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Bulk and surface electronic structures, calculated using density functionaltheory and a tight-binding model Hamiltonian, reveal the existence of twotopologically invariant (TI) surface states in the family of cubic Biperovskites (ABiO$_3$; A = Na, K, Rb, Cs, Mg, Ca, Sr and Ba). The two TIstates, one lying in the valence band (TI-V) and other lying in the conductionband (TI-C) are formed out of bonding and antibonding states of theBi-$\{$s,p$\}$ - O-$\{$p$\}$ coordinated covalent interaction. Below a certaincritical thickness of the film, which varies with A, TI states of top andbottom surfaces couple to destroy the Dirac type linear dispersion andconsequently to open surface energy gaps. The origin of s-p band inversion,necessary to form a TI state, classifies the family of ABiO$_3$ into two. Forclass-I (A = Na, K, Rb, Cs and Mg) the band inversion, leading to TI-C state,is induced by spin-orbit coupling of the Bi-p states and for class-II (A = Ca,Sr and Ba) the band inversion is induced through weak but sensitive secondneighbor Bi-Bi interactions.

Topologically Invariant Double Dirac States in Bismuth based Perovskites: Consequence of Ambivalent Charge States and Covalent Bonding