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

Abstract

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 $\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor) and then to $\mathcal{N}=2$, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiral topological superconductor recently observed in the experiment. In particular, we compare the critical behavior of the half plateau induced by topological superconductor with that predicted recently by alternative explanations of the half plateau, and show that they can be distinguished in experiments.

8 pages, 4 figures

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• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
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• Emergent Josephson current of $N=1$ chiral topological superconductor in quantum anomalous Hall insulator/superconductor heterostructures
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• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
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• Multicriticality of Two-dimensional Class D Disordered Topological Superconductors
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• Topological superconductivity in Landau levels
• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
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• Renormalization group analysis of Dirac fermions with random mass
• Controllable Majorana fermions on domain walls of a magnetic topological insulator
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• Genuine topological Anderson insulator from impurity induced chirality reversal
• Disordered Quantum Transport in Quantum Anomalous Hall Insulator-Superconductor Junctions
• Edge optical effect as a probe of chiral topological superconductors
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Revealing Superconducting Chiral Edge Modes via Resistance Distributions
• Magnetic orbital motion and 0.5$e^2/h$ conductance of quantum-anomalous-Hall hybrid strips