Abstract
Room-temperature metallicity of lightly doped SrTiO$_3$ is puzzling, because the 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 than the Planckian time ($\tau_P=\hbar/k_BT$). We present a study of electric resistivity, Seebeck coefficient and inelastic neutron scattering extended to very high temperatures, which deepens the puzzle. Metallic resistivity persists up to 900 K and is accompanied by a large Seebeck coefficient whose magnitude (as well as its temperature and doping dependence) indicates that carriers are becoming heavier with rising temperature. Combining this with neutron scattering data, we find that between 500 K and 900 K, the Bohr radius and the electron wave-length become comparable to each other and twice the lattice parameter. According to our results, between 100 K and 500 K, metallicity is partially driven by temperature-induced amplification of the carrier mass. We contrast this mass amplification of non-degenerate electrons with the better-known case of heavy degenerate electrons. Above 500 K, the mean-free-path continues to shrink with warming in spite of becoming shorter than both the interatomic distance and the thermal wavelength of the electrons. The latter saturates to twice the lattice parameter. Available theories of polaronic quasi-particles do not provide satisfactory explanation for our observations.
Highlights
Decades ago [1], Mott argued that the threshold of metallicity in a doped semiconductor depends on the effective range of the Coulomb interaction exerted by an extrinsic atom, the Bohr radius
The combination of room-temperature resistivity and low-temperature effective mass implies a mean-free path that falls below all known length scales of the solid [36]. This has been observed in strange metals with strong correlation among electrons [39], in organic semiconductors [40], but not in inorganic doped band insulators. We address this last issue by measuring the resistivity and the Seebeck coefficient of SrTi1−xNbxO3 up to temperatures as high as 900 K, in which, in contrast to oxygen-reduced strontium titanate, exposition to high temperatures does not modify the number of dopants
We present extended measurements of resistivity and the Seebeck coefficient of Nb-doped strontium titanate to very high temperatures
Summary
Decades ago [1], Mott argued that the threshold of metallicity in a doped semiconductor depends on the effective range of the Coulomb interaction exerted by an extrinsic atom, the Bohr radius. One can turn it to a metal [9] with one carrier per 105 unit cells This dilute metal has attracted renewed attention in recent years for multiple reasons [10]. The low-temperature resistivity displays a quadratic temperature dependence [30,31,32,33,34,35] with a prefactor which smoothly increases with decreasing carrier concentration [32] Such a T-square resistivity is expected in a Fermi liquid with dominant e−-e− scattering. Here, the behavior persists even in the extreme dilute limit in the absence of umklapp
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