We calculate the Kadowaki-Woods ratio (KWR) in Fermi liquids with arbitrary band structures. We find that, contrary to the single band case, the ratio is not generally independent of the effects of electronic correlations (universal). This is very surprising given the experimental findings of a near universal KWR in many multiband metals. We identify a limit where the universality of the ratio, which has been observed experimentally in many strongly correlated electron systems, is recovered. We discuss the KWR in Dirac semimetals in two and three dimensions. In the two-dimensional case we also generalize the KWR to account for the logarithmic factor in the self-energy. In both cases we find that the KWR is independent of correlations, but strongly dependent on the doping of the system: for massless fermions the KWR is proportional to the inverse square of the carrier density, whereas the KWR for systems with massive quasiparticles is proportional to the inverse of the carrier density.
I. INTRODUCTIONFermi liquid theory describes the low temperature behavior of the vast majority of metals extremely well [1][2][3][4][5]. One of the beauties of Fermi liquid theory is that it reduces the description of the interacting electron fluid to a small number of (Landau) parameters. Therefore, ratios in which these parameters cancel, such as the Wilson-Sommerfeld ratio and Wiedemann-Franz law [1,6] provided important tests of Fermi liquid theory.In a Fermi liquid the electronic contributions to the resistivity [ρ el (T ) = AT 2 ] and heat capacity [C el (T ) = γT ] are both governed by the effective mass, m * -roughly speaking A ∝ m * 2 and γ ∝ m * . So the Kadowaki-Woods ratio, A/γ 2 , should be constant in a Fermi liquid [7][8][9][10][11]. More precisely one might expect correlations to leave the Kadowaki-Woods ratio (KWR) unrenormalized because a Kramers-Kronig transformation relates the real and imaginary parts of the self-energy [11][12][13], which determine the electronic contributions to the heat capacity and resistivity respectively. This means that the KWR is somewhat similar to a fluctuation-dissipation theorem.First Rice [14] and later Kadowaki and Woods [15] found that A/γ 2 is approximately constant within classes of materials (transition metals and heavy fermion compounds, respectively). However, the ratio differs by two orders of magnitude between these two classes. It was subsequently discovered that the Kadowaki-Woods ratio (KWR) in transition metals and organic charge transfer salts can be even larger than in the heavy fermions (see Refs. 13, 16 and references therein.)It was long believed [11,17] that the size of the KWR gave an indication of the strength of the electron-electron scattering [44]. However, this has been shown to be incorrect [13,16]. Rather, the large variations in the KWR between different classes of materials can be explained almost entirely by taking into account non-interacting properties of the materials (e.g. electron density and dimensionality) [13,16]. Furthermore, it has been shown ...