Quasiclassical physics andT-linear resistivity in both strongly correlated and ordinary metals

Abstract

We show that near a quantum-critical point generating quantum criticality of strongly correlated metals where the density of electron states diverges, the quasiclassical physics remains applicable to the description of the resistivity ρ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, reminiscent of the phonon mode in solids. We demonstrate that at T , being in excess of an extremely low Debye temperature T D , the resistivity ρ(T ) changes linearly with T , since the mechanism, forming the T dependence of ρ(T ), is the same as the electron-phonon mechanism that prevails at high temperatures in ordinary metals. Thus, in the region of the T -linear resistivity, electron-phonon scattering leads to near material independence of the lifetime τ of quasiparticles that is expressed as the ratio of the Planck constanth to the Boltzmann constant k B , T τ ∼h/k B . We find that at T < T D there exists a different mechanism, maintaining the T -linear dependence of ρ(T ), and making the constancy of τ fail in spite of the presence of T -linear dependence. Our results are in good agreement with exciting experimental observations. Discoveries of surprising universality in the properties of both strongly correlated metals and ordinary ones provide unique opportunities for checking and expanding our understanding of quantum criticality in strongly correlated compounds. When exploring at different temperatures T a linear in temperature resistivity of these utterly different metals, a universality of their fundamental physical properties has been revealed. 1 On one hand, at low T the linear T -resistivityobserved in many strongly correlated compounds such as high-temperature superconductors and heavy-fermion metals located near their quantum-critical points and therefore exhibiting quantum criticality. Here ρ 0 is the residual resistivity and A is a T -independent coefficient. Explanations based on quantum criticality for the T -linear resistivity have been given in the literature; see, e.g., Refs. 2-5, and references therein. On the other hand, at room temperatures the T -linear resistivity is exhibited by conventional metals such as Al, Ag, or Cu. In the case of a simple metal with a single Fermi surface pocket the resistivity reads e 2 nρ = p F /(τ v F ), 6 where e is the electronic charge, τ is the lifetime, n is the carrier concentration, and p F and v F are the Fermi momentum and the Fermi velocity, correspondingly. Writing the lifetime τ (or inverse scattering rate) of quasiparticles in the form 7,8we obtainwhereh is the Planck constant, k B is the Boltzmann constant, and a 1 and a 2 are T -independent parameters. A challenging point for a theory is that experimental facts corroborate Eq. (3) in the case of both strongly correlated metals and ordinary ones provided that these demonstrate the linear T dependence of their resistivity. 1 Moreover, the analysis of data available in the literature for the most various compounds with the linear dependence of ρ(T ) shows that the coeffi...

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