Phonon-assisted Andreev reflection at a Majorana zero mode

Abstract

One of the typical features of Majorana zero mode (MZM) at the end of topological superconductor is a zero-bias peak in the tunneling spectroscopy of the normal lead-superconductor junction. In this paper we study on a model with one phonon mode coupling to the superconductor lead of the normal lead-superconductor junction, which can be viewed as an electron-lead/phonon-coupled-MZM/holelead structure. The phonon-coupled MZM acts as a series of channels in which electron can turn into hole by absorbing and emitting phonons. 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.

Dual Negative Differential of Heat Generation in a Strongly Correlated Quantum Dot Side-Coupled to Majorana Bound States

“…The system under investigation can be described by the following Hamiltonian (Z 1) [28,29,31,32,37].…”

“…To decouple the electron-phonon interaction in Eq. 1, we next perform a canonical transformation, [28,29,31,32,37],H…”

“…where the dot level is ε̃d ε d − gω q and Coulomb interaction strengthŨ U − 2gω q with g (λ q /ω q ) 2 . The tunnelling amplitude t kβ and the coupling strengths between the dot and MBSs λ are individually given by t̃k α t kα X and λ̃ λX with X exp [−g (a † − a)] [28,29]. The other quantities inHMBSs are the same as in Eq.…”

“…In fact, due to the unique charge neutral and zero energy properties, the above detection schemes still come with great difficulties and it is not sure if the existence of the MBSs can be completely determined. Recently, impacts of electron-phonon interaction on the MBSs-assisted transport have been studied [28,29]. This is triggered by two motivations: one is that the electronphonon interaction will induce significant decoherence effects that will change the transport behaviors and roles in quantum computation [30]; the other is that the phonons will play important roles in Majorana-induced Andreev reflection processes [28].…”

“…Recently, impacts of electron-phonon interaction on the MBSs-assisted transport have been studied [28,29]. This is triggered by two motivations: one is that the electronphonon interaction will induce significant decoherence effects that will change the transport behaviors and roles in quantum computation [30]; the other is that the phonons will play important roles in Majorana-induced Andreev reflection processes [28]. With continuing improvement of nanofabrication techniques, the length of the device becomes smaller than that of electron-phonon scattering, and thus the electron-phonon interaction is the main cause of heat generation by electrical current [30][31][32][33][34].…”