Disordered non-interacting electronic systems near criticality in two dimensions

• Main Author: Bhardwaj, Shanthanu
• Format: Dissertation
• Language: English
• Subjects: quantum physics; theoretical physics
• ISBN: 9781321645316; 1321645317

The nature of the plateau transition in the integer quantum Hall (IQH) effect is an intriguing problem that has been the focus of intense experimental and theoretical research. The vast majority of existing theories of the IQH effect focus on models of non-interacting electrons in a strong magnetic field subject to disorder. There are two complementary approaches to this problem -- the first, a field-theoretic approach, was developed for short-range (Gaussian white-noise) disorder, where the correlation length of the disorder potential is much shorter than the magnetic length. A different, ``network model'', approach was developed for strong magnetic fields and smooth disorder where the correlation length is much longer than the magnetic length.
In this thesis, we will initially use the former approach to calculate the multifractal exponents of the wavefunction in the IQH state in the bulk as well as near the boundary. The rest of the thesis will focus on using the network model approach to study the IQH and spin quantum Hall effect by mapping the network models to a superspin ladder and then studying this system as well as the sigma model which is its continuum limit.