Topological Properties of Interacting Fermionic Systems
Year: 2012
Type: dissertation
Abstract: This thesis is a study of three categories of problems in fermionic systems for which topology plays an important role: (i) The properties of zero modes arising in systems of fermions interacting with a bosonic background, with a special focus on Majorana modes arising in the superconductor state. We propose a method for counting Majorana modes and we study a mechanism for controlling their number parity in lattice systems, two questions that are of relevance to the protection of quantum bits. (ii) The study of dispersionless bands in two dimensions as a platform for correlated physics, where it is shown the possibility of stabilizing the fractional quantum Hall effect in a flat band with Chern number. (iii) The extension of the hierarchy of quantum Hall fluids to the case of time-reversal symmetric incompressible ground states describing a phase of strongly interacting topological insulators in two dimensions.
Author: Luiz H. Santos
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2170789615