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We study transport across p-n junctions of gapped two-dimensional semi-Diracmaterials: nodal semimetals whose energy bands disperse quadratically andlinearly 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 thoseof mono- and bi-layer graphene as a function of propagation angle. Wedemonstrate that tunneling across the junction depends on the orientation ofthe tunnel barrier relative to the crystalline axes, leading to stronglynon-monotonic current-voltage characteristics, including negative differentialconductance in some regimes. In multi-valley systems these features provide anatural route to engineering valley-selective transport.

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