  A new class of multi-scale structures, referred to as `parabolic
metamaterials' is introduced and studied in this paper. For an elastic
two-dimensional triangular lattice, we identify dynamic regimes, which
corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such
regimes lead to a highly localised and focussed unidirectional beam when the
lattice is excited. We also show that the flexural rigidities of elastic
ligaments are essential in establishing the `parabolic metamaterial' regimes.
