Quasiparticle and Non-Quasiparticle Transport in Doped Quantum Paraelectrics

Charge transport in doped quantum paralectrics (QPs) presents a number of puzzles, including a pronounced T² regime in the resistivity. We analyze charge transport in a QP within a model of electrons coupled to a soft transverse optical (TO) mode via a two-phonon mechanism. For T above the soft-mode frequency but below some characteristic scale (E₀), the resistivity scales with the occupation number of phonons squared, i.e., as T². The T² scattering rate does not depend on the carrier number density and is not affected by a crossover between degenerate and non-degenerate regimes, in agreement with the experiment. Temperatures higher than E₀ correspond to a non-quasiparticle regime, which we analyze by mapping the Dyson equation onto a problem of supersymmetric quantum mechanics. The combination of scattering by two TO phonons and by a longitudinal optical mode explains the data quite well.