  Recently, the search for Majorana fermions (MFs) has become one of the most
important and exciting issues in condensed matter physics since such an exotic
quasiparticle is expected to potentially give rise to unprecedented quantum
phenomena whose functional properties will be used to develop future quantum
technology. Theoretically, the MFs may reside in various types of topological
superconductor materials that is characterized by the topologically protected
gapless surface state which are essentially an Andreev bound state.
Superconducting doped topological insulators and topological crystalline
insulators are promising candidates to harbor the MFs. In this review, we
discuss recent progress and understanding on the research of MFs based on
time-reversal-invariant superconducting topological materials to deepen our
understanding and have a better outlook on both the search for and realization
of MFs in these systems. We also discuss some advantages of these bulk systems
to realize MFs including remarkable superconducting robustness against
nonmagnetic impurities.
