Scaling Behavior of Level Statistics in Quantum Hall Regime

概要

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The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electronsysterns subject to strong magnetic fields, is analyzed nunaerically in the light of the randommatrix theory. The energy dependences of' the effective level repulsion parameter, the two levelcorrelation, the GUE-GOD crossover pararneter, and the rigidity (or 43-statistics) of the leveldistributions are investigated for different systern sizes by unfolding the original data and bydividing the unfolded spectrurn into small regions. It is shown that the critical exponent of thelocalization length as a function of energy can be determined through the energy dependenceof the level statistics. The analyses are carried out not only for the lowest Landau band (LB)but also for the second lowest LB. Furthermore the effect of finite range of disordered potentialis studied. The short-ranged potential case in the second lowest LB is found to be pathologicalas in other studies of critical behavior, and it is confirrrred that this pathological behavior isiznproved in the case of disordered potential with finite ranges.
社団法人日本物理学会の論文
1996-06-15