@article{LeeSutrisnoHofmannetal.2020,
  author    = {Lee, Ching Hua and Sutrisno, Amanda and Hofmann, Tobias and Helbig, Tobias and Liu, Yuhan and Ang, Yee Sin and Ang, Lay Kee and Zhang, Xiao and Greiter, Martin and Thomale, Ronny},
  title     = {Imaging nodal knots in momentum space through topolectrical circuits},
  series = {Nature Communications},
  volume    = {11},
  journal   = {Nature Communications},
  doi       = {10.1038/s41467-020-17716-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-230407},
  year      = {2020},
  abstract  = {Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological "drumhead" surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment which maps out the topological drumhead region of a Hopf-link. Topological phases with knotted configurations in momentum space have been challenging to realize. Here, Lee et al. provide a systematic design and measurement of a three-dimensional knotted nodal structure, and resolve its momentum space drumhead states via a topolectrical RLC-type circuit.},
  language  = {en}
}