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

The influence of electron-phonon interaction on the transmission phase shift of an electron passing through a quantum dot is investigated by using scattering theory. The transmission phase versus the intradot level shows a series of phonon-induced dips. These dips are highly sensitive to the electron-phonon interaction strength lambda, and they are much more pronounced than phonon-assisted subpeaks appearing in the conductance. Phonon-induced 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 proportional to lambda(2) for small lambda but T-d proportional to lambda at large lambda.