Dirac Fermions with Disorder in Two Dimensions: Exact Result

Details Dirac Fermions with Disorder in Two Dimensions: Exact Result Dirac Fermions with Disorder in Two Dimensions: Exact Result

1995-08-22

arxiv.org/abs/cond-mat/9508091v2

Physics

Condensed Matter

extended introduction and additional chapter on 'species multiplication' including two figures

Scientific paper

10.1103/PhysRevB.53.9653

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a random vector potential. It is shown that the imaginary part of the one-particle Green's function can be written as the imaginary part of another Green's function which has only poles on the lower half-plane. Therefore, it is possible to perform a Cauchy integration for a Lorentzian distribution in analogy with the Lloyd model. The results are compared with calculations performed in the continuum limit based on renormalization group and bosonization methods.

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