Charged flavour textures and skyrmion pairing in twisted bilayer graphene

We numerically study the charged spin and pseudospin textures that emerge upon doping the strong-coupling insulators in magic-angle twisted bilayer graphene [1]. Using unbiased self-consistent Hartree-Fock calculations, we show that such textures can be directly probed within the microscopic interacting Bistritzer-MacDonald model. For even integer filling, we demonstrate explicitly that singly charged skyrmions bind to form paired skyrmions, and calculate their dependence on the system parameters. By constructing beyond mean-field variational states, we analyze the effective mass and internal structure of the paired skyrmions as a function of twist angle, and comment on connections to a recently proposed theory of skyrmion superconductivity [2]. We also study spin skyrmions about the quantized anomalous Hall state, where we show the existence of spin texture lattices at finite doping.

[1] Y. H. Kwan, G. Wagner, N. Bultinck, S. H. Simon, and S. A. Parameswaran, in preparation

[2] E. Khalaf, S. Chatterjee, N. Bultinck, M. P. Zaletel, and A. Vishwanath, Charged skyrmions and topological origin of superconductivity in magic-angle graphene, Science advances 7, eabf5299 (2021)