Recent progress of scanning tunneling microscopy/spectroscopy study of Majorana bound states in the FeTe_0.55Se_0.45superconductor

Majorana bound states (MBSs) are spatially-localized zero-energy quasiparticles following non-Abelian braiding statistics that hold a great promise for fault-Tolerant topological quantum computing. Different platforms have been designed to realize the MBSs in condensed matter, including semiconducting nanowire in proximity to conventional superconductors, superconductor-Topological insulator layered heterostructures, 1D atomic chains on superconducting surface. Recently, iron-based superconductors have emerged as a new platform for studying Majorana zero mode. A sharp zero-bias peak inside a vortex core that does not split when moving away from the center is observed by scanning tunneling microscopy (STM) in FeTe0.55Se0.45. This zero-energy mode is assigned to the MBS. In this topic review, we present an overview of the recent experimental works of STM studies on the MBS. We start with the STM identification of MBSs in the vortices in FeTe0.55Se0.45 and discuss the advantages FeTe0.55Se0.45 compared with other platforms. We then review the topological origin of the MBS and discuss the reason why the MBS is not seen in every single vortex. We also review the recently observed nearly quantized conductance plateau feature of the MBS owing to its particle-Antiparticle equivalence. Finally, we give perspective on future experimental works in this field, where the next important steps towards braiding of MBS can be expected.