  Xenes, graphene-like two-dimensional (2D) monoelemental crystals with a
honeycomb symmetry, have been the focus of numerous experimental and
theoretical studies. In comparison, single-element 2D materials with a
triangular lattice symmetry have not received due attention. Here, taking Pb as
an example, we investigate the triangular-lattice monolayer made of group-IV
atoms employing first-principles density functional theory calculations. The
flat Pb monolayer supports a mirror-symmetry-protected spinless nodal line in
the absence spin-orbit coupling (SOC). The introduction of an out-of-plane
buckling creates a glide mirror, protecting an anisotropic Dirac nodal loop.
Both flat and buckled Pb monolayers become topologically trivial after
including SOC. A large buckling will make the Pb sheet a 2D semiconductor with
symmetry-protected Dirac points below the Fermi level. The electronic
structures of other group-IV triangular lattices such as Ge and Sn demonstrate
strong similarity to Pb. We further design a quasi-3D crystal PbHfO$_2$ by
alternately stacking Pb and 1T-HfO$_2$ monolayers. The new compound PbHfO$_2$
is dynamically stable and retains the properties of Pb monolayer. By applying
epitaxial strains to PbHfO$_2$, it is possible to drive an insulator-to-metal
transition coupled with an anti-ferroelectric-to-paraelectric phase transition.
Our results suggest the potential of the 2D triangular lattice as a
complimentary platform to design new type of broadly-defined Xenes.
