Fundamentals of the Theory of Metals

Singular or non-Fermi liquids

“…Landau noticed this singularity but ignored its implication. 5 Indeed, as long as the e ective interactions do not favor superconductivity or as long as we are at temperatures much higher than the superconducting transition temperature, it is not important for Fermi-liquid theory.…”

“…For pure metals, the low-frequency limit is determined by the anomalous skin e ect [5] and (k; 0) ∼ k −1 . According to expression (160), this 1=k behavior then implies that the dispersion at small frequencies generally goes as !…”

Transport in one dimensional quantum systems

“…This path is very attractive since it represents the counterpart of the usual Landau phenomenological approach to Fermi liquid in higher-D electronic systems. It should be pointed out that even in a 3D system the continuum field theory is not enough to describe a current decay and Umklapp processes are finally responsible for a finite intrinsic resistivity ρ(T ) ∝ T 2 [81].…”

Giant quantum oscillations of the longitudinal magnetoresistance in quasi-two-dimensional metals

“…Moreover, the oscillating part of the transport properties is always small compared to the non-oscillating part. For example, in a metal with a spherical Fermi surface, the oscillating part ∆σ of the conductivity σ is of the order of [1] …”

“…In the opposite limit, when t ≪ ω c , the Landau levels are broadened only through the impurities effects, exactly like in 2D metals. It is worth noting that the 3D de Haas-van Alphen and Shubnikov-de Haas theories are not directly applicable to quasi-2D metals because the saddle-point method used in the calculations of the 3D case [1] breaks down with the spectrum (2) when ω c ≥ t. The (semiphenomenological) theory of the de Haas-van Alphen effect in quasi-2D metals [6] has revealed a crossover between the 2D and 3D limits for the behavior of the magnetization oscillations. It was with the same idea of a reduced dimensionality driven by the ratio t/ω c that we studied the magnetoresistance oscillations in quasi-2D metals [7].…”