Studies on quasicrystals, superconducting micronetworks, and Josephson junction arrays

This thesis consists of three parts. In the first part, we study electronic and acoustic properties of one dimensional quasi crystals. Several approaches are used to study this system, including: (i) the first direct solution of the Hamiltonian -including a general treatment of the boundary effects and the number of layers -, (ii) perturbation theory, and (iii) a truly novel and powerful method based on real-space renormalization group (RG) ideas which provides a clear and simple picture of the electron spectral behavior and the nature of the wave functions. Furthermore, our RG approach provides a systematic method of obtaining the bifurcation diagram of the energy spectra and the magnitude of the energy level splittings. Our results are very general and apply to both diagonal and off-diagonal quasiperiodicity. The second part of this thesis deals with analytical calculations of quasicrystalline diffraction patterns. The third part of this thesis deals with the diamagnetic properties of superconducting networks and Josephson junction arrays. Quantum interference effects have been observed recently in arrays of submicron superconductors. These interferences occur as a result of the coherence of the electronic wave functions. The basic phenomenon is the quantization of the magnetic flux in multi connected geometries. The diamagnetic properties of such micronetworks are very sensitive to the topology and connectedness of the multiply connected structures, therefore they exhibit complex forms of phase diagrams when they are inmersed in a magnetic field. Of paramount importance for us are both the physical understanding and accurate quantitative prediction of the critical temperature of a given network since this quantity is of direct relevance to the many superconducting arrays experiments performed in several laboratories worldwide. Our results give a quantitative prediction of the critical temperature for complex networks. Furthermore, we have obtained the only analytical expressions for the phase boundary of complex networks which for the first time prove in a rigourous way the origin of its overall and fine structure. In all three chapters the emphasis has been made on analytical results. Furthermore, most of the more technical calculations and the connections to experiments (the GaAsAlAs Fibonacci superlattice, the AI-Mn diffraction pattern, and several superconducting networks) have been presented in detail in the appendices.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Nori, Franco Mauro

Contributors dc:contributor

• Fradkin, Eduardo H.

• quasicrystals
• superconducting micronetworks
• Josephson junction arrays
• Hamiltonian
• perturbation theory
• real-space renormalization group (RG)

Statement dc:rights

• 1987 Franco Mauro Nori

Language dc:language

en

Identifier

3471866

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23894