Distinguishing Majorana bound states from Andreev bound states through differential conductance and current noise spectrum

Abstract

We investigate the quantum transport through a quantum dot coupled with a superconducting (SC) nanowire. By elaborating the differential conductance and current noise spectrum, we focus on the distinct characteristics of the topological Majorana bound states (MBSs) and trivial Andereev bound states (ABSs) hosted in SC wire. For MBSs with a topological quality factor $q=1$, we observe the degenerate features manifested as the zero-bias peak (ZBP) in differential conductance and the Rabi dips degeneracy (RDD) in noise spectrum. In contrast, for ABSs with $q<1$, the splitting of these degenerate features depends on the linewidth, arising from realistic measurement conditions. Furthermore, we identify the critical quality factors $q_{\rm c}$ and $q_{\rm s}$ associated with the emergences of ZBP and RDD, respectively. The value of $q_{\rm c}$ is temperature-dependent, and we establish a suitable temperature window to ensure the visibility of single ZBP in the experiments. Whereas, $q_{\rm c}$ depends on the coupling strength rather than the temperature. Typical values for these quality factors are approximately $q_{\rm c}\approx 0.93$ and $q_{\rm s}\approx 0.99$. Our results suggest that the degenerate Rabi spectrum signal could serve as a hallmark for the presence of MBSs, which goes beyond the scope of differential conductance.