Abstract
Recent experiments [Barbero et al. Phys. Rev. B 95, 094505 (2017)] have established that bulk superconductivity $({T}_{c}\ensuremath{\sim}8.3\text{--}8.7\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ can be induced in $\mathrm{Al}{\mathrm{B}}_{2}\text{\ensuremath{-}}\mathrm{type}\phantom{\rule{0.16em}{0ex}}\mathrm{Zr}{\mathrm{B}}_{2}$ and $\mathrm{Hf}{\mathrm{B}}_{2}$, highly covalent refractory ceramics, by vanadium (V) doping. These $\mathrm{Al}{\mathrm{B}}_{2}\text{\ensuremath{-}}\mathrm{structured}$ phases provide an alternative to earlier diamondlike or diamond-based superconducting and superhard materials. However, the underlying mechanism for doping-induced superconductivity in these materials is yet to be addressed. In this paper, we have used first-principles calculations to probe electronic structure, lattice dynamics, and electron-phonon coupling (EPC) in V-doped $\mathrm{Zr}{\mathrm{B}}_{2}$ and consequently examine the origin of the superconductivity. We find that, while doping-induced stress weakens the EPC, the concurrently induced charges strengthen it. The calculated critical transition temperature $({T}_{c})$ in electron (and V)-doped $\mathrm{Zr}{\mathrm{B}}_{2}$ is at least one order of magnitude lower than experiments, despite considering the weakest possible Coulomb repulsion between electrons in the Cooper pair, hinting a complex origin of superconductivity in it.
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