  The unambiguous detection of the Majorana zero mode (MZM), which is essential
for future topological quantum computing, has been a challenge in recent
condensed matter experiments. The MZM is expected to emerge at the vortex core
of topological superconductors as a zero-energy vortex bound state (ZVBS),
amenable to detection using scanning tunneling microscopy/spectroscopy
(STM/STS). However, the typical energy resolution of STM/STS has made it
challenging to distinguish the MZM from the low-lying trivial vortex bound
states. Here, we review the recent high-energy-resolution STM/STS experiments
on the vortex cores of Fe(Se,Te), where the MZM is expected to emerge, and the
energy of the lowest trivial bound states is reasonably high. Tunneling spectra
taken at the vortex cores exhibit a ZVBS well below any possible trivial state,
suggesting its MZM origin. However, it should be noted that ZVBS is a necessary
but not sufficient condition for the MZM; a qualitative feature unique to the
MZM needs to be explored. We discuss the current status and issues in the
pursuit of such Majorananess, namely the level sequence of the vortex bound
states and the conductance plateau of the ZVBS. We also argue for future
experiments to confirm the Majorananess, such as the detection of the doubling
of the shot noise intensity and spin polarization of the MZM.
