Symmetry-guaranteed nodal-line semimetals in an fcc lattice

Abstract

We demonstrate theoretically that nodal-line semimetals (NLSs) can be realized in an fcc lattice with orbitals belonging to the same irreducible representation, such as ${{p}_{x},{p}_{y},{p}_{z}}$ or ${{d}_{xy},{d}_{yz},{d}_{zx}}$ orbitals on every lattice site. The three orbitals are divided into two subgroups in terms of the parity with respect to the mirror reflections on high-symmetry planes of the fcc lattice, which, with rotation symmetry, endows symmetry-guaranteed NL passing through $W$ points in the Brillouin zone. Depending on the parameters, there also appears an accidental NL around the $\mathrm{\ensuremath{\Gamma}}$ point. We notice that the symmetry-guaranteed NL addressed in the present work can be found in band structures of elemental solids taking the fcc structure, such as Cu, Ag, Au, In, Ga, etc., as well as opal, which is an fcc photonic crystal of ${\mathrm{SiO}}_{2}$ spheres. Furthermore, we clarify that the fcc lattice of Si spheres exhibits a NL in a frequency band where no other photonic band exists, which provides a unique platform to realize topological NLSs under intensive search, and can be explored for achieving slow light.