Bonding and Electronic Nature of the Anionic Framework in LaPd${}_3$S${}_4$

Abstract

Double Dirac materials are a topological phase of matter in which a non-symmorphic symmetry enforces greater electronic degeneracy than normally expected up to eightfold. The cubic palladium bronzes NaPd${}_3$O${}_4$ and LaPd${}_3$S${}_4$ are built of Pd${}_3$X${}_4$ (X = O, S) anionic frameworks that are ionically bonded to A cations (A = Na, La). These materials were recently identified computationally as harboring eightfold fermions. Here we report the preparation of single crystals and electronic properties of LaPd${}_3$S${}_4$. Measurements down to T = 0.45 K and in magnetic fields up to $\mu$0H = 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd${}_3$O${}_4$ and LaPd${}_3$S${}_4$, we identify the origin of the stability of the anionic Pd${}_3$X${}_4$ framework at higher electron counts for X = S than X = O, and propose chemical tuning strategies to enable shifting the 8-fold fermion points to the Fermi level.