Z 2 topology of bismuth

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 ($\ensuremath{\approx}400$ nm) and more.