Title: Magnetic-field driven evolution of zero-energy mode on Bi islands deposited on Fe(Te,Se)

Abstract: We investigate the magnetic-field dependent evolution of the zero-bias conductance peaks (ZBCPs) on the nanoscale bismuth islands grown on the FeTe$_{0.55}$Se$_{0.45}$ substrate. The ZBCPs can be observed throughout the entire region on these islands, and their characteristics align with the signatures of Majorana zero modes. Remarkably, the evolution of ZBCPs on these islands exhibits anomalous behavior under varying magnetic fields: The magnitude of ZBCPs is first enhanced at weak fields lower than 2 T and then suppressed as the fields further increase. We attribute the non-monotonic evolution of the ZBCPs to the magnetic-field-enhanced topological edge states on these Bi islands. Our findings provide valuable insights into the probable origin of the Majorana zero modes in the Bi-island platform and the magnetic-field response of topological edge states.