Heavy Fermion Materials: Quantum Interference, Hidden Order, and Defects

Heavy-fermion materials exhibit a multitude of phenomena which are believed to arise from the competition between Kondo screening and antiferromagnetic ordering. Of particular interest are the non-Fermi-liquid properties observed in the quantum critical region of the heavy-fermion phase diagram, whose microscopic origin is a topic of much debate. Recent scanning tunneling spectroscopy (STS) experiments have shed light on this debate by providing insight into the electronic and magnetic structure of heavy-fermion materials. I present a theoretical discussion of these phenomena and their origins. I show that the microscopic origin of the differential conductance (dI/dV) in Kondo systems arises from the particle-hole asymmetry of the conduction band as well as the quantum interference between electrons tunneling from the STS tip into the conduction band and into the magnetic f-electron states. Then, defects are presented as a means to differentiate, in real space, between electronic correlations arising from Kondo screening, and antiferromagnetic correlations between the magnetic moments. Next, the experimental STS data from the hidden order transition of URu2 Si2 is shown to be consistent with the emergence of a coherent Anderson lattice. Then, Kondo droplets, finite-size Kondo lattices consisting of tens to hundreds of magnetic atoms, are shown to be nanoscale replicas of heavy-fermion materials and a novel approach to understanding complexity. Finally, a discussion of continuous-time quantum Monte Carlo is presented as a means to further validate the use of large-N theory, which was used extensively in this work.