Spin-dependent electron–phonon interaction on quantum transport through an Aharonov-Bohm interferometer with a quantum dot connected to Majorana zero mode

• The spin dependent phonon-assistant transport properties are discussed in the Aharonov-Bohm interferometer. • The electron phonon interaction causes to the split of the spectral peak and the current fluctuation. • The spin polarization strength leads to the increase (decrease) of the up-spin (down-spin) spectral function. • The magnetic flux can change the position of the peak structure of the spectral function. We theoretically investigate the spin-dependent transport through an Aharonov-Bohm interferometer in the presence of electron phonon interaction. We calculate the spectral function, the current and the liner conductance with the variation of the electron phonon interaction, spin polarization and magnetic flux. The small electron phonon interaction enhances the spectral function and the large one causes the split of the spectral peak. The spin polarization strength leads to the increase (decrease) of the up-spin (down-spin) spectral function. Besides, the current first increases and then decreases to zero with the increase of electron phonon interaction. The up-spin (down-spin) current decreases first and increases (decreases) with the variable spin polarization. The current and linear conductance present a 4π periodic with the change of magnetic flux. Our research can provide the relevant physical mechanism for the electron phonon interaction in quantum dot coupled Majorana zero mode system.