Model non-Hermitian topological operators without skin effect: A general principle of construction, by Daniel J. Salib, Sanjib Kumar Das, Bitan Roy

SciPost Physics Core Home Authoring Refereeing Submit a manuscript About Model non-Hermitian topological operators without skin effect: A general principle of construction Daniel J. Salib, Sanjib Kumar Das, Bitan Roy SciPost Phys. Core 9, 013 (2026) · published 27 February 2026 doi: 10.21468/SciPostPhysCore.9.1.013 pdf BiBTeX RIS Submissions/Reports Abstract We propose a general principle of constructing non-Hermitian (NH) operators for insulating and gapless topological phases in any dimension ($d$) that over an extended NH parameter regime feature real eigenvalues and zero-energy topological boundary modes, when in particular their Hermitian counterparts are also topological. However, the topological zero modes disappear when the NH operators simultaneously accommodate real and imaginary (in periodic systems) or display complex (in systems with open boundary conditions) eigenvalues. These systems are always devoid of NH skin effects, as has also been confirmed from the scaling of the inverse participation ratio, thereby extending the realm of the bulk-boundary correspondence to NH systems in terms of solely the left or right zero-energy boundary localized eigenmodes. We showcase these general and robust outcomes for NH topological insulators in $d=1,2$ and $3$, encompassing their higher-order incarnations, as well as for NH topological Dirac, Weyl, and nodal-loop semimetals. Possible realizations of proposed NH topological phases in designer materials, optical lattices, and classical metamaterials are highlighted. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhysCore.9.1.013TI - Model non-Hermitian topological operators without skin effect: A general principle of constructionPY - 2026/02/27UR - https://scipost.org/SciPostPhysCore.9.1.013JF - SciPost Physics CoreJA - SciPost Phys. CoreVL - 9IS - 1SP - 013A1 - Salib, Daniel J.AU - Das, Sanjib KumarAU - Roy, BitanAB - We propose a general principle of constructing non-Hermitian (NH) operators for insulating and gapless topological phases in any dimension ($d$) that over an extended NH parameter regime feature real eigenvalues and zero-energy topological boundary modes, when in particular their Hermitian counterparts are also topological. However, the topological zero modes disappear when the NH operators simultaneously accommodate real and imaginary (in periodic systems) or display complex (in systems with open boundary conditions) eigenvalues. These systems are always devoid of NH skin effects, as has also been confirmed from the scaling of the inverse participation ratio, thereby extending the realm of the bulk-boundary correspondence to NH systems in terms of solely the left or right zero-energy boundary localized eigenmodes. We showcase these general and robust outcomes for NH topological insulators in $d=1,2$ and $3$, encompassing their higher-order incarnations, as well as for NH topological Dirac, Weyl, and nodal-loop semimetals. Possible realizations of proposed NH topological phases in designer materials, optical lattices, and classical metamaterials are highlighted.ER - × @Article{10.21468/SciPostPhysCore.9.1.013, title={{Model non-Hermitian topological operators without skin effect: A general principle of construction}}, author={Daniel J. Salib and Sanjib Kumar Das and Bitan Roy}, journal={SciPost Phys. Core}, volume={9}, pages={013}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhysCore.9.1.013}, url={https://scipost.org/10.21468/SciPostPhysCore.9.1.013},} Ontology / Topics See full Ontology or Topics database. Topological materials Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Daniel J. Salib, 1 Sanjib Kumar Das, 1 Bitan Roy 1 Lehigh University Funders for the research work leading to this publication Lehigh University National Science Foundation [NSF]