Coexistence of triple nodal points, nodal links, and unusual flat bands in intermetallic APd3 ( A=Pb , Sn)

Abstract

We investigate the electronic structure and several properties, and topological character, of the cubic time-reversal invariant intermetallic compounds PbPd$_3$ and SnPd$_3$ using density functional theory based methods. These compounds have a dispersionless band along the $\Gamma-X$ line, forming the top of the Pd $4d$ bands and lying within a few meV of the Fermi level $E_F$. Effects of the flat band on transport and optical properties have been inspected by varying the doping concentration treated with the virtual crystal approximation for substitution on the Pb site. In the absence of spin-orbit coupling (SOC), we find triple nodal points and three-dimensional nodal loops, which are known to lead to surface bands and drumhead states, respectively, which we discuss for PbPd$_3$. SOC removes degeneracy in most of the zone, providing a topological index $Z_2$=1 on the $k_z=0$ plane that indicates a topological character on that plane. The isovalent and isostructural compound SnPd$_3$ shows only minor differences in its electronic structures, so it is expected to display similar electronic, transport, and topological properties.