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  • 1.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Stålhammar, Marcus
    Stockholm University, Faculty of Science, Department of Physics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Knotted non-Hermitian metals2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 16, article id 161115Article in journal (Refereed)
    Abstract [en]

    We report on the occurrence of knotted metallic band structures as stable topological phases in non-Hermitian (NH) systems. These knotted NH metals are characterized by open Fermi surfaces, known in mathematics as Seifert surfaces, that are bounded by knotted lines of exceptional points. Quite remarkably, and in contrast to the situation in Hermitian systems, no fine tuning or symmetries are required in order to stabilize these exotic phases of matter. By explicit construction, we derive microscopic tight-binding models hosting knotted NH metals with strictly short-ranged hopping, and investigate the stability of their topological properties against perturbations. Building up on recently developed experimental techniques for the realization of NH band structures, we discuss how the proposed models may be experimentally implemented in photonic systems.

  • 2.
    Stålhammar, Marcus
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Rødland, Lukas
    Arone, Gregory
    Stockholm University, Faculty of Science, Department of Mathematics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Hyperbolic nodal band structures and knot invariants2019In: SciPost Physics, E-ISSN 2542-4653, Vol. 7, no 2, article id 019Article in journal (Refereed)
    Abstract [en]

    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.

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