The recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral (d + id mixed with p−ip) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three M points in the Brillouin Zone, and a 2 × 2 pattern in real space. In simple treatments though, this leads to a full gap at fillings ± (1/2 + 1/8), slightly away from half-filling. The selection of spin-singlet or spin triplet orders, both for the IVCW and the superconductor, arise fcase corresponds to the Hundsrom SO(4) symmetry breaking terms. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.

扭曲双层石墨烯中莫特绝缘相和超导相的最新发现引起了巨大的研究兴趣。在这里，我们从费米液态开始，对双分子层石墨烯中的超导性开发了一种弱耦合方法。一个关键的观察结果是，铁电学几乎充满了一半，而铁电学则由嵌套的费米袋组成，这些费米袋来自相反的山谷，从而导致山谷波动增加，进而可以介导超导性。在随机相位近似内研究了这种情况。我们发现，谷氨酸间电子与任一手性（d  + i d与p -i p混合）或螺旋形状因数是主要的不稳定性。近似的SO（4）自旋谷对称性意味着自旋单重态和三重态对的简并性。随着相互作用的增加，可能会出现相应的谷间相干波（IVCW）阶，同时在布里渊区的三个M点同时凝结，在现实空间中出现2×2的模式。但是，在简单的处理中，这会导致填充物±（1/2 + 1/8）处的完整间隙，与半填充物略有不同。对于IVCW和超导体，自旋单峰或自旋三重态阶的选择出现在fcase对应于Hundsrom SO（4）对称破缺项的情况下。还讨论了从相位波动超导体派生的莫特绝缘子，它既显示对称性也显示了固有的拓扑顺序。