While first-principles calculations with different levels of sophistication predict a topologically trivial ${\mathbb{Z}}_2$ state for bulk bismuth, some photoemission experiments show surface states consistent with the interpretation of bismuth being in a topologically nontrivial ${\mathbb{Z}}_2$ 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 nontrivial phase are actually consistent with a trivial ${\mathbb{Z}}_2$ 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 bulklike only for thicknesses of about 1000 bilayers ($\approx 400$ nm) and more.

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• First-principles calculations
• Surface states
• Topological phases of matter
• Topological materials
• GW method
• Tight-binding model
• Wannier function methods