Nontrivial $d$-electrons driven superconductivity of transition metal diborides

Leveraging the progress of first-principles modellings in understanding the mechanisms of superconductivity of materials, in this work we investigate the phonon-mediated superconducting properties of transition metal diborides. We report that TaB$_2$ and NbB$_2$ show superconducting transition temperatures as high as 27.0 and 26.0~K at ambient conditions, respectively, comparable with those obtained for CaB$_2$ or MgB$_2$. By mode-by-mode analysis of the electron-phonon-coupling, we reveal that the high superconducting temperature of transition metal diborides is due mainly to the strong coupling between $d$ electrons of the transition metals and the acoustic phonon modes along out-of-plane vibrations. This fact is distinct from that of CaB$_2$ or MgB$_2$, where the superconductivity stems mainly from the boron $p_x$ and $p_y$ orbitals, which couple strongly to the optical phonon modes dominated by in-plane B atomic vibrations. Further, we find that transition metal diborides present only a superconducting gap at low temperatures, whereas CaB$_2$ or MgB$_2$ are double superconducting gap superconductors. In addition, we investigate the strain effect on the superconducting transition temperatures of diborides, predicting that $T_c$ can be further enhanced by optimizing the phonon and electronic interactions. This study sheds some light on the exploring high $T_c$ boron-based superconductor materials.