Quantum Critical Matter and Phase Transitions in Rare Earths and Actinides

Abstract

Abstract In this chapter, we discuss quantum critically, the notion that properties of a material are governed by the existence of a phase transition at zero temperature. The point where a second-order (continuous) phase transition takes places is known as a quantum critical point (QCP). Materials that exhibit a QCP can be tuned through their quantum phase transition (QPT) by, for example, pressure, chemical doping or disorder, frustration, and magnetic field. The study of QPTs was initially theoretically driven, showing that high-temperature properties of a material with a QPT are directly influenced by the properties of the QCP itself. We start this chapter by discussing the predictions of quantum critical and Hertz–Millis theory. Experimentally, we will mainly limit ourselves to f-electron-based materials: the rare earths Li(Ho,Y)F4, Ce(Cu,Au)6, YbRh2Si2, the Cerium series Ce(Co, Rh, Ir)In5, and one actinide-based material, URu2Si2. These “heavy fermion” metals (4f or 5f) represent prototype materials of quantum critical matter, and we will critically review their experimental signatures and their evolving theoretical descriptions. We conclude with other manifestations of QPTs beyond the rare earths and actinides.