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

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.

17 pages, 14 figures. Changes made on V2 (version-2): Minor revision of the text and an additional information is added in the appendix

References in corpus (14)

• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological Field Theory of Time-Reversal Invariant Insulators
• Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
• Superconductivity Appears in the Vicinity of an Insulating-Like Behavior in CeO${}_{1-x}$F${}_x$BiS${}_2$
• Direct Evidence for the Dirac-Cone Topological Surface States in Ternary Chalcogenide TlBiSe2
• Half-Heusler Topological Insulators: A First-Principle Study with the Tran-Blaha Modified Becke-Johnson Density Functional
• Three-Dimensional Topological Insulators in I-III-VI${}_2$ and II-IV-V${}_2$ Chalcopyrite Semiconductors
• Electronic Structures and Surface States of Topological Insulator Bi${}_{1-x}$Sb${}_x$
• Topological nature and the multiple Dirac cones hidden in Bismuth high-Tc superconductors
• New class of 3D topological insulator in double perovskite
• Fcc breathing instability in BaBiO_3 from first principles
• Two different topological insulator phases in NaBaBi
• Strain-induced topological transition in SrRu${}_2$O${}_6$ and CaOs${}_2$O${}_6$

Cited by in corpus (4)

• Orbital-selective Kondo entanglement and antiferromagnetic order in USb${}_2$
• Pressure and Inversion Symmetry Breaking Field Driven First Order Phase Transition and Formation of Dirac Circle in Perovskites
• Defining the Topological Influencers and Predictive Principles to Engineer Band Structure of Halide Perovskites
• Feeble Metallicity and Robust Semiconducting Regime in Structurally Sensitive Ba(Pb, Sn)O${}_3$ Alloys