Collective Electron Dynamics in Mesoscopic Systems

Doktorsavhandling, 2002

This work is devoted to a theoretical investigation of collective electron dynamics in low dimensional materials and mesoscopic structures. A common feature of these studies is the focus on the properties of the low energy dynamics of conduction electrons. One class of studied materials is the high-Tc superconductor Nd2CuO4 and related compounds. We consider electronic collective modes propagating along theCuO2 planes, which are predicted by anyon models of superconductivity, and investigate their effect on neutron and light scattering spectra. The concept of two-dimensional (2D) collective modes is also used for the explanation of anomalous acoustic properties experimentally discovered in these materials. We further consider a similar problem of the interaction of acoustic waves with 2D electrons in the fractional quantum Hall regime. Within the composite fermion approach to the description of the fractional quantum Hall effect, it is found that the renormalized sound velocity exhibits an oscillatory dependence on the sound wave vector. This effect results from the hybridization of the phonons with the low-lying collective modes in the system of composite fermions. Tunnel spectroscopy is an important tool for studying the properties of superconducting materials. The current transport in normal metal - insulator - superconductor contacts is studied in the case of resonant impurity levels present within the insulating layer. We employ a mesoscopic scattering theory for studying the interplay between resonant tunneling and Andreev reflection processes. Different types of conductance behavior have been found which depend on the relation between the gap energy in the superconductor and the resonance energies and widths of the localized levels. In the last part of the thesis, a qubit implementation of an rf SQUID with a single-mode quantum point contact is discussed. By employing the path integral technique, we derive an effective Hamiltonian for the low energy Andreev levels in the contact, which are coupled to the quantum fluctuations of flux in the SQUID. We analyze the dynamics and optimal parameters of the SQUID for applications to qubits.