  Topological semimetal phases in two-dimensional (2D) materials have gained
widespread interest due to their potential applications in developing nanoscale
devices. Despite the prediction of the Dirac/Weyl points in a wide variety of
2D candidates, materials featuring topological nodal lines are still in great
scarcity. Herein, we predict two stable thinnest films of aluminum diboride
with hyper- and hypo-stoichiometries of Al$_2$B$_2$ and AlB$_4$ as new 2D
nonmagnetic Dirac nodal line semimetals (NLSMs) which promise to offer many
novel features. Our elaborate electronic structure calculations combined with
analytical studies reveal that, in addition to the multiple Dirac points, these
2D configurations host various type-I closed nodal lines (NLs) around the Fermi
level, all of which are semimetal states protected by the time-reversal and
in-plane mirror symmetries. The most intriguing NL in Al$_2$B$_2$ encloses the
K point and crosses the Fermi level with a considerable dispersion, thus
providing a fresh playground to explore exotic properties in dispersive Dirac
nodal lines. More strikingly, in the case of 2D superconductor AlB$_4$ which
exhibits a high transition temperature, we provide the first evidence for a set
of 2D nonmagnetic open type-II NLs in weak spin-orbit coupling limit,
coinciding with closed type-I NLs near the Fermi level. The coexistence of
superconductivity and nontrivial band topology in AlB$_4$ not only makes it a
promising material to exhibit novel topological superconducting phases, but
also the rather large energy dispersion of type-II nodal lines in this
configuration, may offer a distinguished platform for realization of novel
topological features in two-dimensional limit.
