标题： 共格石墨烯旋转堆叠中的对称性破缺；理论与实验的比较 显示英文标题

标题： Symmetry breaking in commensurate graphene rotational stacking; a comparison of theory and experiment

摘要： 石墨烯以Bernal结构堆叠（层间相对旋转60度）由于层间键仅在两个石墨烯单元胞原子中的一个上形成，导致其电子性质与孤立石墨烯不同。 各种实验表明，非Bernal旋转可以恢复这种破坏的对称性；因此，这些堆叠方式已成为理论研究的重点。 大多数理论预测带结构会有显著变化，从发展出范霍夫奇点以及角度依赖的电子局域化，这会导致当层间相对旋转角度趋近于零时费米速度趋于零。 在这项工作中，我们通过直接测量发现，非Bernal旋转仅由于弱的有效层间耦合而对石墨烯对称性产生很小的扰动，从而保持了石墨烯的对称性。 我们既未检测到范霍夫奇点，也未发现费米速度有显著变化。 这些结果表明，我们目前对这种材料带结构起源的理论理解存在重大问题。 显示英文摘要

摘要： Graphene stacked in a Bernal configuration (60 degrees relative rotations between sheets) differs electronically from isolated graphene due to the broken symmetry introduced by interlayer bonds forming between only one of the two graphene unit cell atoms. A variety of experiments have shown that non-Bernal rotations restore this broken symmetry; consequently, these stacking varieties have been the subject of intensive theoretical interest. Most theories predict substantial changes in the band structure ranging from the development of a Van Hove singularity and an angle dependent electron localization that causes the Fermi velocity to go to zero as the relative rotation angle between sheets goes to zero. In this work we show by direct measurement that non-Bernal rotations preserve the graphene symmetry with only a small perturbation due to weak effective interlayer coupling. We detect neither a Van Hove singularity nor any significant change in the Fermi velocity. These results suggest significant problems in our current theoretical understanding of the origins of the band structure of this material.