Correlated insulators and skyrmion superconductivity in magic angle twisted bilayer graphene

When two sheets of graphene are twisted relative to each other by an angle around 1 degree, a fascinating array of interaction-driven phases, including correlated insulators and superconductors, is observed. I will discuss the nature of these correlated insulators and how they give rise to superconductivity upon doping. Starting by projecting the Coulomb interaction onto the flat bands, I will show that the flatband-projected interacting Hamiltonian is characterized by a hidden approximate U(4)xU(4) symmetry which allows us to map the problem to that of a pair of tunnel-coupled multilayer Chern insulators with opposite Chern numbers. This mapping enables us to obtain the ground state at some integer fillings exactly. I will then discuss how superconductivity emerges upon doping such insulators via a topological mechanism based on pairing skyrmion textures. Remarkably, this new mechanism of superconductivity, which is distinct from weak coupling phonon-mediated pairing and unconventional pairing mechanisms in cuprates, arises solely from repulsive interactions. I will discuss how these insights not only clarify why certain correlated moire materials do not become superconducting, but they also point to promising new platforms where robust superconductivity is anticipated.

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[2] Khalaf, Chetterjee, Bultinck, Zaletel, Vishwanath, arXiv:2004.00638
[3] Khalaf, Kruchkov, Tarnopolsky, Vishwanath, Physical Review B 100 (8), 085109 (2019)