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Linear-in-T resistivity in dilute metals: A Fermi liquid perspective

TitleLinear-in-T resistivity in dilute metals: A Fermi liquid perspective
Publication TypeJournal Article
Year of Publication2019
AuthorsE.. H. Hwang, and S. Das Sarma
JournalPhys. Rev. B
Date PublishedFEB 4
Type of ArticleArticle

We consider a short-range deformation-potential scattering model of electron-acoustic phonon interaction to calculate the resistivity of an ideal metal (i.e., no other scattering mechanism except acoustic phonon scattering) as a function of temperature (T) and electron density (n). The resistivity calculation is based on the Boltzmann transport theory within the relaxation-time approximation in the nearly-free-electron single-band approximation. We consider both 3D metals and 2D metals and focus on the dilute limit, i.e., low effective metallic carrier density (and hence low effective Fermi wave number k(F)) of the system. The main findings are (1) a phonon-scattering-induced linear-in-T resistivity could persist to arbitrarily low temperatures in the dilute limit independent of the Debye temperature (T-D), although, eventually, the low-T resistivity turns over to the expected Bloch-Grfineisen (BG) behavior with T-5(T-4) dependence, in 3D (2D), respectively, with the crossover temperature, T-BG, from the linear-in-T to the BG behavior, being proportional to the Fermi momentum, is small in the dilute limit; (2) because of low values of n, the phonon-induced resistivity could be very high in the system, orders of magnitude above the corresponding room temperature resistivity of ordinary metals; and (3) the resistivity shows an intrinsic saturation effect at very high temperatures (for T > T-D) and, in fact, weakly decreases with increasing T above a high crossover temperature with this crossover being dependent on both T-D and n in a nonuniversal manner-this high-temperature crossover is not directly connected with the Mott-Ioffe-Regel limit and is a reflection of phonon phase-space restriction. We discuss the qualitative trends in the resistivity as a function of temperature, density, phonon velocity, and system dimensionality. We also provide ``high-temperature{''} linear-in-T resistivity results for 2D and 3D Dirac materials. Our work brings out the universal features of phonon-induced transport in dilute metals, and we comment on possible implications of our results for strange metals, emphasizing that the mere observation of a linear-in-T metallic resistivity at low temperatures or a very high metallic resistivity at high temperatures is not necessarily a reason to invoke an underlying quantum critical strange-metal behavior. Dilute metals may very well have highly unusual (compared with normal metals) transport properties arising from quantitative, but not qualitatively new, underlying physics. We discuss the temperature variation of the effective transport scattering rate showing that, for reasonable parameters, the scattering rate could be below or above k(B)T and, in particular, purely coincidentally, the calculated scattering rate happens to be k(B)T in normal metals with no implications whatsoever for the so-called Planckian behavior. Our work manifestly establishes that an apparent Planckian dissipative behavior could arise from the usual electron-phonon interaction without implying any strange metallicity or a failure of the quasiparticle paradigm in contrast to recent claims.