Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene

Understand

We study ferromagnetism and its stability in twisted bilayer graphene.

• We work with a Hubbard-like interaction that corresponds to the screened Coulomb interaction in a well-defined limit where the Thomas-Fermi screening length $l_\text{TF}$ is much larger than monolayer graphene's lattice spacing $l_g \ll l_\text{TF}$ and much smaller than the Moir\'e super lattice's spacing $ l_\text{TF} \ll l_{\text{Moir\'e}}$.
• We show that in the perfectly flat band "chiral" limit and at filling fractions $\pm 3/4$, the saturated ferromagnetic (spin and valley polarized) states are ideal ground states candidates in the large band-gap limit.
• By assuming a large enough substrate (hBN) induced sub-lattice potential, the same argument can be applied to filling fractions $\pm 1/4$.