Non-Hermitian Hopf insulators

• URL: http://arxiv.org/abs/2504.15154v1
• Date: Mon, 21 Apr 2025 14:57:46 GMT
• Title: Non-Hermitian Hopf insulators
• Authors: Daichi Nakamura, Kohei Kawabata,
• Abstract summary: We classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands.<n>Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class AIII)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity gives rise to distinctive complex-energy gap structures, known as point gaps, and associated topological phases with no analogs in Hermitian systems. However, non-Hermitian counterparts of Hopf insulators have remained largely elusive. Here, we generally classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands. Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class A). Explicitly constructing prototypical models from the Hermitian Hopf insulator, we further demonstrate that these non-Hermitian topological phases lead to anomalous point-gapless boundary states spectrally detachable from the bulk bands.

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