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Majorana zero modes (MZMs) are Majorana-fermion-like quasiparticles existing in crystals or hybrid platforms with topologically non-trivial electronic structures. They obey non-Abelian braiding statistics and are considered promising to realize topological quantum computing. Discovery of MZM in the vortices of the iron-based superconductors (IBSs) has recently fueled the Majorana research in a way which not only removes the material barrier requiring construction of complicated hybrid artificial structures, but also enables observation of pure MZMs under higher temperatures. So far, MZMs have been observed in iron-based superconductors including FeTe0.55Se0.45, (Li0.84Fe0.16)OHFeSe, CaKFe4As4, and LiFeAs. In this topical review, we present an overview of the recent STM studies on the MZMs in IBSs. We start with the observation of MZMs in the vortices in FeTe0.55Se0.45 and discuss the pros and cons of FeTe0.55Se0.45 compared with other platforms. We then review the following up discovery of MZMs in vortices of CaKFe4As4, impurity-assisted vortices of LiFeAs, and quantum anomalous vortices in FeTe0.55Se0.45, illustrating the pathway of the developments of MZM research in IBSs. Finally, we give perspective on future experimental works in this field. [ABSTRACT FROM AUTHOR]

For iron-based superconductors, the phase diagrams under pressure or strain exhibit emergent phenomena between unconventional superconductivity and other electronic orders, varying in different systems. As a stoichiometric superconductor, LiFeAs has no structure phase transitions or entangled electronic states, which manifests an ideal platform to explore the pressure or strain effect on unconventional superconductivity. Here, we observe two types of superconducting states controlled by orientations of local wrinkles on the surface of LiFeAs. Using scanning tunneling microscopy/spectroscopy, we find type-I wrinkles enlarge the superconducting gaps and enhance the transition temperature, whereas type-II wrinkles significantly suppress the superconducting gaps. The vortices on wrinkles show a C2 symmetry, indicating the strain effects on the wrinkles. By statistics, we find that the two types of wrinkles are categorized by their orientations. Our results demonstrate that the local strain effect with different directions can tune the superconducting order parameter of LiFeAs very differently, suggesting that the band shifting induced by directional pressure may play an important role in iron-based superconductivity. The evolution of superconductivity in LiFeAs with respect to pressure or strain remains elusive. Here, the authors observe different response of superconducting states due to different orientations of local wrinkles on the surface of LiFeAs. [ABSTRACT FROM AUTHOR]

The iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation. Despite the discovery of Majorana zero modes (MZM) in iron-based superconductors, sample inhomogeneity may destroy MZMs during braiding. Here, authors observe MZM in impurity-assisted vortices due to tuning of the bulk Dirac fermions in a homogeneous superconductor LiFeAs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]