Finite-size effects on metallization versus chiral Majorana fermions

The search for chiral Majorana fermions in quantum anomalous Hall insulator/\textit{s}-wave superconductor heterostructures has attracted intense interest, yet remains controversial due to the lack of conclusive evidence. A key issue is that the heterostructure's metallization can produce half-integer conductance signatures resembling those of chiral Majorana fermions, thereby complicating their identification. In this Letter, we investigate how the competition between metallization and chiral Majorana fermions depends on superconductor thickness, revealing its critical role through three distinct regimes: (i) For thin superconductors ($\sim$10 nm), metallization shows periodic oscillations with thickness, matching the Fermi wavelength. (ii) Intermediate thicknesses ($\sim$100 nm) exhibit periodic windows for observing chiral Majorana fermions. (iii) Thick superconductors ($\sim$1000 nm) sustain stable chiral Majorana fermions that are insensitive to thickness variations. These results suggest that superconductor thickness is a key control parameter for advancing efforts to conclusively identify chiral Majorana fermions.