Effect of electron-phonon interaction on Fano interference in the parallel double quantum dot structure

The effect of electron-phonon interaction on the Fano line-shape in the linear conductance spectrum in the parallel double quantum dot structure is studied. The local and non-local phonon modes are considered and the corresponding electron transport formulae are derived on an equal footing. It is found that the inelastic conductance vanishes in the zero bias and zero temperature case. The local and non-local phonon modes influence the Fano lineshape distinctly. The non-local phonon can change the Fano lineshape effectively, while the local phonon mainly shifts the initial Fano lineshape. These properties are still distinct for the finite temperature case when the inelastic scattoring process is more complex.