|Protected Gapless Edge States In Trivial Topology
|Physics - Mesoscopic Systems and Quantum Hall Effect; Physics - Mesoscopic Systems and Quantum Hall Effect; Physics - Strongly Correlated Electrons
|Phys. Rev. B 107, 075126 (2022)
Bulk-boundary correspondence serves as an important feature of the strong
topological insulators, including Chern insulators and $Z_2$ topological
insulators. Under nontrivial band topology, the protected gapless edge states
correspond to the Wannier obstruction or Wilson-loop winding in the bulk.
Recent studies show that the bulk topological features may not imply the
existence of protected gapless edge states. Here we address the opposite
question: Does the existence of protected gapless edge states necessarily imply
the Wannier obstruction or Wilson-loop winding? We provide an example where the
protected gapless edge states arise without the aforementioned bulk topological
features. This trivialized topological insulator belongs to a new class of
systems with non-delta-like Wannier functions. Interestingly, the gapless edge
states are not protected by the crystalline symmetry; instead the protection
originates from the mirror antisymmetry, a combination of chiral and mirror
symmetries. Although the protected gapless edge states cannot be captured by
the bulk topological features, they can be characterized by the spectral flow
in the entanglement spectrum.
7 pages, 4 figures
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