Band structure of the strip Lieb lattice with the straight edges and λ = 0.5t. The on-site energy U is applied on the outermost A- and B-type atoms and is tuned to different values from 0 to 100t. Here, for clarity, only the edge modes localized near the upper boundary are shown. The red (blue) lines correspond to the edge states for the spin-up (spin-down) part. The green line corresponds to the flat bands.