Analysis of Two Dimensional Electronic States in Strong Magnetic Field by Random Matrix Model

Electronic states in a two dimensional random system with a perpendicular strong magnetic field are analyzed by using a model Hamiltonian matrix which has random elements reflecting the characteristics of the random potential such as the correlation length. The random matrix model is suitable for numerical calculations and has advantages compared to preparing the random potential by distributing impurities particularly when discussing correlated potential. As an example, the fractal dimensionality of extended states in the lowest Landau band is considered. It is found that the extended states have multifractal properties. The results are compared with those obtained through the random potential model.