Phonon-Assisted Andreev Reection at Majorana Zero Mode

One of the typical features of Majorana zero mode (MZM) at the edge of topological superconductor is a zero-bias peak in the tunneling spectroscopy of the normal-superconductor (NS) junction. We study on a model with one phonon mode coupling to the superconductor lead of the NS junction, which can be viewed as an electron-lead/phonon-coupled-MZM/hole-lead structure. The phonon-coupled MZM acts as a series of channels in which electron can turn into hole by transmitting phonons to itself. These channels present in the local density of states(LDOS) as a series of stripes, generating the corresponding peaks in the tunneling spectroscopy. In LDOS, the electron-phonon interaction narrows and redistributes the weight among stripes. In the tunneling spectroscopy, the heights of peaks present a feature of the multi-phonon process. With these investigations, our work illuminates the mechanism of phonon-assisted Andreev reflection at a Majorana zero mode.