  We study transport across p-n junctions of gapped two-dimensional semi-Dirac
materials: nodal semimetals whose energy bands disperse quadratically and
linearly along distinct crystal axes. The resulting electronic properties ---
relevant to materials such as TiO$_2$/VO$_2$ multilayers and
$\alpha$-(BEDT-TTF)$_2$I$_3$ salts --- continuously interpolate between those
of mono- and bi-layer graphene as a function of propagation angle. We
demonstrate that tunneling across the junction depends on the orientation of
the tunnel barrier relative to the crystalline axes, leading to strongly
non-monotonic current-voltage characteristics, including negative differential
conductance in some regimes. In multi-valley systems these features provide a
natural route to engineering valley-selective transport.
