Bound state in continuum-like solutions in one-dimensional heterostructures

We examine the one-dimensional Dirac equation with modulated or position-dependent velocity. In particular, it is shown that using suitable velocity profiles it is possible to create bound state in continuum (BIC)-like as well as discrete energy bound state solutions. -- Highlights: ► We study the one-dimensional massless Dirac equation with modulating Fermi velocity. ► We find a transformation which maps the problem to that of a Schroedinger free particle. ► For suitable velocity profiles bound states in continuum (BIC)-like as well as discrete energy states are found.