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We use the framework of supersymmetric transformations in the construction ofcoupled systems of Dirac fermions. Its energy operator is a composite of thegenerators of the associated superalgebra, and the two coupled Dirac fermionsacquire different Fermi velocities. We discuss in detail the peculiar spectralproperties of the new system. The emergent phenomena like level crossing orgeneration of bound states in the continuum (BICs) are illustrated in twoexplicit examples.

Coupled system of Dirac fermions with different Fermi velocities via composites of SUSY operators