Quantum Phase Transitions in Multi-Impurity and Lattice Kondo Systems

Abstract

The main purpose of this dissertation is to provide a detailed development of a self-consistent perturbative renormalization group (RG) method to investigate the quantum phases and quantum phase transitions of multi-impurity Kondo systems (e.g., two impurities or a lattice<br /> of impurities). The essence of the RG method is an extension of the standard “poor man's scaling” by including the dynamical effects of the magnetic fluctuations in the Kondo vertex. Such magnetic fluctuations arise due to the indirect carrier-mediated exchange interaction (RKKY interaction) between the impurities and compete with the Kondo effect to determine the ground-state. The aim is to take the most ‘economic’ route and avoid intensive numerical computations as far as possible. In general, it is shown in detail how a relatively small amount of such magnetic fluctuations can suppress and ultimately, destroy the Kondo-screened phase in a universal manner, and without incurring a magnetic instability in the system. The renormalization group method and its extensions are further applied to several distinct experimental realization of the multi-impurity Kondo effect; namely, Kondo adatoms studied via scanning tunneling spectroscopy, a highly-tunable double-quantum-dot system based on semiconducting heterostructures, and finally, the heavy fermionic compounds as Kondo lattices. We will demonstrate the qualitative and quantitative agreement of the RG theory with the experimental findings, which supports the validity of the method. In the case of Kondo lattices, we further include the possibility of a magnetic ordering in the lattice to see whether a magnetic ordering can happen simultaneously with or before the Kondo breakdown (or even prevent it altogether). In the last chapter, we consider the fate of the local moments in the absence of full Kondo screening while Kondo fluctuations are still present. This partially-screened phase needs itself an extensive study since it can support other phases besides a simple magnetic ordering (e.g., quantum spin glass or exotic non-Fermi-liquid phases). Finally, the dissertation is concluded with a summary of findings and future research prospects.