  Vortices in topological superconductors host Majorana zero modes (MZMs),
which are proposed to be building blocks of fault-tolerant topological quantum
computers. Recently, a new single-material platform for realizing MZM has been
discovered in iron-based superconductors, without involving hybrid
semiconductor-superconductor structures. Here we report on a detailed scanning
tunneling spectroscopy study of a FeTe0.55Se0.45 single crystal, revealing two
distinct classes of vortices present in this system which differ by a
half-integer level shift in the energy spectra of the vortex bound states. This
level shift is directly tied with the presence or absence of zero-bias peak and
also alters the ratios of higher energy levels from integer to
half-odd-integer. Our model calculations fully reproduce the spectra of these
two types of vortex bound states, suggesting the presence of topological and
conventional superconducting regions that coexist within the same crystal. Our
findings provide strong evidence for the topological nature of
superconductivity in FeTe0.55Se0.45 and establish it as an excellent platform
for further studies on MZMs.
