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

## TL;DR

This study predicts and analyzes two topologically invariant surface states in cubic Bi perovskites, revealing their origin from covalent bonding and charge states, with implications for surface energy gaps and band inversion mechanisms.

## Contribution

It introduces the existence of two TI surface states in Bi perovskites and explains their formation from covalent interactions and charge state ambivalence, highlighting different inversion mechanisms.

## Key findings

- Two TI surface states identified in cubic Bi perovskites.
- TI states are formed from Bi-O covalent bonding and charge states.
- Surface states couple and gap out below a critical film thickness.

## Abstract

Bulk and surface electronic structures, calculated using density functional theory and a tight-binding model Hamiltonian, reveal the existence of two topologically invariant (TI) surface states in the family of cubic Bi perovskites (ABiO$_3$; A = Na, K, Rb, Cs, Mg, Ca, Sr and Ba). The two TI states, one lying in the valence band (TI-V) and other lying in the conduction band (TI-C) are formed out of bonding and antibonding states of the Bi-$\{$s,p$\}$ - O-$\{$p$\}$ coordinated covalent interaction. Below a certain critical thickness of the film, which varies with A, TI states of top and bottom surfaces couple to destroy the Dirac type linear dispersion and consequently 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. For class-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 second neighbor Bi-Bi interactions.