Fig. 6: Schematic and PCB implementation of Hopf-Link experiment. | Nature Communications

Fig. 6: Schematic and PCB implementation of Hopf-Link experiment.

From: Imaging nodal knots in momentum space through topolectrical circuits

Fig. 6

a Schematic of our 2-leg ladder LC circuit array, whose Laplacian takes the form of the Hopf-link at resonance when the component admittances are chosen according to (15)–(18). b Each rectangle in (a) corresponds to a parallel combination of an inductor and a logical capacitor whose specifications are indicated in Supplementary Table 1. As explained in the main text, each inductor can be accurately tuned to vary kykz near the drumhead region. c Schematic representation of one repeating unit cell of the circuit used to construct final experiment. The switches are set to open when the inductors are being tuned, and closed when the impedance of the entire circuit is measured to map out the drumhead region. d Experimental PCB realization of one repeating unit. Visible are the inductors equipped with ferrite rods or shorted wire loops, which respectively increase/decrease the inductances in a tunable manner. e Renderings of the same PCB to emphasize its physical structure. Each large cylinder represents a variable inductor, while the components prefixed by “C” represent capacitors that are connected in parallel to form the logical capacitors in Fig. 9. Detailed specifications of these components are given in Supplementary Tables 1 and 2.

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