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Room-temperature metallicity of lightly doped SrTiO$_3$ is puzzling, becausethe combination of mobility and the effective mass would imply a mean-free-path(mfp) below the Mott Ioffe Regel (MIR) limit and a scattering time shorter thanthe Planckian time ($\tau_P=\hbar/k_BT$). We present a study of electricresistivity, Seebeck coefficient and inelastic neutron scattering extended tovery high temperatures, which deepens the puzzle. Metallic resistivity persistsup to 900 K and is accompanied by a large Seebeck coefficient whose magnitude(as well as its temperature and doping dependence) indicates that carriers arebecoming heavier with rising temperature. Combining this with neutronscattering data, we find that between 500 K and 900 K, the Bohr radius and theelectron wave-length become comparable to each other and twice the latticeparameter. According to our results, between 100 K and 500 K, metallicity ispartially driven by temperature-induced amplification of the carrier mass. Wecontrast this mass amplification of non-degenerate electrons with thebetter-known case of heavy degenerate electrons. Above 500 K, themean-free-path continues to shrink with warming in spite of becoming shorterthan both the interatomic distance and the thermal wavelength of the electrons.The latter saturates to twice the lattice parameter. Available theories ofpolaronic quasi-particles do not provide satisfactory explanation for ourobservations.

Heavy non-degenerate electrons in doped strontium titanate