Fig. 4: Simulated drumhead state measurements under various OBCs.

The black diamond-shaped points indicate points in reciprocal space with admittance eigenvalues smaller than their respectively admittance thresholds j_x, j_y corresponding to x, y open boundaries, as obtained from Xyce circuit simulations. These points are contained in regions of the surface BZ which are bounded by the projected 3D theoretically computed bulk nodal structures (colored green, red and blue). a shows 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 thresholds are chosen to be j_x = 0.0027Ω⁻¹ and j_y = 0.0020 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 thresholds are chosen to be j_x = 0.0030Ω⁻¹ and j_y =  0.0025 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 thresholds are chosen to be j_x = 0.0028 Ω⁻¹ and j_y = 0.0032 Ω⁻¹.