The electron tunneling current through nanostructures is considered in the presence ofthe electron-phonon interactions. In the Keldysh nonequilibrium formalism, the lesser,greater, advanced and retarded self-energies components are expressed by means ofappropriate Langreth rules. We discuss the key role played by the entailed Hilberttransforms, and provide an analytic way for their evaluation. Particular attention isgiven to the current-conserving lowest-order-expansion for the treament of theelectron-phonon interaction; by means of an appropriate elaboration of the analyticproperties and pole structure of the Green’s functions and of the Fermi functions, wearrive at a surprising simple, elegant, fully analytic and easy-to-use expression of theHilbert transforms and involved integrals in the energy domain.
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|Titolo:||Hilbert transform evaluation for electron-phonon self-energies|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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