Fig. 1: Electronic and phonon properties of Bi₂O₂Se from first-principle calculations.

a Unit cell of the tetragonal phase and sketch of the ellipsoid Fermi surface at the Γ point of Brillouin zone. b Electronic band structures without spin-orbit coupling along high-symmetry lines of the Brillouin zone of the body-centered tetragonal unit cell. c Phonon dispersion at ambient pressure. d Local potential energy surface with respect to ion displacement along the lowest optical phonon mode, which changes from single-well to double-well by exerting large negative hydrostatic pressure. e One-to-one correspondence between the lattice parameter (a) and the hydrostatic pressure (P). f Frequency evolution of the three lowest optical modes with a, including two transverse modes: TO₁ (blue triangles) and TO₂ (magenta circles) and a longitudinal mode: LO (black squares) . The lattice constant at ambient pressure (3.873 Å) is taken to be the optimized value from DFT calculations and the experimental lattice parameter is 3.88 Å.