Theory of Kondo effect in nanoscale systems and studies of III-V diluted magnetic semiconductors

In this thesis, we study the interplay of local magnetic moments and quantum particles (electrons or holes) in two qualitatively different systems. The first half of this thesis describes our efforts to understand a new generation of low temperature Scanning Tunneling Microscope (STM) experiments that probe Kondo physics at the single impurity level through the local density of states. We develop a scattering theory of electrons in the surface states of the noble metals (such as Cu(111)) that gives exceptional quantitative agreement with recent “quantum mirage” experiments in quantum corrals. We then study the Kondo physics generated by a small nanometer size ferromagnetic particle in electrical contact with a metallic host and delineate a number of important regimes and situations that are experimentally accessible. The second of these projects bears directly on recent STM experiments of Co nanoparticles on single-wall metallic nanotubes.; In much of the remainder of the thesis we describe work relating to magnetic impurities in the diluted ferromagnetic semiconductor Ga_{1− x}Mn_xAs. On both the insulating and metallic side of the transition (occurring for x ≈ 0.03), we study the effects of the strong spin-orbit coupling in the valence bands of GaAs on the Mn-Mn interactions. In the insulating limit we derive an effective Hamiltonian describing spin 3/2 polarons hopping between the Mn sites and coupled to the Mn spins. We study the model in meanfield theory at zero temperature and find a strong disorder-induced magnetic anisotropy which plays an important role in the physics. In the metallic limit, we compute the effective RKKY interaction between two Mn spins within the spherical approximation. In Monte Carlo calculations we find a number disorder-dependent features of the magnetization, susceptibility and Curie temperature consistent with experiment but not captured in other models.; In the final chapter we discuss the problem of quantum decoherence in modern semiclassical language. In particular, using the classical mechanics which underlies any semiclassical approach, we attempt to present an intuitive and general theory of quantum decoherence. We place an emphasis on the types of processes that lead to the loss of quantum properties when a particle interacts with environmental degrees of freedom. We show that “dephasing” (randomization of the phase of the particle) almost always contributes to decoherence, but trajectory changes also play an important role and cannot be neglected in general.