We report on the mechanism of energy transfer in Van der Waals heterostructures of the two-dimensional semiconductor ${\mathrm{WS}}_2$ and graphene with varying interlayer distances, achieved through spacer layers of hexagonal boron nitride ($h$-BN). We record photoluminescence and reflection spectra at interlayer distances between 0.5 and 5.8 nm ($0–16h$-BN layers). We find that the energy transfer is dominated by states outside the light cone, indicative of a Förster transfer process, with an additional contribution from a Dexter process at 0.5 nm interlayer distance. We find that the measured dependence of the luminescence intensity on interlayer distances above 1 nm can be quantitatively described using recently reported values of the Förster transfer rates of thermalized charge carriers. At smaller interlayer distances, the experimentally observed transfer rates exceed the predictions and, furthermore, depend on excess energy as well as on excitation density. Since the transfer probability of the Förster mechanism depends on the momentum of electron-hole pairs, we conclude that, at these distances, the transfer is driven by nonrelaxed charge carrier distributions.

中文翻译：

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WS2-石墨烯异质结构中能量传递机制的距离依赖性

我们报告了二维半导体范德华异质结构中的能量转移机制${\mathrm{WS}}_2$和具有不同层间距离的石墨烯，通过六方氮化硼间隔层实现（$H$-BN）。我们在 0.5 至 5.8 nm 之间的层间距离处记录光致发光和反射光谱（$0–16H$-BN层）。我们发现能量转移主要由光锥外的状态决定，这表明存在 Förster 转移过程，另外还有 0.5 nm 层间距离处的 Dexter 过程的贡献。我们发现，测量到的发光强度对 1 nm 以上层间距离的依赖性可以使用最近报道的热化电荷载流子的福斯特传输率值来定量描述。在较小的层间距离下，实验观察到的传输速率超出了预测，而且还取决于多余的能量以及激发密度。由于福斯特机制的转移概率取决于电子-空穴对的动量，因此我们得出结论，在这些距离处，转移是由非松弛载流子分布驱动的。