We propose a theory for how the weak phonon-mediated interaction ($J_{\rm A}\!=\!1\!\sim\!4$meV) wins over the prohibitive Coulomb repulsion ($U\!=\!30\!\sim\!60$meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A$_3$C$_{60}$ family of molecular superconductors: Each AA stacking region of MATBG resembles a C$_{60}$ molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced $J_{\rm A}$ has the form of an inter-valley anti-Hund's coupling and is less suppressed than $U$ by the Kondo screening near a Mott insulator. Additionally, we also considered an intra-orbital Hund's coupling $J_{\rm H}$ that originates from the on-site repulsion of a carbon atom. Under a reasonable approximation of the realistic model, we prove that the renormalized local interaction between quasi-particles must have a pairing (negative) channel in a doped correlated insulator at $ν=\pm(2+δν)$, albeit the bare interaction is positive definite. The proof is non-perturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal $U$ for superconductivity is predicted. We also analyzed the pairing symmetry. In a large area of the parameter space of $J_{\rm A}$, $J_{\rm H}$, the ground state has a nematic $d$-wave singlet pairing, which, however, can lead to a $p$-wave-like nodal structure due to the Berry's phase on Fermi surfaces (or Euler obstruction).
Magnetic-impurity resonance states for different pairing symmetries in twisted bilayer graphene
在本工作中，我们研究了不同对称性的扭曲双层石墨烯超导相的磁杂质共振态。利用Yuan和Fu在[Phys. Rev. B 98，045103（2018）]中提出的双轨道模型，我们发现当杂质位于出射蜂窝晶格的一个位置时，共振态的空间分布将打破$D_3$群的三重和二重旋转对称性，而这些对称性属于该点群的不可约表示。当磁性杂质位于出射蜂窝晶格的中心时，在靠近杂质的位置出现共振峰可以被认为是非$s$波配对的有力证据。
Vortical versus skyrmionic states in the topological phase of a twisted bilayer with $d$-wave superconducting pairing
最近的研究表明，当超导体Bi $_2$ Sr $_2$ CaCu $_2$ O $_{8+δ}$的两个扭曲单层在一定的扭曲角下发生耦合时，会出现手性拓扑相.在这项工作中，我们揭示了这种扭曲的超导双层膜的行为与$d_{x^2-y^2}$配对对称的存在下施加磁场。具体来说，我们表明，紧急涡旋物质可以作为吸烟枪检测拓扑超导在这样的双层。此外，我们报告了两个不同的skyrmionic状态，表征手性拓扑相位，并提供充分的考虑他们的实验签名和他们的演变与扭曲角。
