We explore the impact of strain on charge carrier mobility of monolayer $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-P, the four well-known atomically thin allotropes of phosphorus, using density functional theory. Owing to the highly anisotropic band dispersion, the charge carrier mobility of the pristine allotropes is significantly higher (more than 5 times in some cases) in one of the principal directions (zigzag or armchair) compared to the other. Uniaxial strain (up to 6% compressive/tensile) leads to band gap alteration in each of the allotropes, especially a direct to indirect band gap semiconductor transition in $\gamma$-P and a complete closure of the band gap in $\gamma$- and $\delta$-P. We find that the charge carrier mobility is enhanced typically by a factor of ∼5–10 in all the allotropes due to uniaxial strain; notably, among them an ∼250 (30) times increase of the hole (electron) mobility along the armchair (zigzag) direction is observed in $\beta$-P ($\gamma$-P) under a compressive strain, acting in the armchair direction. Interestingly, the preferred electronic conduction direction can also be changed in the case of $\alpha$- and $\gamma$-P by applying strain.

中文翻译：

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原子稀磷同素异形体的应变可调电荷载流子迁移率

我们探索应变对单层电荷载流子迁移率的影响 $\alpha$-， $\beta$-， $\gamma$-， 和 $\delta$-P，是使用密度泛函理论的四个众所周知的原子上稀有的磷同素异形体。由于高度各向异性的带分散，原始同素异形体在另一个主方向（曲折或扶手椅）上的电荷载流子迁移率明显高于另一个主方向（在某些情况下，超过5倍）。单轴应变（高达6％的压缩/拉伸）会导致每个同素异形体中的带隙改变，尤其是直接或间接的带隙半导体跃迁。$\gamma$-P并完全消除了带隙 $\gamma$- 和 $\delta$-P。我们发现，由于单轴应变，在所有同素异形体中，载流子迁移率通常提高约5-10倍。值得注意的是，在其中，观察到沿扶手椅（之字形）方向的空穴（电子）迁移率增加了约250（30）倍。$\beta$-P（$\gamma$-P）在压缩应变下，沿扶手椅方向作用。有趣的是，在以下情况下，也可以更改首选的电子传导方向：$\alpha$- 和 $\gamma$-P通过施加应变。