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We study the quantum phase transitions of a disordered two-dimensionalquantum anomalous Hall insulator with $s$-wave superconducting proximity, whichare governed by the percolation theory of chiral Majorana fermions. Based onsymmetry arguments and a renormalization group analysis, we show there aregenerically two phase transitions from Bogoliubov-de Gennes Chern number$\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor)and then to $\mathcal{N}=2$, in agreement with the conclusion from the bandtheory without disorders. Further, we discuss the critical scaling behavior ofthe $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiraltopological superconductor recently observed in the experiment. In particular,we compare the critical behavior of the half plateau induced by topologicalsuperconductor with that predicted recently by alternative explanations of thehalf plateau, and show that they can be distinguished in experiments.

Quantum phase transition of chiral Majorana fermion in the presence of disorder