## Nonlocal interactions beyond Hubbard model in twisted bilayer graphene near magic angle

**Abstract**: Recent experiments on the twisted bilayer graphene have discovered the

correlated insulator phase and the neighboring superconductivity with

certain fillings of the charge carriers. To understand the correlation

effects, we build the localized Wannier states (WSs) for the four

narrow bands around the charge neutrality point and construct the

corresponding low energy tight binding model. Furthermore, we project

the gate-screened Coulomb interaction onto the constructed localized

WSs. Due to the nontrivial topological properties of the four narrow

bands, the projected interaction becomes nonlocal and contains new

terms beyond the cluster Hubbard model. These new terms lead to strong

correlations between different lattice sites even without the

hoppings. At the one-quarter filling, the largely degenerate ground

states are found to be SU(4) ferromagnetic in the strong coupling

limit. The kinetic terms select the ground state in which the two

valleys with opposite spins are equally mixed, with vanishing magnetic

moment per particle. Our results suggest the fundamental difference

between the twisted bilayer graphene and other unconventional

superconductors described by the Hubbard model.

Reference:

1. Jian Kang and Oskar Vafek, Phys. Rev. X, 8, 031088 (2018).

2. Jian Kang and Oskar Vafek, arXiv:1810.08642. PRL accepted