Band alignment and bending in Dirac semimetal Na$_3$Bi thin films on Al$_2$O$_3$ substrates

Dirac semimetals Na$_3$Bi and Cd$_3$As$_2$ are interesting due to topologically protected degenerate Weyl nodes with linear dispersions at the Fermi level and topological Fermi-arc surface states. Recently, thin films of Na$_3$Bi have been epitaxially grown on Al$_2$O$_3$ substrates and their electron transport properties have been measured. However, the interfaces between the Dirac semimetal films and the substrates have not been characterized yet. Here we investigate electronic and topological properties of thin Na$_3$Bi films on Al$_2$O$_3$ substrates near the Fermi level, by using density-functional theory with spin-orbit coupling. We also discuss effects of band alignment and band bending on the electronic and topological properties and compare with experimental data.