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arXiv · 0901.3057

Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential

V. Janis
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Abstract

We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We use the Bethe-Salpeter equations for the two-particle vertex in the electron-hole and the electron-electron scattering channels and derive for systems with time reversal symmetry a nonlinear integral equation the two-particle irreducible vertices from both channels must obey. We use this equation to test the existence of the diffusion pole in the two-particle vertex. We find that a singularity of the diffusion pole can exist only if it is integrable, that is only in the metallic phase in dimensions $d>2$.

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V. Janis. 2009-01-20. Integrability of the diffusion pole in the diagrammatic description of noninteracting electrons in a random potential. https://doi.org/10.1088/0953-8984%2F21%2F48%2F485501

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