Non-Hermitian topological Euler insulators

• URL: http://arxiv.org/abs/2608.25411v1
• Date: Wed, 26 Aug 2026 06:14:30 GMT
• Title: Non-Hermitian topological Euler insulators
• Abstract summary: Topological Euler insulators emerge in multiband systems with real Bloch Hamiltonians and wavefunctions.<n>We extend the conception of topological Euler insulators to non-Hermitian systems and propose a theoretical framework to unlock their nontrivial Euler topology.<n>Our study establishes the presence of topological Euler bands in non-Hermitian systems and unveils their intriguing physical characteristics, thereby broadening the existing territory of topological matter in non-Hermitian open systems.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological Euler insulators emerge in multiband systems with real Bloch Hamiltonians and wavefunctions. Their fragile topologies are characterized by the Euler class of degenerate bands and protected by the $PT$ or $C_2T$ symmetry in two dimensions, which go beyond the tenfold $K$-theory classification of topological matter. In this work, we extend the conception of topological Euler insulators to non-Hermitian systems and propose a theoretical framework to unlock their nontrivial Euler topology. Focusing on two-dimensional, three-band non-Hermitian lattice models with symmetric Hamiltonians, we formulate a comprehensive description of their topological Euler bands, entanglement spectrum and bulk-boundary correspondence. Three typical models of non-Hermitian Euler insulators are constructed and investigated explicitly to illustrate our theory. Unique topological phase transitions and anomalous edge-band overlaps with non-Hermitian origins are further identified. Our study establishes the presence of topological Euler bands in non-Hermitian systems and unveils their intriguing physical characteristics, thereby broadening the existing territory of topological matter in non-Hermitian open systems.

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