We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the dissipative non-Hermitian realm where the knotted nodal lines are generic and thus stable towards any small perturbation. We show that these nodal structures, taking the forms of Turk's head knots, appear in both continuum- and lattice models with relatively short-ranged hopping that is within experimental reach. To determine the topology of the nodal structures, we devise an efficient algorithm for computing the Alexander polynomial, linking numbers and higher order Milnor invariants based on an approximate and well controlled parameterisation of the knot.
Cited by 6
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Hu et al., Knots and Non-Hermitian Bloch Bands
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Lee et al., Enhanced higher harmonic generation from nodal topology
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Bergholtz et al., Exceptional topology of non-Hermitian systems
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Koch et al., Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
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Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Stockholm University [Univ Stockholm]
- 2 Universitetet i Oslo / University of Oslo [UiO]
- 3 Technische Universität Dresden / Dresden University of Technology [TUD]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
- Vetenskapsrådet / Swedish Research Council