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

TL;DR

This paper theoretically investigates how electron-phonon interactions affect resonant tunneling and Fano resonance in quantum dots, revealing voltage-dependent decoherence effects and phonon-related resonance shape changes.

Contribution

It provides a detailed analysis of bias-voltage effects on decoherence in quantum dots with e-ph interaction, highlighting limitations of canonical transformation methods.

Findings

Elastic phonon processes suppress resonant amplitude below threshold voltage.

Inelastic phonon processes cause dephasing and broaden resonance at higher voltages.

Fano resonance shape becomes more symmetric with increasing bias voltage, matching experimental observations.

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 Keldysh Green function method and perturbation with respect to the e-ph interaction. With optical phonons of energy $\omega_0$, only the elastic process takes place when $eV<\omega_0$, in which electrons emit and absorb phonons virtually. The process suppresses the resonant amplitude. When $eV>\omega_0$, 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 cannot be obtained by the canonical transformation method to consider the e-ph interaction if its effect on the tunnel coupling is neglected. 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.