Aspects of the half-filled Landau level
Abstract/Contents
- Abstract
- This thesis examines the paradigmatic integer quantum Hall to insulator transition (IQHIT) from the perspective of composite-fermions. A treatment of the disorder faithful to the flux attachment constraint is shown to be crucial in obtaining a composite-fermion description of this quantum critical point and explaining the phenomenology. The disorder in composite-fermion coordinates is a combination of flux and potential disorders. In the simplest mean-field approximation, these two are proportional in space leading to a Hamiltonian analogous to a spin-1/2 in a random magnetic field with a Zeeman term that has a gyromagnetic ratio of g = 2. The breaking of average time-reversal symmetry by such a disorder is shown to be of critical importance. Using this approach, we show how the traditional Halperin-Lee-Read theory of the half-filled Landau level can be consistent with the particle-hole symmetry either with or without disorder. For the former, a reinterpretation of the IQHIT in electron coordinates between the filling fractions ν = 1 and ν = 0 in terms of a transition between the composite-fermion filling fractions ν_cf = −1 and ν_cf = 0 is crucial. Further, this suggests that the IQHIT is self-dual under flux attachment with just a change of sign. We corroborate this using an effective field theory approach and numerical calculations of the critical properties at a mean-field level. Such a self-duality can be then used to obtain the universal critical resistivity tensor. Going beyond the mean-field theory, we study the leading effects of gauge fluctuations. We find that the experimentally observed dynamical scaling exponent of z = 1 can be obtained from the gapless plasmon modes due to the finite conductivity at the critical point. The characteristic scale of this effect is shown to be similar to what's seen in the experiments. Further, by extending this theory to fractional quantum Hall transitions, we show how the Debye screening effects in the presence of Coulomb interactions can lead to an explanation for the conjectured superuniversality of quantum Hall transitions. Finally, we propose an RG-flow as suggested by a perturbative study in the gauge fluctuations and the inverse conductivity of composite-fermions
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Kumar, Prashant |
|---|---|
| Degree supervisor | Raghu, Srinivas, 1978- |
| Thesis advisor | Raghu, Srinivas, 1978- |
| Thesis advisor | Kivelson, Steven |
| Thesis advisor | Manoharan, Harindran C. (Harindran Chelvasekaran), 1969- |
| Degree committee member | Kivelson, Steven |
| Degree committee member | Manoharan, Harindran C. (Harindran Chelvasekaran), 1969- |
| Associated with | Stanford University, Department of Physics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Prashant Kumar |
|---|---|
| Note | Submitted to the Department of Physics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Prashant Kumar
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...