Marcus Stålhammar, Lukas Rødland, Gregory Arone, Jan Carl Budich, Emil J. Bergholtz
SciPost Phys. 7, 019 (2019) ·
published 8 August 2019
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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.
Mr Stålhammar: "Dear Referee, Thank you for..."
in Report on Hyperbolic Nodal Band Structures and Knot Invariants