Symmetry-Guaranteed and Accidental Nodal-Line Semimetals in FCC Lattice

We demonstrate theoretically that nodal-line semimetal (NLS) states can be realized in face-center-cubic (fcc) lattice with orbits belonging to one irreducible representation, such as [$p_x$, $p_y$, $p_z$] and/or [$d_{xy}$, $d_{xz}$, $d_{yz}$]. It is shown that the three orbits are subdivided with respect to the odd- and even-parity upon mirror reflection on high symmetry planes, which yields an analytic expression for the trajectory of NL in momentum space when a tight-binding (TB) model is adopted. It becomes clear that there are two kinds of NLs, a symmetry-guaranteed one around the surface of the first Brillouin zone (BZ), and an accidental one around the BZ center governed by the hopping integrals. As a realization of the idea, we analyze the fcc photonic crystal composed of dielectric spheres by solving the Maxwell's equations. Two symmetry-guaranteed and one accidental NLS photonic states are observed. This provides a good platform to confirm experimentally the existence of topological NLS state, and on its own right the topological surface band characterized by the almost flat dispersion is useful for achieving slow light yearned for many applications.