### Abstract

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.

Original language | English |
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Article number | 155462 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 82 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2010 Oct 29 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*82*(15), [155462]. https://doi.org/10.1103/PhysRevB.82.155462