Majorana fermion is the particle whose antiparticle is itself. Searching for Majorana fermion is one of the most important research in high energy physics. However, there is no solid evidence about the existence of this kind of real particle. In condensed matters, there is a quasiparticle which is always bounding with topological defect. Since the creation and annihilation operators of this quasiparticle are self-conjugation operator, the quasiparticle is called Majorana zero mode (MZM). MZMs obey the non-Abel statistics. Braiding MZMs is one of the routes to carry out the fault-tolerant topological quantum computing.

Prof. GAO Hongjun's group and Prof. DING Hong's group from the Institute of Physics of the Chinese Academy of Sciences have been cooperating together to study iron-based superconductor since 2017. They study MZM by using scanning tunneling microscopes (STM). They observed pure MZM in the vortex on the surface of FeTe_0.55Se_0.45 for the first time at 2017. Then, they carried out further study aimed at the phenomenon that some vortex may not host MZMs. The inhomogeneity of the chemical potential of FeTe_0.55Se_0.45 breaks the strong topological bulk state in same area, which leads to the absence of topological surface states.

In addition, they observed nearly quantized Majorana conductance plateau in the vortex in FeTe_0.55Se_0.45, which is a compellent evidence for the existence of MZM. They also observed MZM in the vortex in CaKFe₄As₄ single crystal, which expands the study of MZM to iron-phosphorus-based superconductors.

This Majorana platform also presents new challenges for the basic understanding of defect excitations in superconductors with a topological nontrivial band structure, and new possibilities for creating MZMs under different physical conditions. In general, superconductors can host two kinds of defect excitations as in-gap bound states: the YSR states localized at a magnetic impurity and the Caroli-de-Gennes-Matricon (CdGM) states inside a magnetic vortex core. YIN Jiaxin et al. studied Fe_1+x(Te, Se) under the guidance of Prof. PAN Suhen and Prof. DING. They observed a robust zero bias peak (ZBP) at interstitial Fe atoms. But there has been a lack of further understanding of this ZBP.

Recently, a theory work proposed that a quantum anomalous vortex (QAV) can be induced near the Fe atom located at C₄ symmetric site when the exchange coupling is strong enough. The role of the magnetic field is played by the exchange coupling of the spin and orbital moment of the Fe impurity located at the C₄ symmetric sites, which generates circulating supercurrents by the spin-orbit coupling and modulates the phase of the superconducting order parameter. An MZM emerges inside the QAV core from the superconducting TSS, since the Berry phase of the Dirac fermions transforms the total angular momentum quantum number of the CdGM vortex core states into integers.

Prof. GAO's group and Prof. DING's group, together with Prof. WANG Ziqiang, studied the bound states on single Fe adatom on the surface of FeTe_0.55Se_0.45. They observed both YSR states and ZBP. The ZBP, which is always coexisted with in-gap states with integer energy level spacing, doesn't shift or split when crossing the Fe adatom. This result conforms the property that the CdGM states have integer energy level spacing in the topological vortex in the quantum limit.

In addition, the ZBP disappears at 4 K, which is the same as the behavior of MZM in magnetic field-induced vortex. The ZBP does not split under a very high magnetic field (8 T). All the results provide compelling evidences to the existence of QAV and MZM in QAV.

Furthermore, they manipulated the exchange coupling between Fe adatom and substrate by changing the position between the STM tip and Fe adatom. The change of the exchange coupling leads to the reversible transition between YSR states and MZM. In addition, they observed the hybridization between the MZMs in QAV and field induced-vortex.

The study on magnetic Fe adatoms deposited on the surface of FeTe_0.55Se_0.45 superconductors revealed the spontaneous formation of anomalous vortex matter with integer quantized core states and MZMs in zero external field, and the reversible transition between the YSR impurity and the QAV with increasing exchange interaction strength.

Together with the observed fusion hybridization of the MZMs in the QAV nucleated at the Fe adatom and the nearby field-induced Abrikosov vortex, these findings provide compelling evidences to the existence of QAV and MZM.

This research paves a new path to study the interaction and braiding of MZMs. The results have been published online in Nature Communications.

This research was supported by grants from the National Natural Science Foundation of China, the National Key Research and Development Projects of China, and the Chinese Academy of Sciences.