Fig. 3

Topolectrical graphene circuit with a zig-zag edge. a circuit diagram. Three types of capacitors connect the nodes in three different orientations, resulting in a two-site unit cell with sublattices denoted by A and B. The circuit is periodically connected in the y-direction with circumference L_y, and grounded on its left and right edges. b Admittance bandstructure j_ZZ(k_y) at the resonant AC frequency \(\tilde \omega\) = 10³s⁻¹, L_y = 12, and capacitor parameters (α, β, γ) = (0.8, 0.2, 1) mF. At both edges (red/blue), lines of degenerate modes with \(j_{0,k_y} \approx 0\) span across the extensive range \(\left| {k_y} \right| < \pi {\mathrm{/}}2\). This leads to the TBR depicted in c, which displays the impedance \(Z_{(x,0),(x,L_y/2)}^{{\mathrm{AA}}}\) between diametrically opposite nodes x sites from the left edge (x = 0). d Impedances \(Z_{(x_1,0),(x_2,0)}^{{\mathrm{AA}}}\) and \(Z_{(x,0),(x,y)}^{{\mathrm{AA}}}\) across intervals perpendicular and parallel to the edges. Note the rapid rise in impedance close to the edge