Valley-Selective Landau-Zener Oscillations in Semi-Dirac p-n Junctions

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.