Chapter 2 - Non-Fermi Liquid Behavior in Heavy Fermion Systems

Abstract

Landau's Fermi liquid theory successfully describes the low temperature properties of most normal metals. However, numerous U-, Ce-, and Yb-based heavy fermion systems show deviations from Fermi liquid behavior, e.g., the specific heat follows a T ln(T0/T) or power-law in T behavior, the temperature dependence of the resistivity is approximately linear in T and the magnetic susceptibility has anomalies at low T. The non-Fermi liquid (NFL) behavior is frequently attributed to the presence of a nearby quantum critical point (QCP). First we briefly review the fundamentals of Landau's phenomenological Fermi liquid theory. Then we discuss the microscopic origin of heavy electrons through the Kondo and Anderson lattices. According to Doniach's picture the competition of the Kondo effect with the Ruderman–Kittel–Kasuya–Yosida interaction leads to a magnetically ordered phase and a Fermi liquid phase separated by a QCP. This instability of the Fermi liquid is the origin of the NFL behavior. To stress that QCPs and NFL behavior are a natural occurrence in low dimensional critical phenomena, we discuss several examples: the multichannel Kondo model, Luttinger liquids, the anisotropic Heisenberg chain and long-range order in two dimensions. The essentials of the Hertz–Millis–Moriya theory for criticality near a QCP for interacting itinerant electrons are presented. Disorder driven quantum criticality is briefly addressed. The results for a microscopic model for quantum criticality due to nested Fermi surfaces are analyzed. Several experimental examples, Ce(Ru1–xFex)2Ge2, CeIn3, YbRh2Si2, CeCu5.9Au0.1, and CeAuSb2, showing the breakdown of the Fermi liquid are described.