Abstract
We discuss twisted bilayer graphene (TBG) based on a theorem of flat-band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single-particle density matrix of the flat-band states is irreducible and we argue that this result can be applied to the quasi-flat-bands of TBG that emerge around the charge-neutrality point for twist angles around the ...
Abstract
We discuss twisted bilayer graphene (TBG) based on a theorem of flat-band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single-particle density matrix of the flat-band states is irreducible and we argue that this result can be applied to the quasi-flat-bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle theta similar to 1.05 degrees. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG (n = 0). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling (n = +/- 2).
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