Extended Data Fig. 5: Numerical simulations.

a, Geometry of the lattice. The system consists of the sites located in the dashed red rectangle. In the y-direction the system is periodic, as indicated by the repetition of the system in pale colours. The three types of links between sites are indicated by the three shades of blue. The links that are multiplied with a complex phase factor are those that cross the dashed lines. b, Potential energy applied in the x-direction. The position of the edge is chosen in the center of the system, and its width ℓ and its height V₀ are free parameters. In this example, ℓ = a. The shaded region is an example of a zone that can be used to selectively filter the spectrum. c, Full quasienergy spectrum of the system with \({J}_{1}^{{\prime} }/{J}_{1}=0.1\), ℏω = 1.5J₁, ℓ = a and V₀ = 2.25J₁. The system is in the anomalous regime, that is, two pairs of edge modes are visible, linking the two bulk energy bands in the two gaps of the model. The gray circle indicates the eigenstate whose wavefunction is represented in e. d, Exemplary quasienergy spectrum. For this example, the same spectrum as in c is plotted with a color scale that represents the overlap with the shaded region of graph b. e, Wavefunction of the eigenstate at q_y = ± π/L_y and at energy ε ≈ 0 corresponding to the introduced edge edge state. The position of the sites is represented as the black dots and the tunneling bonds are shown in gray. Around these dots, the color indicates the modulus square of the wavefunction, and the direction of the arrow indicates its phase. The position of the edge is shown as a black line.