The unambiguous detection of Majorana bound states (MBSs) in topological superconductors has been a central topic of condensed matter physics for recent years. So far, the presence of MBSs was demonstrated experimentally in a number of topologically nontrivial superconducting systems. In this connection, clear evidences of Majorana bound states are only obtained by the detection of zero-bias conductance peaks in tunneling transport measurements. In recent years, it became clear that various additional signatures of Majorana modes need to be investigated in order to complete our understanding.
In our presentation, we summarize two unambiguous fingerprints which can act as a ‘smoking gun’evidence. First we study the anomalous nonlocal conductance due to chiral Majorana edge states in a superconductor/ferromagnet hybrid as shown in Fig. 1(a). We obtain the important result that the chiral nature of the Majorana edge states causes an anomalously long-range and chirality-sensitive nonlocal transport in this device. This, in turn, enables us to identify conclusively the moving direction and further properties of the chiral Majorana edge states . Secondly, we propose a novel experiment for achieving the first experimental observation of the anomalous proximity effect caused by Majorana bound states. In particular, we discuss the differential conductance of a semiconductor/superconductor hybrid as shown in Fig. 1(b), which contains a planar topological Josephson junction realized in recent experiments. The conductance spectrum changes drastically through the topological phase transition because the Majorana bound state appearing only in the topologically nontrivial phase can penetrate into the dirty normal segment and form the resonant transmission channel there . In general, our results allow contrasting singlet and triplet superconductivity employing properties of Majorana modes beyond zero bias peaks.
 S. Ikegaya, S. Tamura, D. Manske, and Y. Tanaka, arXiv: 2007.12888 (2020)