Flat-band ferromagnetism in twisted bilayer graphene

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 $\theta \sim 1.05^{\circ }$. 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 ($n=\pm 2$).

11 pages, 5 figures

References in corpus (8)

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• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Optical Signature of Flat Bands in Topological Hourglass Semimetal Nb3SiTe6
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Phase diagram of a coupled trimer system at half filling using the Hubbard model
• Frustration-free free fermions
• Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition
• Magnetism of magic-angle twisted bilayer graphene