On the Breakdown of Landau-Fermi Liquid Theory in the Cuprates

Abstract

One of the key features of the high temperature cuprate superconductors that distinguishes them from other metals is the clear breakdown of Landau-Fermi liquid behavior in the normal state [1]. Although Landau theory is based on a perturbative treatment of the interactions, in practice it is found to be very robust and applicable even in cases where naive estimates would have it fail completely e.g. the normal phase of ³He and of the related transition metal oxide, Sr₂RuO₄. The breakdown of Landau behavior in the cuprates is already clearly demonstrated at optimal doping by the linear temperature dependence of the resistivity and it becomes even more pronounced in underdoped cuprates with the appearance of the spin gap at the temperature scale T* which exceeds the critical temperature for superconductivity, T _c There has been much debate over the meaning of this temperature, T^* [2]. One school argues for an actual phase transition to a state with a hidden order parameter which accounts for the failure to observe a symmetry breaking at T^*. However there are no reports of singular behavior in thermodynamic properties at T^*, even in well characterized underdoped cuprates such as YBa₂Cu₄O_8. This raises the question whether there can be a breakdown of Landau behavior without symmetry breaking and if so, what would be the driving force that is so special to the cuprates. In this lecture, this possibility will be examined with emphasis on the role of Umklapp electron-electron scattering. First, the simpler and well understood case of ladder systems will be reviewed. Then the case of two dimensions will be examined and the results of a recent series of numerical calculations based on a 1-loop renormalization group treatment will be discussed. The last section is devoted to the conclusions.