Transmission phase shift of phonon-assisted tunneling through a quantum dot

TL;DR

This paper investigates how electron-phonon interactions affect the transmission phase shift in quantum dots, revealing phonon-induced dips and dephasing behaviors that depend on interaction strength.

Contribution

It provides a detailed analysis of phonon-induced phase shifts and dephasing in quantum dot electron transport using scattering theory, highlighting the sensitivity to interaction strength.

Findings

Phonon-induced dips in transmission phase are highly sensitive to electron-phonon coupling.

Dephasing probability increases monotonically with interaction strength, following different scaling laws.

Phonon effects are more pronounced in phase shifts than in conductance features.

Abstract

The influence of electron-phonon interaction on the transmission phase shift of an electron passing through a quantum dot is investigated by using the scattering theory. The transmission phase versus the intra-dot level shows a serial of phonon-induced dips. These dips are highly sensitive to electron-phonon interaction strength $\lambda$, and they are much more pronounced than phonon-assisted sub-peaks appeared in the conductance. Phonon-induce dephasing is also studied, and the results show that the dephasing probability $T_d$ monotonically increases with the electron-phonon interaction strength $\lambda$. The dephasing probability $T_d \propto\lambda^2$ for small $\lambda$ but $T_d\propto \lambda$ at large $\lambda$.