Conductance of a Quantum Dot in the Presence of a Phonon Field

We theoretically investigate the electrical transport property of a quantum dot with longitudinal optical phonons. The conductance through the dot connected to two leads is calculated by the nonequilibrium Green function within the Landauer--Buttiker framework. The numerical examples of the
conductance with different electron--phonon coupling strengths show that the presence of a phonon field typically results in the suppression of the main peak accompanied by some phonon side peaks. Both the main peak and the side peaks are sensitive to the electron--phonon coupling strength, which is related to temperature. Our results for this system are consistent with some related previous works but the calculation is comparatively simple.