  We study solutions of $2 \times 2$ systems $(h D_t + \mathcal{D}) \Psi_t = 0$
on $\mathbb{R}^2$ in the semiclassical regime $h \rightarrow 0$. Our Dirac
operator $\mathcal{D}$ is a standard model for interfaces between topological
insulators: it represents a semimetal at null energy, and distinct topological
phases at positive / negative energies. Its semiclassical symbol has two
opposite eigenvalues, intersecting conically along the curve $\Gamma$ of
positions / momenta where the material behaves like a semimetal.
  We prove that wavepackets solving $(h D_t + \mathcal{D}) \Psi_t = 0$,
initially concentrated in phase space on $\Gamma$, split in two parts. The
first part travels coherently along $\Gamma$ with predetermined direction and
speed. It is the dynamical manifestation of the famous "edge state". The second
part immediately collapses.
  Our approach consists of: (i) a Fourier integral operator reduction; (ii) a
careful WKB analysis of a canonical model; (iii) a reconstruction procedure. It
yields concrete formulas for the speed and profile of the traveling modes. As
applications, we analytically describe dynamical edge states for models of
magnetic, curved, and strained topological insulators.
