TY - JOUR A1 - Lee, Ching Hua A1 - Sutrisno, Amanda A1 - Hofmann, Tobias A1 - Helbig, Tobias A1 - Liu, Yuhan A1 - Ang, Yee Sin A1 - Ang, Lay Kee A1 - Zhang, Xiao A1 - Greiter, Martin A1 - Thomale, Ronny T1 - Imaging nodal knots in momentum space through topolectrical circuits JF - Nature Communications N2 - 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. KW - nodal knots KW - topolectrical circuits Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-230407 VL - 11 ER -