# Coexistence of Triple Nodal Points, Nodal Links, and Unusual Flat Bands in intermetallic ${\cal A}$Pd$_3$ (${\cal A}$=Pb, Sn)

## TL;DR

This study explores the electronic and topological properties of intermetallic compounds PbPd3 and SnPd3, revealing flat bands, nodal points, and topological features influenced by spin-orbit coupling, with implications for their transport and optical behaviors.

## Contribution

It provides a detailed analysis of the topological electronic structure and flat bands in PbPd3 and SnPd3, highlighting the effects of spin-orbit coupling and doping on their properties.

## Key findings

- Presence of flat bands near the Fermi level affecting transport.
- Identification of triple nodal points and nodal loops in the absence of SOC.
- Topological index Z2=1 indicating non-trivial topology on the k_z=0 plane.

## 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.