Hexagonal germanium in the lonsdaleite structure has a direct band gap, but it is not an efficient light emitter due to the vanishing oscillator strength of electronic transitions at the fundamental gap. Transitions involving the second lowest conduction band are instead at least three orders of magnitude stronger. The inversion of the two lowest conduction bands would therefore make hexagonal germanium ideal for optoelectronic applications. In this work, we investigate the possibility to achieve this band inversion by applying strain. To this end we perform ab initio calculations of the electronic band structure and optical properties of strained hexagonal germanium, using density-functional theory with the modified Becke-Johnson exchange-correlation functional and including spin-orbit interaction. We consider hydrostatic pressure, uniaxial strain along the hexagonal $c$ axis, as well as biaxial strain in planes perpendicular to and containing the hexagonal $c$ axis to simulate the effect of a substrate. We find that the conduction-band inversion, and therefore the transition from a pseudodirect to a direct band gap, is attainable for moderate tensile uniaxial strain parallel to the lonsdaleite $c$ axis.

中文翻译：

---

朗斯代尔锗中的应变诱导发光

lonsdaleite结构中的六方锗具有直接的带隙，但由于基本间隙处电子跃迁的振荡器强度消失，因此它不是有效的发光体。相反，涉及第二最低导带的跃迁至少要强三个数量级。因此，两个最低导带的倒置将使六角形锗成为光电应用的理想选择。在这项工作中，我们研究了通过施加应变来实现此带反转的可能性。为此，我们从头开始使用密度泛函理论和改进的Becke-Johnson交换相关函数并包括自旋轨道相互作用，计算应变六方锗的电子能带结构和光学性质。我们考虑静水压力，沿六角形的单轴应变$C$ 轴以及垂直于并包含六边形的平面中的双轴应变 $C$轴以模拟基材的效果。我们发现对于平行于lonsdaleite的中等拉伸单轴应变，可以实现导带反转，并因此实现从伪直接向直接带隙的转变$C$ 轴。