The stability and topological behaviors in lanthanide antiperovskite nitrides: a high-throughput study

TL;DR

The work develops a double-screening, high-throughput DFT framework to identify thermodynamically and dynamically stable lanthanide antiperovskite nitrides Ln$_3$XN while addressing strong $f$-electron correlations by independently treating itinerant and localized limits. Applying this approach to 854 candidates yields 149 thermodynamically stable and 37 dynamically stable compounds, with 35 exhibiting nontrivial topological features. Topological classification via SOC and symmetry analysis uncovers Dirac and semi-Dirac crossings near the Fermi level (exemplified by Er$_3$TlN), highlighting lanthanide APV nitrides as a rich platform for correlated and topological quantum phenomena. The results guide future synthesis and experimental exploration of these materials for emergent quantum properties.

Abstract

Antiperovskite (APV) nitrides exhibit a diverse range of electronic properties, including superconductivity, magnetic effects, and nontrivial topological behaviors. In this study, we propose a new family of APV nitrides by incorporating 4$f$-electron metals, known for strong electron correlations, localized magnetic moments, and spin-orbit coupling, to further explore the unique properties of APVs. A high-throughput density functional theory (DFT) calculation was utilized to identify stable lanthanide APV nitride compounds. To address the challenge of strong electron correlation, we developed a double-screening framework that assumes either a fully itinerant or localized nature of the $f$-electrons during calculations. Using this approach, we systematically identified 37 stable lanthanide APV nitride compounds from both thermodynamic and dynamical perspectives. Furthermore, we report nontrivial topological behaviors observed among these stable lanthanide APV nitride compounds, as computed by DFT. Notably, Dirac and semi-Dirac cones are observed near the Fermi level for Er$_3$TlN. This study opens a pathway to investigate lanthanide APVs, revealing potential novel physical properties by leveraging the rich physics of both APVs and $f$-electrons.

Figures (5)

• Figure 1: (a) Crystal structure of lanthanide antiperovskite nitrides Ln$_3$XN . (b) Schematic representation of the screening funnel used to identify promising Ln$_3$XN candidates. The pseudo-potentials of Ln and Ln_3, representing the itinerant and localized limits of 4f electrons respectively, were used independently. A candidate passes the screening only if both itinerant and localized conditions are met.
• Figure 2: (a) Colormap showing the number of thermodynamically stable Ln$_3$XN compounds as a function of the X element. The lower-left and upper-right triangles correspond to results obtained using the itinerant and localized limits of the 4f electrons, respectively. (b) Calculated formation energies and (c) energies above the convex hull for La$_3$XN compounds. The dashed lines represent the criteria for formation energy and energy above the convex hull, respectively.
• Figure 3: (a) Colormap showing the number of dynamically stable Ln$_3$XN compounds as a function of the X element. The lower-left and upper-right triangles correspond to results obtained using the itinerant and localized limits of the 4f electrons, respectively. Calculated phonon dispersions of (b) Ho$_3$TlN, (c) Ho$_3$HgN, and (d) Ho$_3$GaN, in both itinerant and localized limits. The dashed lines represent the criterion for phonon energy.
• Figure 4: Computed electronic structures and density of states for Er$_3$TlN using DFT+$U$ ($U = 10$ eV) (a) without spin-orbit coupling and (b) with spin-orbit coupling. Three symmetry enforced band crossings are marked by circles in the panel (b).
• Figure 5: Computed symmetry enforced band crossing for Er$_3$TlN at three different $k$-points, (a) $\mathbf{k}_a=(0.141, 0, 0)$, (b) $\mathbf{k}_b=(0.207, 0, 0)$, and (c) $\mathbf{k}_c=(0.088, 0.088, 0.088)$. For each $k$-point, one 2D plot along the high-symmetry path and two 3D plots from different viewing angles are provided. Along the $\Gamma$--$X$ path ($\zeta00$), $k_y$ and $k_z$ are equivalent, while $k_x$, $k_y$, and $k_z$ are all equivalent along the $\Gamma$--$R$ path ($\zeta\zeta\zeta$).