Imaging nodal knots in momentum space through topolectrical circuits

Ching Hua Lee (), Amanda Sutrisno, Tobias Hofmann, Tobias Helbig, Yuhan Liu, Yee Sin Ang (), Lay Kee Ang, Xiao Zhang (), Martin Greiter and Ronny Thomale ()
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Ching Hua Lee: National University of Singapore
Amanda Sutrisno: Singapore University of Technology and Design
Tobias Hofmann: University of Würzburg, Am Hubland
Tobias Helbig: University of Würzburg, Am Hubland
Yuhan Liu: The University of Chicago
Yee Sin Ang: Singapore University of Technology and Design
Lay Kee Ang: Singapore University of Technology and Design
Xiao Zhang: Sun Yat-sen University
Martin Greiter: University of Würzburg, Am Hubland
Ronny Thomale: University of Würzburg, Am Hubland

Nature Communications, 2020, vol. 11, issue 1, 1-13

Abstract: 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.

Date: 2020
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DOI: 10.1038/s41467-020-17716-1

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