  Topological metals with protected band-crossing points have been attracting
great interest. Here we report novel topological band features in a family of
metal diboride materials. Using first- principles calculations, we show that
these materials are metallic, and close to Fermi level, there appears
coexistence of one pair of nodal rings and one pair of triply-degenerate nodal
points (TNPs). The nodal ring here is distinct from the previously studied ones
in that its formation requires four entangled bands, not just two as in
previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably,
we show that FNR features Dirac-cone-like surface states, in contrast to the
usual drumhead surface states for two-band nodal rings. Due to the presence of
inversion symmetry, the TNP here is also different from those discussed
previously in inversion-asymmetric systems. Especially, when spin-orbit
coupling is included, the TNP here transforms into a novel Dirac point that is
close to the borderline between the type-I and type-II Dirac point categories.
We discuss their respective symmetry protections, and construct effective
models for their characterization. The large linear energy range (> 2 eV) in
these materials should facilitate the experimental detection of the signatures
of these nontrivial band crossings.
