  The electrons found in Dirac materials are notorious for being difficult to
manipulate due to the Klein phenomenon and absence of backscattering. Here we
investigate how spatial modulations of the Fermi velocity in two-dimensional
Dirac materials can give rise to localization effects, with either full
(zero-dimensional) confinement or partial (one-dimensional) confinement
possible depending on the geometry of the velocity modulation. We present
several exactly solvable models illustrating the nature of the bound states
which arise, revealing how the gradient of the Fermi velocity is crucial for
determining fundamental properties of the bound states such as the zero-point
energy. We discuss the implications for guiding electronic waves in few-mode
waveguides formed by Fermi velocity modulation.
