  Two-dimensional pentagonal structures based on the Cairo tiling are the basis
of a family of layered materials with appealing physical properties. In this
work we present a theoretical study of the symmetry-based electronic and
optical properties of these pentagonal materials. We provide a complete
classification of the space groups that support pentagonal structures for
binary and ternary systems. By means of first-principles calculations, their
electronic band structures and the local spin textures in momentum space are
analyzed. Our results show that pentagonal structures can be realized in chiral
and achiral lattices with Weyl nodes pinned at high-symmetry points and nodal
lines along the Brillouin zone boundary; these degeneracies are protected by
the combined action of crystalline and time-reversal symmetries. Additionally,
we discuss the linear and nonlinear optical features of some penta-materials,
such as the shift current, which shows an enhancement due to the presence of
nodal lines and points, and their possible applications.
