Hilbert transform evaluation for electron-phonon self-energies

Giuseppe Bevilacqua (), Guido Menichetti and Giuseppe Pastori Parravicini
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Giuseppe Bevilacqua: University of Siena
Guido Menichetti: University of Pisa
Giuseppe Pastori Parravicini: University of Pisa

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 1, 1-7

Abstract: Abstract The electron tunneling current through nanostructures is considered in the presence of the electron-phonon interactions. In the Keldysh nonequilibrium formalism, the lesser, greater, advanced and retarded self-energies components are expressed by means of appropriate Langreth rules. We discuss the key role played by the entailed Hilbert transforms, and provide an analytic way for their evaluation. Particular attention is given to the current-conserving lowest-order-expansion for the treament of the electron-phonon interaction; by means of an appropriate elaboration of the analytic properties and pole structure of the Green’s functions and of the Fermi functions, we arrive at a surprising simple, elegant, fully analytic and easy-to-use expression of the Hilbert transforms and involved integrals in the energy domain.

Keywords: Computational; Methods (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2015-60730-0

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