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Screening effects in nanoscale junctions with strong electron-phonon couplingopen new physical scenarios. We propose an accurate many-body approach to dealwith the simultaneous occurrence of the Franck-Condon blockade and thescreening-induced enhancement of the polaron mobility. We derive a transparentanalytic expression for the electrical current: transient and steady-statefeatures are directly interpreted and explained. Moreover, the interplaybetween phononic and electronic excitations gives rise to a novel mechanism ofnegative differential conductance. Experimental setup to observe thisphenomenon are discussed.

Screening-induced negative differential conductance in the Franck-Condon blockade regime