Interplay of Superconductivity and Magnetism in the Two Dimensional Kondo Lattice Model

Since the original discovery of heavy fermion behavior in the late seventies by Andres et al. [1], heavy fermions keep attracting scientific interest due to their exotic and unusual properties. These are inter-metallic compounds that contain rare earth elements, like cerium, praseodymium, and ytterbium, and actinides like uranium. The term “heavy” refers to their large effective electronic mass, as large as 1000 times the normal metal ones. The active physics in these materials results from the magnetic moments, associated to the partially filled f -shells of rare earth or actinide ions, being immersed into a quantum sea of mobile conduction electrons. In most rare earth metals and insulators, local moments tend to order magnetically, but in heavy electron metals the quantum mechanical jiggling of the local moments induced by delocalized electrons is fierce enough to melt magnetic order. The mechanism by which this takes place involves a remarkable piece of quantum physics known as the “Kondo effect” [2] that describes the process by which a magnetic impurity get screened by conduction electrons, forming the so-called Kondo singlet below a characteristic temperature/energy scale named the Kondo temperature, TK . Even though the Kondo effect refers strictly speaking to a very dilute concentration of magnetic ions, typically few part per million, the same physics is believed to play a role in heavy fermions. Heavy fermion materials have become recently popular also in the study of the quantum critical behavior of matter in the vicinity of a zero temperature second-order phase transition. Indeed, heavy fermions realize prototypical examples of quantum critical points that separate at zero temperature magnetic and paramagnetic phases. Experimentally, quantum critical points are attained by tuning non-thermal control parameters, such as pressure, chemical doping or applied magnetic field, so as to drive continuously to zero the magnetic ordering temperature. One of presently lively discussions up to date is about the appearance of two types of magnetic quantum critical points, depending on the behavior of the Kondo singlet as the transition is approached from paramagnetic side. If the Kondo singlet remains across the magnetic transition, the latter is of a spin-density-wave type in which the only critical degrees of freedom are the fluctuations of the magnetic order parameter. In this scenario, the Fermi volume does not change and contains both f and conduction electrons.