Abstract
Noninteracting electrons in a smooth two-dimensional random potential are localized in the large magnetic field limit. In contrast to Anderson localization, eigenstates with large localization lengths occur with a probability proportional to a universal power of their size, with the power given in terms of percolation critical exponents. Adding a parallel electric field causes extended states to appear in numbers proportional to a power of . This implies a nonlinear broadening of steps in the quantized Hall conductivity. The results for a parallel electric field are obtained by considering a graded percolation problem, in which the probability that a site is occupied varies with position.
- Received 19 January 1983
DOI:https://doi.org/10.1103/PhysRevB.27.7539
©1983 American Physical Society