Fig. 5: Pressure-tuned topological and Lifshitz transitions revealed from electronic band structure and susceptibility calculations.
a Band structure as obtained from first principles calculation at two values of pressure P = 0 GPa, and 2.3 GPa, marked by solid and dashed lines, respectively. The band structure is shown along a path in the reciprocal space (see Supplementary Table 5), and the color of the bands denotes the band inversion driving the change of topology (symmetry indicators z2w1 = 1, z2w2 = 1, z2w3 = 0, z4 = 0 P = 0 GPa and z2w1 = 0, z2w2 = 0, z2w3 = 0, z4 = 3 for P = 2.3 GPa). b Leading eigenvalue of the random phase approximation (RPA) susceptibility evaluated along the same path in momentum space as in (a) for P = 2.3 GPa and a Hubbard interaction of U = 6.5 eV. The leading divergence discussed in the main text arises along the Y1-Γ line. c Surface spectral function for a slab at P = 2.3 GPa, with a surface cone arising at \(\underline{{\Gamma }}\) located at ~ 50 meV. The coordinates of \(\underline{{Z}}\), \(\underline{{\Gamma }}\) and \(\underline{{R}}\) in terms of the basis vectors of the reciprocal cell in the semi-infinite slab geometry are (0,1/2), (0,0), and (1/2,1/2), respectively. Fermi surface as obtained from the first principles calculations at d, P = 0 GPa, e, P = 1.63 GPa, and f, P = 2.3 GPa in the first Brillouin zone. Blue (purple) Fermi surface sheets mark the electron-like (hole-like) pockets. In (e and f), the Lifshitz transition fusing electron-like pockets and extending over Brillouin zone boundaries, respectively, is visible. Additionally, in (f), a hole in the hole-like pocket along qx emerges.
