Fig. 4: Field maps and transport along the perimeter of a wheel graph: observation of chiral edge states.

a Field maps of thermal fluctuations in the W₅ network. These plot the root-mean-square thermomechanical amplitude of the zero-detuning mode for each resonator in the network (integrated between Ω_j ± 2 × 2π kHz), for homogeneous fluxes Φ = ± π/2. At these frequencies and fluxes, the edge states are mapped. b Amplitude response of the five-mode wheel network W₅ with equal-handed flux Φ = ± π/2 (Fig. 3, bottom) to continuous wave driving of the central resonator a₁ (left) and perimeter resonator a₂ (middle and right). Coupling rates J/(2π) = J_s/(2π) = 4 kHz. Driving the perimeter resonator a₂ excites the edge mode at zero detuning, while driving the hub resonator a₁ does not. Measured amplitudes are in good agreement with the predicted responses (black lines, Methods), with all necessary parameters (coupling J, dissipation γ_j and driving strength f_j) determined independently. c Field maps of locally driven edge states: Amplitude response at each site of the network when resonantly driving a₂ (Δ_m = 0, indicated by dotted lines in panel a). Clockwise (counter-clockwise) chiral transport along the perimeter is observed for Φ = π/2 (Φ = − π/2) from the decay away from the source, due to the trade-off between vibration transfer and decay at each site (see Supplementary Fig. 3). Differences in clockwise and counter-clockwise transport are explained by disorder in the dissipation rates (Supplementary Table I). Experimental data is shown on the left, theoretical simulations of the driven experiments (including the measured dissipation rates) are shown on the right.