Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations

We introduce a systematic method to spectrally design quasi-one-dimensional crystal models described by the Dirac equation in the low-energy regime. The method is based on the supersymmetric transformation applied to an initially known pseudo-spin-1/2 model. This allows extending the corresponding susy partner so that the new model describes a pseudo-spin-1 system. The spectral design allows the introduction of a flat-band and discrete energies at will into the new model. The results are illustrated in two examples where the Su-Schriefer-Heeger chain is locally converted into a stub lattice.