Fig. 3: Simulated nodal structure measurements under PBCs. | Nature Communications

Fig. 3: Simulated nodal structure measurements under PBCs.

From: Imaging nodal knots in momentum space through topolectrical circuits

Fig. 3

Points in reciprocal space corresponding to admittance eigenvalues smaller than a threshold js are colored black, which collectively delineate their theoretically computed respective nodal links or knots (orange). a Two entangled unknots, defined as the Hopf-link. The black dots combine the simulation results with circuit dimensions of \(\left(22\times 22\times 16\right)\), \(\left(23\times 23\times 20\right)\), \(\left(16\times 22\times 19\right)\), \(\left(22\times 22\times 14\right)\), \(\left(25\times 20\times 23\right)\) and \(\left(25\times 24\times 23\right)\). The admittance threshold is chosen to be js = 0.00335 Ω−1. b Depicts a trefoil knot showing the combined simulations of circuit system sizes of \(\left(20\times 20\times 20\right)\), \(\left(21\times 21\times 21\right)\), \(\left(24\times 15\times 15\right)\), \(\left(21\times 20\times 25\right)\), \(\left(18\times 19\times 17\right)\), \(\left(17\times 18\times 21\right)\), \(\left(23\times 21\times 19\right)\), \(\left(19\times 25\times 23\right)\) and \(\left(20\times 20\times 22\right)\). The admittance bound is threshold js = 0.0032 Ω−1. c Illustrates a figure-8 knot with \(\left(23\times 23\times 23\right)\), \(\left(20\times 20\times 25\right)\), \(\left(20\times 20\times 21\right)\), \(\left(19\times 16\times 18\right)\), \(\left(17\times 14\times 16\right)\), \(\left(19\times 25\times 25\right)\) and \(\left(25\times 21\times 22\right)\) unit cells in the respective directions. The admittance threshold is chosen to be js = 0.0037 Ω−1.

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