Observation of Zero-Energy Modes with Possible Time-Reversal Symmetry Breaking on Step Edge of CaKFe_4As_4

Topologically nontrivial Fe-based superconductors attract extensive attentions due to their ability of hosting Majorana zero modes (MZMs) which could be used for topological quantum computation. Topological defects such as vortex lines are required to generate MZMs. Here, we observe the robust edge states along the surface steps of CaKFe_4As_4. Remarkably, the tunneling spectra show a sharp zero-bias peak (ZBP) with multiple integer-quantized states at the step edge under zero magnetic field. We propose that the increasing hole doping around step edges may drive the local superconductivity into a state with possible spontaneous time-reversal symmetry breaking. Consequently, the ZBP can be interpreted as an MZM in an effective vortex in the superconducting topological surface state by proximity to the center of a tri-junction with different superconducting order parameters. Our results provide new insights into the interplay between topology and unconventional superconductivity, and pave a new path to generate MZMs without magnetic field.