Drude conductivity of a granular metal

David Perkins, Robert Smith

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We present a complete derivation of the analog to Drude conductivity in granular metals using diagrammatic methods. The derivation of Drude conductivity in a homogeneous metal using Kubo linear response theory is somewhat involved, with the evaluation of a singular double integral being required to cancel the diamagnetic response. We first provide a history and careful derivation of this standard result, before analyzing the equivalent situation in the model of a granular metal as a lattice of metallic grains connected by tunneling. A singular triple integral occurs here, and its evaluation gives the result expected from the Einstein relation and Fermi’s golden rule.
Original languageEnglish
Article number168170
Number of pages15
JournalAnnals of Physics
Early online date9 Apr 2020
Publication statusPublished - Jul 2020


  • Diagrammatic quantum field theory
  • Electronic transport
  • Granular metals


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