The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTeSe, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

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 FeTe 0.55 Se 0.45 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 FeTe 0.55 Se 0.45 and establish it as an excellent platform for further studies on MZMs.Majorana zero modes (MZMs) are proposed to be building blocks of fault-tolerant topological quantum computation 1 due to their non-Abelian statistics. Several systems are predicted to host MZMs, such as intrinsic p-wave superconductors 2,3 , and multiple heterostructures combining strong spin-orbital coupling (SOC) and superconductivity 4-12 .Recently, a new single-material platform of iron-based superconductors (FeSC) has been discovered 13-15 , in which topological nontrivial bands and high-T c superconductivity coexist naturally 16 without the need of proximity effect common to other proposals. This has led to the observation of a pronounced zero-bias conductance peak (ZBCP) in vortices of FeTe 0.55 Se 0.45 17 and a related compound 18 .While a ZBCP that does not split across the vortex core is regarded as a strong indication of MZM and topological nature of the superconducting vortex 4,17-19 , the observation of ZBCP alone is not enough to prove it. Although several pieces of evidence including spatial profile, tunneling barrier dependence, magnetic field dependence and temperature evolution are fully consistent with MZM in FeTe 0.55 Se 0.45 17 , more convincing verification requires demonstration of the nontrivial topology of the superconducting vortex and underlying band structure. The single crystal of FeTe 0.55 Se 0.45 is a unique platform to demonstrate the fundamental distinction between the trivial and topological vortices. Its large ratio 17,20 of Δ /E F enables realization of the quantum limit 21 , where the low-lying quasiparticle bound states, the so-called Caroli-de Gennes-Matricon bound states (CBSs) 22 , become discrete levels observable separately within the hard superconducting gap. These bound states are the eigenstates of the vortex planar angular momentum 21-23 with the eigenvalue determined by topological phase of the host superconductor 4,24 . Even thou...