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

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