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

Abstract

We present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system (Chern insulator), topology nearly always (except when the system obeys charge-conjugation symmetry) results in a significant extension of the edge-state structure beyond the minimal one required to satisfy the Chern numbers. The effect arises from the universal gapless linear-in-momentum Hamiltonian of the nodal semimetal describing the system right at the phase transition, whose form is enforced by the change of the Chern number. Its emergent approximate chiral symmetry results in an edge-state band in the vicinity of the node, in the region of momenta where such form is dominant. Upon opening the gap, this edge-state band is modified in the gap region, becoming "protected" (connected to the valence bulk band with one end and conduction band with the other) in the topologically nontrivial phase and "nonprotected" (connected to either the valence or conduction band with both ends) in the trivial phase. The edge-state band persists in the latter as long as the gap is small enough.

arXiv commentMain Text: 4+ pages, 2 figures; Supplemental Material: 8 pages, 3 figures. The first two authors contributed equally. v2: identical to the published version

References in corpus (15)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Topological Anderson Insulator
• Fingerprint of Different Spin-Orbit Terms for Spin Transport in HgTe Quantum Wells
• Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state
• Quantum Anomalous Hall Effect in Magnetically Doped InAs/GaSb Quantum Wells
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• On the Role of Self-Adjointness in the Continuum Formulation of Topological Quantum Phases

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