Doping-induced superconductivity of ZrB2 and HfB2

Unlike the widely studied $s$-type two-gap superconductor ${\mathrm{MgB}}₂$, the chemically similar compounds ${\mathrm{ZrB}}₂$ and ${\mathrm{HfB}}₂$ do not superconduct above 1 K. Yet it has been shown that small amounts of self or extrinsic doping (in particular with vanadium), can induce superconductivity in these materials. Based on results of different macroscopic and microscopic measurements, including magnetometry, nuclear magnetic resonance (NMR), resistivity, and muon-spin rotation (${\ensuremath{\mu}}⁺\mathrm{SR}$), we present a comparative study of ${\mathrm{Zr}}_0.96{\mathrm{V}}_0.04{\mathrm{B}}₂$ and ${\mathrm{Hf}}_0.97{\mathrm{V}}_0.03{\mathrm{B}}₂$. Their key magnetic and superconducting features are determined and the results are considered within the theoretical framework of multiband superconductivity proposed for ${\mathrm{MgB}}₂$. Detailed Fermi surface (FS) and electronic structure calculations reveal the difference between ${\mathrm{MgB}}₂$ and transition-metal diborides.