Fig. 1. Topological states in 2D. Top row: Schematic comparison of a 2D chiral superconductor and the QH/QAH state. In both systems, TR symmetry is broken and the edge states carry a definite chirality. Bottom row: Schematic comparison of a 2D TR-invariant TSC and the QSH insulator. Both systems preserve TR symmetry and have a helical pair of edge states, where opposite spin states counterpropagate. The dashed lines show that the edge states of the superconductors are Majorana fermions so that the E < 0 part of the quasiparticle spectra is redundant. In terms of the edge-state degrees of freedom, we have (QSH) = (QH/QAH) ² = (Helical SC)² = (Chiral SC)⁴. The QAH state can be obtained from the QSH state by magnetic doping, and the chiral TSC state can be obtained from the QAH state by proximity contact with a conventional superconductor. The superscripts 1, 2, 4 denote relation of the number of degree of freedom of edge states in these topological matter. Adapted from Ref. [26], APS.

Fig. 2. Chiral Majorana fermion: (a) Basic idea: the quantum anomalous Hall chiral edge state splits into two chiral Majorana fermions; (b) the hybrid quantum anomalous Hall-superconductor device for chiral Majorana fermion. Adapted from Ref. [41], APS.

Fig. 3. Braiding of chiral Majorana fermion: (a) The QAH-TSC-QAH device realize the non-Abelian gate which is equivalent to a Hadamard gate H followed by a Pauli-Z gate Z; (b) quantum interference in the QAH-TSC-QAH-TSC Corbino junction. Adapted from Ref. [38], PNAS.