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

We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We analyze Bethe-Salpeter equations for the two-particle vertex in the electron-hole and the electron-electron scattering channels and derive for sys...

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Bibliographic Details
Published in:Journal of physics. Condensed matter 2009-12, Vol.21 (48), p.485501-485501 (8)
Main Author: JANIS, V
Format: Article
Language:English
Subjects:
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Electron states
Electronic structure of disordered solids
Exact sciences and technology
Physics
Theories and models
localized states
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Summary:We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We analyze Bethe-Salpeter equations for the two-particle vertex in the electron-hole and the electron-electron scattering channels and derive for systems with electron-hole symmetry a nonlinear integral equation that the two-particle irreducible vertices from both channels must obey. We use this equation and a parquet decomposition of the full vertex to set restrictions on an admissible form of the two-particle singularity induced by probability conservation. We find that such a singularity in two-particle functions can exist only if it is integrable, that is, only in the metallic phase in dimensions d>2.
ISSN:0953-8984
1361-648X
DOI:10.1088/0953-8984/21/48/485501