Inverse Participation Number and Fractal Dimensionality of Electronic States in a Two Dimensional System in Strong Perpendicular Magnetic Field

概要

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We study the system size dependence of the inverse participation number (JPN) ofthe electronic eigenstates of a two-dimensional disordered system subject to a strongperpendicular magnetic field with periodic boundary condition in one direction, andDirichlet boundary conditions in the other. Two tzypes of random potentials are con-sidered, random arrays of J-function potentials, and of Gattssian potentials with afinite range of the order of the magnetic length. The fractal climensionality d" of themost extended states is estimated to be 1.39 for 11;.e d-potential case and 1.56 for thefinite-ranged impurity model. The edge states have d"= 1. Their insensitivity to theimpurity potential is explicitly demonstrated. Through the analysis of the energydependence of d', it is found that there is a continuous change of states from the edgestates to the bulk extended states with lowering energy.
社団法人日本物理学会の論文
1989-05-15