The recent discovery of high-temperature superconductivity in iron-based compounds has attracted much attention. How to further increase the superconducting transition temperature (T_c) and how to understand the superconductivity mechanism are two prominent issues facing the current study of iron-based superconductors. The latest report of high-T_c superconductivity in a single-layer FeSe is therefore both surprising and significant. Here we present investigations of the electronic structure and superconducting gap of the single-layer FeSe superconductor. Its Fermi surface is distinct from other iron-based superconductors, consisting only of electron-like pockets near the zone corner without indication of any Fermi surface around the zone centre. Nearly isotropic superconducting gap is observed in this strictly two-dimensional system. The temperature dependence of the superconducting gap gives a transition temperature T_c~ 55 K. These results have established a clear case that such a simple electronic structure is compatible with high-T_c superconductivity in iron-based superconductors.

The Majorana fermion, which is its own antiparticle and obeys non-Abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor because of contamination from impurity states or other closely packed Caroli–de Gennes-Matricon (CdGM) states, which hampers further manipulations of MZMs. Here, using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect-free regions of $({\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16})\mathrm{OHFeSe}$, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can naturally be attributed to a MZM arising from the chiral topological surface state of a bulk superconductor. Thus, $({\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16})\mathrm{OHFeSe}$ provides an ideal platform for studying MZMs and topological quantum computing.