Using an ab-initio density functional theory based electronic structure method with a semi-local density approximation, we study thin-film electronic properties of two topological insulators based on ternary compounds of Tl (Thallium) and Bi (Bismuth). We consider TlBiX$_2$ (X=Se, Te) and Bi$_2$$X$_2$Y (X,Y= Se,Te) compounds which provide better Dirac cones, compared to the model binary compounds Bi$_2$X$_3$ (X=Se, Te). With this property in combination with a structurally perfect bulk crystal, the latter ternary compound has been found to have improved surface electronic transport in recent experiments. In this article, we discuss the nature of surface states, their locations in the Brillouin zone and their interactions within the bulk region. Our calculations suggest a critical thin film thickness to maintain the Dirac cone which is significantly smaller than that in binary Bi-based compounds. Atomic relaxations or rearrangements are found to affect the Dirac cone in some of these compounds. And with the help of layer-projected surface charge densities, we discuss the penetration depth of the surface states into the bulk region. The electronic spectrum of these ternary compounds agrees very well with the available experimental results.Comment: 9 pages, 11 figures, 1 table, Accepted for publication in Physical Review
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