Resonant tunneling and Fano resonance in quantum dots with electron-phonon interaction

Abstract

We theoretically study the resonant tunneling and Fano resonance in quantum dots with electron-phonon (e-ph) interaction. We examine the bias-voltage $(V)$ dependence of the decoherence, using the Keldysh Green function method and perturbation with respect to the e-ph interaction. With optical phonons of energy ${\ensuremath{\omega}}_{0}$, only the elastic process takes place when $eV<{\ensuremath{\omega}}_{0}$, in which electrons emit and absorb phonons virtually. The process suppresses the resonant amplitude. When $eV>{\ensuremath{\omega}}_{0}$, the inelastic process is possible, which is accompanied by real emission of phonons. It results in the dephasing and broadens the resonant width. The bias-voltage dependence of the decoherence is not easy to obtain by the canonical transformation method of the e-ph interaction with neglecting the renormalization of tunnel coupling. With acoustic phonons, the asymmetric shape of the Fano resonance grows like a symmetric one as the bias voltage increases, in qualitative accordance with experimental results.