  Ultrathin films of topological Dirac semimetal, Na$_3$Bi, has recently been
revealed as an unusual electronic materials with field-tunable topological
phases. Here we investigate the electronic and transport properties of
ultrathin Na$_3$Bi as an electrical contact to two-dimensional (2D) metal, i.e.
graphene, and 2D semiconductor, i.e. MoS$_2$ and WS$_2$ monolayers. Using
combined first-principle density functional theory and nonequilibrium Green's
function simulation, we show that the electrical coupling between Na$_3$Bi
bilayer thin film and graphene results in a notable interlayer charge transfer,
thus inducing sizable $n$-type doping in the Na$_3$Bi/graphene
heterostructures. In the case of MoS$_2$ and WS$_2$ monolayers, the lateral
Schottky transport barrier is significantly lower than many commonly studied
bulk metals, thus unraveling Na$_3$Bi bilayer as a high-efficiency electrical
contact material for 2D semiconductors. These findings opens up an avenue of
utilizing topological semimetal thin film as electrical contact to 2D
materials, and further expands the family of 2D heterostructure devices into
the realm of topological materials.
