First-Principles Exploration of Pentagonal TiN$_8$ and MoN$_8$ Monolayers as New Magnetic Topological Insulator

TL;DR

This work identifies a new class of two-dimensional magnetic topological insulators in pentagonal MN$_8$ monolayers, showing that TiN$_8$ hosts a QAH state with $C=-1$ while MoN$_8$ realizes a high-Chern-number phase with $C=2$ through spin-polarized, covalent M–N bonding and SOC-induced gaps. Using first-principles DFT+$U$ calculations, VASP, and Wannier-based topology analyses, the authors quantify magnetic anisotropy, exchange interactions, and stability, and they develop a minimal two-band TB model to explain the origin of topology from the $d_{xz}$ and $d_{yz}$ orbitals at the $ ext{Γ}$ and $ ext{K}$ points. The work leverages MLWFs and edge-state calculations to confirm nontrivial chiral edge modes and provides a theoretical framework for designing sturdy magnetic TIs in 2D pentagonal lattices, with potential implications for spintronics and quantum computing. Overall, the paper expands the material landscape for QAH insulators and demonstrates how targeted orbital physics in low-symmetry pentagonal lattices can yield robust topological phases.

Abstract

The quest for robust, intrinsically magnetic topological materials exhibiting the quantum anomalous Hall (QAH) effect is a central challenge in condensed matter physics and the application of revolutionary electronics. However, progress has been hampered by the limited number of candidate materials, which often suffer from poor stability and complex synthesis. Here, we introduce a new paradigm by exploring the emergent magnetism and nontrivial band topology in the largely overlooked family of two-dimensional (2D) pentagonal MN$_8$ monolayers. Employing first-principles calculations, we reveal that these systems host out-of-plane ferromagnetic ground states, a key feature that unlocks nontrivial topological properties driven by the localized $d$-orbitals of the embedded transition metals. Remarkably, we identify TiN$_8$ as a QAH insulator characterized by a Chern number of $C=-1$. Even more strikingly, MoN$_8$ is predicted to be a rare high-Chern-number QAH insulator, boasting a Chern number of $C=2$. Our findings establish the penta-MN$_8$ family as a fertile and versatile platform for realizing exotic topological quantum states. This work not only significantly expands the material landscape for magnetic topological insulators but also provides a solid theoretical foundation for designing next-generation spintronic and quantum computing devices.

Figures (6)

• Figure 1: Lattice structures of TiN$_8$/MoN$_8$. (a, b) Top and side views of the optimized TiN$_8$ and MoN$_8$ crystal structures, respectively. (c) Pentagon sublattice showing bond lengths and angles for TiN$_8$/MoN$_8$; Magenta, gray, and red spheres represent the M, N1, and N2 sites, respectively. (d) The triangle structure network composed of M atoms in supercell, the six Nereast Neighbor sites are denoted as green arrows. (e)/(f) The phonon dispersions of TiN$_8$/MoN$_8$, respectively. (g) evolution of the potential energy for a 4 × 4 × 1 supercell during the AIMD simulations at 300 K and a snapshot of the equilibrium structure (inset) at the end of 5 ps. (h) The first Brillouin zone of the MN$_8$.
• Figure 2: (a) Orbital-projected band structures of TiN$_8$ for the spin-up and spin-down subspaces, respectively. (b) Ligand coordination environments of TiN$_8$. (c) Electron Localization Function (ELF) maps of TiN$_8$, illustrating electron distribution and bonding character. (d) Simplified depiction of how the crystal structures of TiN$_8$ modulates outer electron arrangements, thereby mediating the magnetic origin in these systems. (e) Orbital-projected band structures of MoN$_8$ for the spin-up and spin-down subspaces, respectively. (f) Ligand coordination environments of MoN$_8$. (g) ELF maps of MoN$_8$. (h) Simplified depiction of outer electron arrangements of MoN$_8$.
• Figure 3: Exchange interactions. (a-c) Three different types of magnetic configurations implemented in square lattice, which are (a) FM, (b) AFM-stripe and (c) AFM-zigzag, respectively. (d) Chirality in the triangle lattice, and MN$_8$ lattice. (e, f) Curie/Néel of TiN$_8$ and MoN$_8$, respectively.
• Figure 4: Elements-projected band structures of (a) TiN$_8$ without SOC, (b) TiN$_8$ with SOC, (c) MoN$_8$ without SOC, and (d) MoN$_8$ with SOC. The SOC-induced band gaps at high-symmetry points are labeled as Gap1 and Gap2 in the corresponding panels. (e, f) Chiral edge states of TiN$_8$ and MoN$_8$, respectively, with the associated Chern numbers indicated on the right.
• Figure 5: Simplified TB band structures using the basis set of ⟨$d_{xz}$, $d_{yz}$⟩$^T$. (a) Band structure with TB parameters: $V_{dd\pi}$ = 0.04, $V_{dd\delta}$ = 0.01, and SOC strength $\lambda$ = 0. (b) Band structure with $V_{dd\pi}$ = 0.04, $V_{dd\delta}$ = 0.01, and $\lambda$ = 0.02, highlighting the effect of SOC strength of $\lambda$. (c) Berry curvature distribution in the Brillouin zone calculated with $V_{dd\pi}$ = 0.04, $V_{dd\delta}$ = 0.01, and $\lambda$ = 0.02. (d) Evolution of WCCs under varying TB parameters, illustrating the corresponding changes in topological properties.