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We present a paradoxical finding that, in the vicinity of a topological phasetransition in a quantum anomalous Hall system (Chern insulator), topologynearly always (except when the system obeys charge-conjugation symmetry)results in a significant extension of the edge-state structure beyond theminimal one required to satisfy the Chern numbers. The effect arises from theuniversal gapless linear-in-momentum Hamiltonian of the nodal semimetaldescribing the system right at the phase transition, whose form is enforced bythe change of the Chern number. Its emergent approximate chiral symmetryresults in an edge-state band in the vicinity of the node, in the region ofmomenta where such form is dominant. Upon opening the gap, this edge-state bandis modified in the gap region, becoming "protected" (connected to the valencebulk band with one end and conduction band with the other) in the topologicallynontrivial phase and "nonprotected" (connected to either the valence orconduction band with both ends) in the trivial phase. The edge-state bandpersists in the latter as long as the gap is small enough.

physical review. b./physical review. b

Paradoxical extension of the edge states across the topological phase  transition due to emergent approximate chiral symmetry in a quantum anomalous  Hall system