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Majorana quasiparticles (MQPs) in condensed matter play an important role instrategies for topological quantum computing but still remain elusive. Vortexcores of topological superconductors may accommodate MQPs that appear as thezero-energy vortex bound state (ZVBS). An iron-based superconductor Fe(Se,Te)possesses a superconducting topological surface state that has beeninvestigated by scanning tunneling microscopies to detect the ZVBS. However,the results are still controversial. Here, we performed spectroscopic-imagingscanning tunneling microscopy with unprecedentedly high energy resolution toclarify the nature of the vortex bound states in Fe(Se,Te). We found the ZVBSat 0 $\pm$ 20 $\mu$eV suggesting its MQP origin, and revealed that somevortices host the ZVBS while others do not. The fraction of vortices hostingthe ZVBS decreases with increasing magnetic field, while chemical andelectronic quenched disorders are apparently unrelated to the ZVBS. Theseobservations elucidate the conditions to achieve the ZVBS, and may lead tocontrolling MQPs.

Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)