Recently, higher-order topology has been expanded to encompass aperiodic quasicrystals, including those with eightfold or twelvefold rotational symmetry. The underlying mechanism for these high-order topological phases is generally protected by $C_n{\mathcal{M}}_z$ symmetry, resulting in the presence of $n$ corner states. However, this mechanism is not applicable to other $C_{2N}$ quasicrystals when $N$ is an odd number. In this work, we propose the realization of a second-order topological superconductor (SOTSC) within a sixfold symmetric bronze-mean hexagonal quasicrystal with six Majorana zero-energy modes. This SOTSC emerges from the combination of vertical and horizontal mirror symmetries, which flips the mass-term sign along the horizontal mirror-invariant line and produces Majorana zero-energy modes at each corner of the quasicrystal sample. Moreover, this mechanism can extend to quasicrystals with $C_{4N+2}$ and $C_{4N}$ rotational symmetries, namely encompassing systems with $C_{2N}$ symmetry. Our findings provide useful guidance for achieving SOTSC in quasicrystals featuring $C_{2N}$ rotational symmetry and introduce bronze-mean hexagonal quasicrystals as a promising platform for exploring quasicrystal SOTSC.

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• Exotic phases of matter
• Symmetry protected topological states
• Topological materials
• Quasicrystals
• Topological superconductors
• Symmetries
• Tight-binding model