Two-dimensional bilayer blue phosphorus Dirac-like material: a multi-orbital tight-binding investigation,Physical Chemistry Chemical Physics

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Two-dimensional bilayer blue phosphorus Dirac-like material: a multi-orbital tight-binding investigation
Physical Chemistry Chemical Physics ( IF 2.9 ) Pub Date : 2024-08-19 , DOI: 10.1039/d4cp01988a
Amine Benhaij ₁ , Omar Mounkachi _{1,

2}

Affiliation

This study presents a theoretical examination of the electronic band structure of AA (AB) stacked bilayer blue phosphorus system within the fifth intralayer (5NN) and second interlayer nearest-neighbor (2NN) multi-orbital tight-binding (MOTB) approach. The variation of energy levels has been investigated through the symmetrical tensile strain of the low-buckled honeycomb lattice. Here, the primary objective is to examine the existence of Dirac electronic features in hexagonal stacked bilayer geometry. Our theoretical calculations predict that the AA bilayer is a new hexagonal two-dimensional material with p_x,y-orbital Dirac-like states at the high-symmetry K point. Consequently, these systems can host massless (massive) Dirac fermions. In particular, the AA bilayer exhibits zero-gap Dirac-like properties and manifests distinguishable Dirac-like cones in the presence of weak spin–orbit coupling when a modest stretch of 2.30% is achieved with a remarkably high Fermi velocity of approximately v_f ≈ 0.12 × 10⁵ m s⁻¹. The behavior of the dispersion bands aligns reasonably well with recent experimental observations. Moreover, a stretch of 7.17% breaks some of the sublattice equivalence and enhances the spin–orbit interaction, resulting in the emergence of an electronic band gap of approximately ≈ 0.27 eV in the proximity of the high-symmetry K point. Furthermore, the tiny gap induced by the spin–orbit interaction implies topological nontriviality in the electronic state (quantum anomalous Hall state) of the honeycomb lattice. These findings categorize the AA bilayer as a rare two-dimensional Dirac-like material. This work provides, to the extent of our knowledge, a pioneering investigation into the existence of Dirac electronic properties in bilayer blue phosphorus. In addition, we present the first derivation of the MOTB model. However, the identified electronic characteristics designate this two-dimensional system as an ideal candidate for high-performance nanoelectronic devices.

中文翻译：

二维双层蓝磷类狄拉克材料：多轨道紧束缚研究

本研究对第五层内 (5NN) 和第二层间最近邻 (2NN) 多轨道紧束缚 (MOTB) 方法中 AA (AB) 堆叠双层蓝磷系统的电子能带结构进行了理论检验。通过低屈曲蜂窝晶格的对称拉伸应变研究了能级的变化。在这里，主要目标是检查六边形堆叠双层几何中狄拉克电子特征的存在。我们的理论计算预测AA双层是一种新的六方二维材料，在高对称性K点具有p _{x , y}轨道狄拉克态。因此，这些系统可以容纳无质量（质量）的狄拉克费米子。特别是，当以大约v _f ≈ 的极高费米速度实现 2.30% 的适度拉伸时，AA 双层表现出零间隙类狄拉克特性，并在弱自旋轨道耦合的情况下表现出可区分的类狄拉克锥体。 0.12×10 ⁵毫秒^-1 。色散带的行为与最近的实验观察结果相当吻合。此外，7.17%的拉伸打破了一些亚晶格等效性并增强了自旋轨道相互作用，导致在高对称性K点附近出现了约0.27 eV的电子带隙。此外，自旋轨道相互作用引起的微小间隙意味着蜂窝晶格的电子态（量子反常霍尔态）的拓扑非平凡性。这些发现将 AA 双层归类为一种罕见的二维类狄拉克材料。据我们所知，这项工作为双层蓝磷中狄拉克电子特性的存在提供了开创性的研究。此外，我们还给出了 MOTB 模型的一阶推导。然而，所确定的电子特性表明这种二维系统是高性能纳米电子器件的理想候选者。

更新日期：2024-08-23

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