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

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 $μ$0H = 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd$_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.

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