Dirac Fermions with Disorder in Two Dimensions: Exact Result

Abstract

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.

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

References in corpus (3)

• Non-magnetic impurities in two dimensional superconductors
• Quantized Hall conductivity of Bloch electrons: topology and the Dirac fermion
• Integer Quantum Hall Effect for Lattice Fermions

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• Anderson localization in a two-dimensional random gap model
• Universality, exponents and anomaly cancellation in disordered Dirac fermions
• Scaling behavior of disordered lattice fermions in two dimensions
• Quantum Fractality on the Surface of Topological Insulators