Covalent bond inducing strong electron-phonon coupling superconductivity in MgB2 -type transition metal diboride WB2

A recent experiment of polycrystalline ${\mathrm{WB}}_{2}$ with hP3 (space-group 191, prototype ${\mathrm{MgB}}_{2}$) and hP12 (space-group 194, prototype ${\mathrm{WB}}_{2}$) structures was reported to realize 17-K superconductivity (SC) at 90 GPa, and the hP3 structure is believed to be responsible for this emergent SC. However, a microscopic understanding of what makes the hP3 structure so different from the hP12 structure and why the hP3 can feature such strong electron-phonon coupling (EPC) SC is still missing. Here, based on first-principles calculations, we found that in the hP3 structure, W $d$ orbitals contribute most to electronic occupation near the ${E}_{\mathrm{F}}$, and ${d}_{{z}^{2}}$ orbitals of two neighboring W atoms have some hybridization to form weak $\ensuremath{\sigma}$ bonds. The further EPC analysis indicates that the dominant ${d}_{{z}^{2}}$ states are strongly coupled with the out-of-plane phonon modes by stretching the $\mathrm{W}\text{\ensuremath{-}}\mathrm{W}\ensuremath{\sigma}$ bond, thereby yielding a large superconducting gap and high ${T}_{\mathrm{c}}$ of $\ensuremath{\sim}35$ K. By contrast, for the hP12 structure, two neighboring W atoms are isolated without charge hybridization to form the covalent bonds, and, accordingly, their phonon modes become very stiffened, which cannot effectively couple to W $d$ orbital states associated with a lower ${T}_{\mathrm{c}}$ of $\ensuremath{\sim}4$ K. Therefore, our findings not only provide an explanation for the emergent strong EPC SC in the hP3 structure, but also have important implications for the design of high-${T}_{\mathrm{c}}$ superconductors among transition metal borides.