Abstract The combined effects of 13C isotope and vacancies on the phonon properties in AB stacked bilayer graphene (BLG) are explored theoretically. We have calculated the phonon density of states (PDOS) by varying the isotope contents (0–100%) and vacancies (0–30%) in both layers and only in the upper layer of the BLG using forced vibrational method. We found that both isotope and vacancy or merging of these two defects significantly affect the PDOS, especially, E2g mode phonon, which is responsible for the Raman G band, shifted downward with the increase of defect concentrations. Moreover, when 13C isotopes are induced only in the upper layer, E2g peak splits into two peaks which corresponds well with the experimental results of 13C/12C dependence G peak splitting in the Raman spectra of BLG. We also explored the defect induced phonon localization in BLG. Our calculated typical mode patterns show that high frequency optical phonons are strongly localized in the vacancy as well as merging 13C isotope and vacancy defected BLG. The calculated average localization length noticed that strong phonon localization exists at 60% 13C isotope concentration. These findings are important for understanding the experimentally observed Raman spectra as well as thermal transport in BLG.

中文翻译：

---

13C同位素和空位对AB堆叠双层石墨烯中声子性质的综合影响

摘要 从理论上探讨了 13C 同位素和空位对 AB 堆叠双层石墨烯 (BLG) 声子性质的综合影响。我们已经使用强制振动方法通过改变两层和仅在 BLG 的上层中的同位素含量 (0-100%) 和空位 (0-30%) 来计算声子态密度 (PDOS)。我们发现同位素和空位或这两个缺陷的合并都会显着影响 PDOS，尤其是 E2g 模式声子，它负责拉曼 G 带，随着缺陷浓度的增加而向下移动。此外，当 13C 同位素仅在上层被诱导时，E2g 峰分裂为两个峰，这与 BLG 拉曼光谱中 13C/12C 依赖性 G 峰分裂的实验结果非常吻合。我们还探讨了 BLG 中缺陷诱导的声子定位。我们计算出的典型模式模式表明，高频光学声子强烈定位在空位中，并合并了 13C 同位素和空位缺陷 BLG。计算出的平均定位长度注意到，在 13C 同位素浓度为 60% 时存在强声子定位。这些发现对于理解实验观察到的拉曼光谱以及 BLG 中的热传输很重要。