistivity cannot be accounted for by electron-phonon scattering \`{a} la Bloch-Gruneisen and consider an alternative scheme based on Landauer transmission between individual dopants hosting large polarons. We find a scaling relationship between the carrier mobility, the electric permittivity and the frequency of transverse optical soft mode in this temperature range. Providing an account of this observation emerges as a challenge to theory.