Quasiparticle and Nonquasiparticle Transport in Doped Quantum Paraelectrics.

Charge transport in doped quantum paraelectrics (QPs) presents a number of puzzles, including a pronounced T^{2} 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 (E_{0}), the resistivity scales with the occupation number of phonons squared, i.e., as T^{2}. The T^{2} scattering rate does not depend on the carrier number density and is not affected by a crossover between degenerate and nondegenerate regimes, in agreement with the experiment. Temperatures higher than E_{0} correspond to a nonquasiparticle 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.