Abstract
Calculations using first principles methods and strong coupling theory are carried out to understand the electronic structure and superconductivity in cubic and tetragonal TiH$_2$. A large electronic density of states at the Fermi level in the cubic phase arises from Ti-$t_{2g}$ states and leads to a structural instability against tetragonal distortion at low temperatures. However, constraining the in-plane lattice constants diminishes the energy gain associated with the tetragonal distortion, allowing the cubic phase to be stable at low temperatures. Calculated phonon dispersions show decoupled acoustic and optic modes arising from Ti and H vibrations, respectively and frequencies of optic modes to be rather high. The cubic phase has a large electron-phonon coupling parameter $\lambda$ and critical temperature of several K. Contribution of the hydrogen sublattice to $\lambda$ is found to be small in this material, which we understand from strong coupling theory to be due to the small H-$s$ DOS at the Fermi level and high energy of hydrogen modes at the tetrahedral sites.
