Topological insulators and superconductors are known to host robust gapless states at their real-space boundaries. Conventionally, these boundary gapless states have been understood in terms of their spectral flow: if the spatial dimension is greater than two, the boundary spectrum bridges the occupied and unoccupied energy bands. However, recent findings indicate that particle-hole and chiral symmetries do not necessarily imply spectral flow. In fact, boundary gapless states can be detached from the bulk spectrum [1]. In this seminar, I will begin by introducing a concrete model that demonstrates detached boundary states in 3D class AIII insulators, followed by an exploration of how non-Hermitian topology offers a framework to understand these detached boundary states. These states can be identified with the image of the map from imaginary-line-gapped to point-gapped topological phases. Additionally, the robustness of the gapless nature of the detached boundary states can be attributed to a nontrivial topological invariant associated with the boundary states [2,3].
[1] Alexander Altland, Piet W. Brouwer, Johannes Dieplinger, Matthew S. Foster, Mateo Moreno-Gonzalez, and Luka Trifunovic, PRX 14, 011057(2024). [2] Daichi Nakamura, KS, Kenji Shimomura, Masatoshi Sato, Kohei Kawabata, arXiv:2407.09458. [3] KS, Daichi Nakamura, Kenji Shimomura, Masatoshi Sato, Kohei Kawabata, arXiv:2407.18273.