The density of states near zero energy in a graphene due to strong point defects with random positions are computed. Instead of focusing on density of states directly, we analyze eigenfunctions of inverse T matrix in the unitary limit. Based on numerical simulations, we find that the squared magnitudes of eigenfunctions for the inverse T matrix show random-walk behavior on defect positions. As a result, squared magnitudes of eigenfunctions have equal a priori probabilities, which further implies that the density of states is characterized by the well-known Thomas-Porter-type distribution. The numerical findings of Thomas-Porter-type distribution are further derived in the saddle-point limit of the corresponding replica field theory of inverse T matrix. Furthermore, the influences of the Thomas-Porter distribution on magnetic and transport properties of a graphene, due to its divergence near zero energy, are also examined.
|期刊||Physical Review B - Condensed Matter and Materials Physics|
|出版狀態||已發佈 - 2010 十月 29|
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