Fig. 1.

Design and implementation of SSH-like left-handed transmission line. a Schematic of the transmission line circuit with alternating capacitances: linear capacitors with capacitance C_a, and back-to-back varactors with nonlinear capacitance C_b. The capacitances act like hoppings in a nonlinear Su–Schrieffer–Heeger (SSH) model. An input voltage is applied at points A or B to probe the topologically trivial or nontrivial lattice. b Photograph of the printed circuit board. c Capacitance C_b versus bias voltage. Dots are calculated from varactor manufacturer data, and the solid curve is the fit based on Eq. (5). d, e Calculated eigenfrequencies of a finite closed linear circuit, versus the capacitance ratio α = C_a/C_b. The characteristic frequency is f_a = ω_a/2π ≈ 19 MHz, and the lattice has 40 sites. Two cases are shown: d C_a-type capacitors at the edge, for which the α > 1 gap is topologically nontrivial; e C_b-type capacitors at the edge, for which the α > 1 gap is trivial. Red dotted curves indicate the band-edge frequencies $f_a\mathrm{∕}\sqrt{2}$ and $\sqrt{\alpha \mathrm{∕}2}{f}_a$. Blue dashes indicate the operating regime of the nonlinear circuit, with α ≈ 1.3 in the linear (low-voltage) limit and α effectively increasing with voltage amplitude