The v=1 quantum Hall effect and its one-dimensional representation
Appears in the following Collection
- Fysisk institutt 
AbstractThe present work is a study of the relationship between a quantum Hall system and its one-dimensional representation. The standard theory, which is based on general arguments, predicts that the edge of the quantum Hall system can be described as a Luttinger liquid with universal parameters determined by the bulk state. In the asymptotic limit the correlation function on the edge should therefore approach a power law with a universal exponent. The Luttinger liquid behaviour has indeed been verified experimentally, in the sense of a power law behaviour. However, the exponent deviates from the value predicted by the theory.
The thesis is focused on the microscopical description of a quantum Hall system, in contrast to the general arguments usually employed. This approach makes it possible to study both the effects of the electron interaction and the interplay between the two edges of the system more directly. Both analytical and numerical techniques have been used to study special cases of the system. It is shown that the electron interaction can lead to renormalization of the exponent and to oscillations in the electron density.
LIST OF PAPERS:
Paper I Mats Horsdal and Jon Magne Leinaas, Explicit mapping between a two-dimensional quantum Hall system and a one-dimensional Luttinger liquid. I. Luttinger parameters, Phys. Rev. B 76, 195321 (2007)
Paper II Mats Horsdal and Jon Magne Leinaas, Explicit mapping between a two-dimensional quantum Hall system and a one-dimensional Luttinger liquid. II. Correlation functions Phys. Rev. B 76, 195322 (2007)
Paper III Mats Horsdal, Effects of interaction induced second Landau level mixing in the nu=1 quantum Hall effect, Submitted to Phys. Rev. B