Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moir'{e} superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($\alpha \approx {0.3}^{\circ }$) and flat bands at magic angles ($\alpha \approx 1^{\circ }$). We show that tuning the twist angle to ${\alpha }^{\ast }\approx {0.8}^{\circ }$ generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with $\pm 6$ electrons per moir'e cell, these bands are half-filled and electronic interactions produce a symmetry-broken ground state (Stoner instability) with spin-polarized regions that order ferromagnetically. Application of an interlayer electric field breaks inversion symmetry and introduces valley-dependent dispersion that quenches the magnetic order. With these results, we propose a solid-state platform that realizes electrically tunable strong correlations.