Fractal dimensionality of wave functions at the mobility edge: Quantum fractal in the Landau levels
- 15 May 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 33 (10) , 7310-7313
- https://doi.org/10.1103/physrevb.33.7310
Abstract
Wave functions at the critical energy separating localized and extended states in disordered electron systems are shown to have fractal structure. We present results for the fractal dimensionality numerically calculated for a two-dimensional system with Landau quantization in strong magnetic fields together with a turbulent structure when the phase of the wave function is considered. Implications for transport properties are discussed.Keywords
This publication has 18 references indexed in Scilit:
- Critical localization in two-dimensional Landau quantizationPhysical Review Letters, 1985
- Fractal Structures Formed by Kinetic Aggregation of Aqueous Gold ColloidsPhysical Review Letters, 1984
- Fractal Character of Eigenstates in Disordered SystemsPhysical Review Letters, 1984
- Renormalization-group analysis of the discrete quasiperiodic Schrödinger equationPhysical Review B, 1984
- Critical behaviour of extended states in disordered systemsJournal of Physics C: Solid State Physics, 1983
- Diffusion-Limited Aggregation, a Kinetic Critical PhenomenonPhysical Review Letters, 1981
- Inverse participation ratio in 2+? dimensionsZeitschrift für Physik B Condensed Matter, 1980
- New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall ResistancePhysical Review Letters, 1980
- Real-space renormalisation-group theory for Anderson localisation: decimation method for electron systemsJournal of Physics C: Solid State Physics, 1980
- An introduction to lattice gauge theory and spin systemsReviews of Modern Physics, 1979