Non-Hermitian three-dimensional two-band Hopf insulator

Abstract

The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider two types of non-Hermitian Hopf insulators, one without and one with the non-Hermitian skin effect. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian models. However, the modulus of the Hopf index remains quantized in the gapped regions. The model without the non-Hermitian skin effect allows an accurate evaluation of its generalized Hopf index and energy spectrum, showing an agreement between the gapless-regime estimations from the systems with periodic- and open- boundary conditions. Near the zero-energy plane, Fermi rings can be observed whenever the Hopf index is quantized at nonzero values, and there is a bulk-boundary correspondence between the modulus of the Hopf index and the number of Fermi rings. The other model manifests the non-Hermitian skin effect in the generalized Brillouin zone and shows the skewed profiles of the bulk states. The Hopf index and energy spectrum are shown to be sensitive to the boundary condition in the presence of the non-Hermitian skin effect.

9 pages, 9 figures, submitted

References in corpus (15)

• Correspondence between winding numbers and skin modes in non-hermitian systems
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
• Topological surface states in three-dimensional magnetic insulators
• Topological Classification of Non-Hermitian Hamiltonians
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Many-body approach to non-Hermitian physics in fermionic systems
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Spontaneous topological pumping in non-Hermitian systems
• Observation of the Hopf Links and Hopf Fibration in a 2D topological Raman Lattice

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• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Non-Hermitian Hopf insulators
• From orthogonal link to phase vortex in generalized dynamical Hopf insulators