We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of relativistic two-dimensional fermions in the lowest Landau level. Employing a supersymmetric technique, we calculate the exact density of states for the Cauchy (Lorentzian) distribution for various types of disorder. We use a numerical technique to establish the localization-delocalization (LD) transition in the lowest Landau level. For some types of disorder, the LD transition is shown to belong to a different universality class, as compared to the corresponding nonrelativistic problem. The results are relevant to the integer quantum Hall plateau transitions observed in graphene.
|Physical Review B - Condensed Matter and Materials Physics
|Published - Nov 8 2007
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics