Abstract: The electron-phonon interaction has important effects on the nonequilibrium transport through the semiconductor quantum dot (QD) or the single molecule transistor.Based on the improved electron-phonon disentangled scheme and the equation of motion approach of the nonequilibrium Green functions,it is found that at low temperature,the phonon sidebands in the spectral function are quite sensitive to the relative positions of the renormalized QD level and the Fermi levels in the leads,showing the broken particle-hole symmetry in the QD.The phonon satellites of the Kondo peak come from two types of spin exchange processes.In the presence of moderate Zeeman splitting,these two types of Kondo satellites can be recognized in the spin resolved spectral function.These features of the spectral functions will also manifest themselves in the nonlinear differential conductance.

Key words: quantum dot,  electron-phonon interaction,  spectral function, Kondo声子伴带