标题： III型Weyl半半金属在超轻单层Li$_2$N中 显示英文标题

标题： Type-III Weyl Semi-Half-Metal in an Ultralight Monolayer Li$_2$N

摘要： 磁有序与能带拓扑之间的相互作用已成为发现具有深远基本物理和下一代电子学意义的新量子态的肥沃领域。 在此，我们理论上预测了单层Li$_2$N中存在一种新的III型Weyl半半金属（SHM）态，独特地结合了磁半金属性和III型Weyl半金属特性。 第一性原理计算揭示了单层Li$_2$N中费米能级附近完全自旋极化且严重倾斜的Weyl锥，这是由$p$轨道铁磁性驱动的。 这源于平价价带和平行导带之间对称保护的能带交叉，导致具有强传输各向异性的III型Weyl费米子。 构建了一个低能区的$k{\cdot}p$汉密尔顿量，并发现了相应的非平庸边缘态以捕捉 Li$_2$N 的拓扑性质。 值得注意的是，在从 -2$\%$到$4\%$的双轴应变范围内，这种外尔 SHM 相位仍然稳健存在，伴随着在 3.7$\%$应变下出现的理想 III 型外尔费米子和类似线状的遍历表面，为探索相关的电子现象提供了一个有前景的平台。 我们的研究结果确立了 Li$_2$N 是实现奇异 III 型外尔 SHM 态的一个可行候选材料，并开辟了一个新的途径来探索磁性、拓扑学和平带物理之间的复杂相互作用。 显示英文摘要

摘要： The interplay between magnetic ordering and band topology has emerged as a fertile ground for discovering novel quantum states with profound implications for fundamental physics and next-generation electronics. Here, we theoretically predict a new type-III Weyl semi-half-metal (SHM) state in monolayer Li$_2$N, uniquely combining magnetic half-metallicity and type-III Weyl semimetal characteristics. First-principles calculations reveal a fully spin-polarized and critically tilted Weyl cone around the Fermi level in monolayer Li$_2$N, driven by $p$-orbital ferromagnetism. This arises from the symmetry-protected band crossing between a flat valence band and a highly dispersive conduction band, leading to type-III Weyl fermions with strong transport anisotropy. A low-energy $k{\cdot}p$ Hamiltonian is constructed and corresponding nontrivial edge states are uncovered to capture the topological nature of Li$_2$N. Notably, this Weyl SHM phase remains robust under biaxial strain ranging from -2$\%$ to $4\%$, with an ideal type-III Weyl fermion emerging alongside a line-like ergodic surface emerging at 3.7$\%$ strain, offering a promising platform for exploring correlated electronic phenomena. Our results establish Li$_2$N as a viable candidate for realizing exotic type-III Weyl SHM states and open a new avenue for exploring the intricate interplay among magnetism, topology, and flat-band physics.