Quasiparticle and Nonquasiparticle Transport in Doped Quantum Paraelectrics

Abstract

Charge transport in doped quantum paralectrics (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 non-degenerate regimes, in agreement with the experiment. Temperatures higher than $E_0$ 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.

5 pages, 2 figures, Supplementary material 23 pages

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• Fermi surface of the most dilute superconductor
• Intrinsic Mobility Limiting Mechanisms in Lanthanum-doped Strontium Titanate
• Multiband Quantum Criticality of Polar Metals
• Charge transport in oxygen-deficient EuTiO${}_3$: the emerging picture of dilute metallicity in quantum-paraelectric perovskite oxides

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• Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics
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• Superconductivity enhancement in polar metal regions of Sr${}_{0.95}$Ba${}_{0.05}$TiO${}_3$ and Sr${}_{0.985}$Ca${}_{0.015}$TiO${}_3$ revealed by the systematic Nb doping
• Theory of superconductivity in doped quantum paraelectrics
• Electron-phonon interaction and phonons in 2d doped semiconductors
• Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate
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• Polaron with Quadratic Electron-phonon Interaction
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• "Quantum bipolaron" superconductivity from quadratic electron-phonon coupling
• A theory of criticality for quantum ferroelectric metals
• Quasi-isotropic orbital magnetoresistance in lightly doped SrTiO${}_3$
• Spin-Phonon Resonances in Nearly Polar Metals with Spin-Orbit Coupling
• T-square dependence of the electronic thermal resistivity in metallic strontium titanate
• Anisotropic resistivity and superconducting instability in ferroelectric metals
• Soliton States From Quadratic Electron-Phonon Interaction
• Electronic thermal resistivity and quasi-particle collision cross-section in semi-metals
• Optical conductivity of an anharmonic large polaron gas at weak coupling
• Phonon-Induced Collective Modes in Spin-Orbit Coupled Polar Metals
• Analytic method for quadratic polarons in nonparabolic bands
• Polarons with arbitrary nonlinear electron-phonon interaction
• Electronic spin susceptibility in metallic strontium titanate
• T-square electric resistivity and its thermal counterpart in RuO${}_2$
• Stability conditions for a large anharmonic bipolaron