Theoretical study of compounds XSb (X = La, Pr, Nd): Realization of inner nodal chains, nodal line frame, and Dirac points

Materials with symmetry protected nodal loops is accompanied by many exotic features, i.e., the presence of drumhead surface states. In addition, the crystallographic symmetries can determine the shape of the nodal loops. Here, based on the first-principles calculations and symmetry analysis, we reveal rich nodal loops in the existing material XSb (X = La, Pr, Nd) in the absence of spin-orbital coupling (SOC), which are enabled by symmetries. For example, a set of three nodal loops forms an inner chain at high symmetry points, and a nodal line penetrate the whole Brillouin zone. The stability of each nodal loop is ensured a mirror, and characterized by a topological invariant in zero-dimensional manifold. Furthermore, we also study the surface correspondence of the nodal loops. There exist drumhead surface states within/out of the projection of the nodal loops. In the presence of SOC, Dirac points emerge on high symmetry line, around which it shows a wide linear dispersion window. Notably, Dirac points are quite near to Fermi level, and Fermi arcs emanating from the projection of Dirac points could be clearly observed. In addition, we verify that these Fermi arcs are fragile, not topologically protected. Our work suggests a family of realistic materials to study the inner chains and Dirac semimetals.