Extended Data Figure 4: Electronic band structure of Os at moderate compressions along the high-symmetry lines in the hcp Brillouin zone.

Energies are given relative to the Fermi energy, which is taken to be zero. Calculations are carried out at pressures of 0 GPa (a, b), 97.5 GPa (c, d), and 134 GPa (e, f). a, c, e, The k -resolved spectral functions A( k , ω) obtained with LDA+DMFT. b, d, f, The band structure obtained with LDA. In both cases, we used the experimental lattice parameters (a = 2.734 Å, c/a = 1.580 at 0 GPa; a = 2.578 Å, c/a = 1.589 at 97.5 GPa; a = 2.540 Å, c/a = 1.590 at 134 GPa). Our LDA+DMFT calculations predict that two ETTs occur in hcp Os upon compression. In a, a band at the Γ point is well below the Fermi energy at ambient pressure; however, it nearly touches the Fermi energy at 97.5 GPa, and the corresponding hole pocket has already appeared at 134 GPa, giving rise to a change of the Fermi surface topology, that is, to an electronic topological transition at about 101.5 GPa (Extended Data Fig. 5). Our LDA+DMFT calculations also indicate that another ETT at the L point should occur above 134 GPa, at about 183 GPa (Extended Data Fig. 5).