$Z_2$ topology of bismuth

Abstract

While first-principles calculations with different levels of sophistication predict a topologically trivial $Z_2$ state for bulk bismuth, some photoemission experiments show surface states consistent with the interpretation of bismuth being in a topologically non-trivial $Z_2$ state. We resolve this contradiction between theory and experiment by showing, based on quasiparticle self-consistent $GW$ calculations, that the experimental surface states interpreted as supporting a non-trivial phase are actually consistent with a trivial $Z_2$ invariant. We identify this contradiction as the result of a crosstalk effect arising from the extreme penetration depth of the surface states into the bulk of Bi. A film of Bi can be considered bulk-like only for thicknesses of about 1000 bilayers ($\approx$ 400 nm) and more.

References in corpus (20)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators with Inversion Symmetry
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• WannierTools: An open-source software package for novel topological materials
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• Higher-Order Topology in Bismuth
• Strong spin-orbit splitting on Bi surfaces
• All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
• One-dimensional Topological Edge States of Bismuth Bilayers
• Anomalous Finite Size Effects on Surface States in the Topological Insulator Bi${}_2$Se${}_3$
• Electronic Structures and Surface States of Topological Insulator Bi${}_{1-x}$Sb${}_x$
• Electronic phase transitions of bismuth under strain from relativistic self-consistent GW calculations
• Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement
• Resolving the Topological Classification of Bismuth with Topological Defects
• Non-trivial Surface-band Dispersion on Bi(111)
• Topologically Nontrivial Bismuth(111) Thin Films Grown on Bi2Te3
• Topological surface states on Bi(111) based on empirical tight-binding calculations
• Effect of strain and many-body corrections on the band inversions and topology of bismuth

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• Origin of the Type-II Weyl state in topological antiferromagnetic YbMnBi2
• STM observation of the hinge-states of bismuth nanocrystals
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• A field-induced reentrant insulator state of a gap-closed topological insulator (Bi_{1-x}Sb_x) in quantum-limit states
• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
• Topological blocking at the Bi(111) surface due to surface relaxation
• Magneto transport and first principle study of strong topological insulator gray Arsenic
• Long-range permeation of wave function and superficial surface state due to strong quantum size effects in topological Bi/BiSb heterojunctions