We present quasiparticle self-consistent $GW$ $(\mathrm{QS}GW)$ calculations of semimetallic bulk Bi. We go beyond the conventional $\mathrm{QS}GW$ method by including the spin-orbit coupling throughout the self-consistency cycle. This approach improves the description of the electron and the hole pockets considerably with respect to standard density functional theory (DFT), leading to excellent agreement with experiment. We employ this relativistic $\mathrm{QS}GW$ approach to conduct a study of the semimetal-to-semiconductor and the trivial-to-topological transitions that Bi experiences under strain. DFT predicts that an unphysically large strain is needed for such transitions. We show, by means of the relativistic $\mathrm{QS}GW$ description of the electronic structure, that an in-plane tensile strain of only 0.3% and a compressive strain of 0.4% are sufficient to cause the semimetal-to-semiconductor and the trivial-to-topological phase transitions, respectively. Thus, the required strain moves into a regime that is likely to be realizable in experiment, which opens up the possibility to explore bulklike topological behavior of pure Bi.

• Received 1 November 2014
• Revised 18 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.125129