Fig. 5: First-principles electronic and phononic structures of H_xTiSe₂.

a Ball-and-stick model of the protonated 1T-TiSe₂ structure in the ground-state adsorption site with one H atom placed in the van der Waals gap at the Se-Se bridge position (also shown in Fig. 1a). The Brillouin zone with high symmetry points is also shown. b Electronic band structure and density of states of 1T-H₁TiSe₂ in the structure shown in panel (a) (red) compared with the pristine 1T-TiSe₂ dispersion (gray). c Orbital character of the electronic band structure of 1T-H₁TiSe₂, with the \({d}_{{z}^{2}}\) character of the bands indicated by the size of the black circles. d Phonon dispersion relations (left panel), density of states (central panel), and electron-phonon spectral function α²F(ω) (right panel) of pressurized 1T-H₁TiSe₂. The spectral contributions of the H-derived modes are highlighted as red dashed lines. The right panel also reports the frequency-dependence of the total electron-phonon coupling λ(ω) as a solid blue line.