The 3-dimensional Fermi liquid description for the normal state of cuprate superconductors

The quasiparticles in the normal state of cuprate superconductors have been shown to behave universally as a 3-dimensional Fermi liquid. Because of interactions and the presence of the Fermi surfaces (or Fermi energies), the quasiparticle energy contains, as a function of the momentum $\boldmath{p}$, a term of the form $(p-p_0)^3 \ln ( | p-p_0 | / p_0 )$, where $p = | \boldmath{p} |$ and $p_0$ is the Fermi momentum. The electronic specific heat coefficient $\gamma(T)$, electrical resistivity, Hall coefficient and thermoelectric power divided by temperature $T$, follow the logarithmic formula $a - b T^2 \ln ( T/T^*)$, $a$, $b$, and $T^*$ being constant. Singularities in the Landau $f$-function produce the $T^2 \ln T$ dependence of the magnetic susceptibility $\chi (T)$, and Knight shift, which gives rise to the phenomenon of the susceptibility maximum. The logarithmic $T$-dependence of the transport properties arises exclusively from the impurity scattering in 3-dimensional (3D) systems, but does not from the electron-electron scattering in 2D systems. The above logarithmic formula has been shown to explain universally the experimental data for the normal state of all cuprate superconductors. The decrease of $\gamma(T)$ or $\chi(T)$ with decreasing $T$ is not due to the appearance of pseudogap or spin gap but due to its $T^2 \ln T$ variation.